On the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic

V. On the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic. By the Rev. Samuel Haughton, M.A., F.R.S., Fellow of Trinity College, Dublin. Received June 9,—Read June 19, 1862. Introduction. Among the experimenters who have made the reflexion of polarized light the object of their researches, there is no one to whom science is more indebted than to M. Jamin, whose accurate observations are a model for subsequent observers. His first paper on this subject was published (1847) in the 19th volume of the 'Annales de Chimie et de Physique,' 3rd series, p. 296, on Metallic Reflexion. In this remarkable paper M. Jamin verified many of the previous observations of Brewster, and added many of his own. He employed two distinct methods in these experiments,— 1st. The method of Comparative Intensities—by observing the relative intensities of the same beam of light reflected from a polished surface, composed partly of glass and partly of the substance to be examined. 2nd. The method of Multiple Reflexions, previously known from the researches of Brewster. The optical constants used by Jamin in this paper are— (a) The angle ($i_1$) of maximum polarization. (b) The angle (A) whose tangent is the ratio of I to J, the square roots of the intensities reflected in the plane of incidence, and in the perpendicular plane. (c) The coefficient ($\varepsilon$) used by Cauchy, which is connected with the other two constants by means of theoretical equations. By the first method of observation, M. Jamin determines the constants $i_1$ and $\varepsilon$ for the following substances:— 1. Steel, 2. Speculum metal; and by the second method of observation, he determines $i_1$ and A for 3. Silver, and $i_1$ for 4. Zinc, and gives the details of experiments on 5. Copper, from which the optical constants may be found. MDCCCLXIII. M. Jamin's next paper on Metallic Reflexion appeared in 1848, in the Annales de Chim. et de Phys. 3rd series, vol. xxii. p. 311. In this paper he makes use of the second method of observation, by multiple reflexion, and gives valuable tables of the results of his experiments with the various colours of the spectrum on the seven following metallic substances: 1. Steel. 2. Speculum metal. 3. Silver. 4. Zinc. 5. Copper. 6. Brass. 7. Bell metal. From these Tables the constants \( i \) and \( A \) may be inferred. In 1850 M. Jamin published his well known paper "On the Reflexion of Light at the Surface of Transparent Bodies," in the Ann. de Chim. et de Phys. 3rd series, vol. xxix. p. 263. In this series of experiments he used a new method of observation, founded on the Quartz Compensator of Babinet. In this elaborate and important paper he publishes the details of his experiments on the following substances: 1. Fire Opal, 2. Hyalite, 3. Realgar, 4. Blende, 5. Diamond, 6. Fluor-spar, 7, 8. Two kinds of glass, and, in addition, gives in a Table at the end of the paper the constants of many other transparent bodies. M. Jamin has also published, in 1851, in the Ann. de Chim. et de Phys. vol. xxxi. p. 165, a memoir "On the Reflexion of Light at the Surface of Liquids," in which he determines the optical constants of many liquids. It occurred to me that the method of observation employed by Jamin for transparent bodies might be advantageously used in the case of metals; and I was thus led to commence the series of experiments the results of which are recorded in the following pages. In these experiments I have added many metallic substances to Jamin's list, and have re-examined the metals observed by him by a different method. In transparent bodies I have examined a few not experimented on by Jamin, and investigated in detail the form of the reflected ellipse, under varying conditions of incidence and azimuth. In the course of my paper I have employed for the second optical constant one more readily determined than those usually employed, but which is readily deduced from the constants $A$ and $k$ of Jamin. At the close of the paper I shall give a Table containing a comparison of the constants found by Jamin and myself for all the bodies which we have both examined. Some years ago, in making observations on polarized light, I found that by adjusting properly the azimuth of the incident polarized beam, and allowing it to fall at the angle of principal incidence, I could obtain a reflected beam of circularly polarized light. On repeating the experiment with different polished surfaces, I found that the coefficient of reflexion, or whatever property it is that gives a surface a metallic reflexion, might be conveniently expressed by the cotangent of the azimuth at which an incident beam of plane-polarized light should be placed so as to give, on reflexion at the principal incidence, a reflected beam of circularly polarized light. The following paper contains an account of my experiments on many substances, and a Table of their Coefficients of Reflexion and Refraction, determined with as much accuracy as I was able to attain with the instruments at my disposal. The apparatus used by me consisted of a large graduated circle (horizontal), provided with two moveable arms, each furnished with graduated circles (vertical); and the large horizontal circle was capable of being hung vertically, so as to allow of experiments being made on liquids as well as solids. The substance to be examined was placed on a stage provided with adjusting screws, so as to bring the surface exactly into the centre, or intersection of the axes of the polarizing and analysing arms. These arms were mounted with Nicol prisms, made for me by Duboscq of Paris, and without sensible deviation. The light employed was generally sunlight, but I sometimes used a moderator lamp with colza oil. I employed the quartz compensator described by M. Jamin*, for the purpose of converting the elliptically polarized reflected light into plane-polarized light, before allowing it to pass through the analyser. The instrument used by me in making my observations on the reflexion of polarized light, was made by Mr. Grubb of Dublin for the late Professor McCullagh, and was presented to me, shortly after McCullagh's death, by his brother. It is substantially the same as that described by M. Jamin in vol. xxix. Ann. de Chim. et de Phys. sér. 3. I procured from M. Duboscq Soleil, of Paris, a compensator of Jamin's pattern, and had it adapted to my own apparatus. In making my observations I used the following precautions: 1. The zero of both polarizer and analyser was determined by direct observation with red sunlight, reflected at the angle of polarization of several glasses found to give a reflected beam capable of being completely cut off by the Nicol prism. 2. The Nicol prisms themselves were carefully tested and found to have no deviation. 3. Each of my recorded observations is the mean of four or five; and when these differed from each other by more than 20', I took the precaution of repeating them. * Annales de Chimie et de Physique, sér. 3. vol. xxix. p. 263 et seq. again, on another day, with my eye fresh and unfatigued, before I finally adopted my mean. 4. I frequently repeated the observations, with the incident light polarized at an equal angle, at the opposite side of the plane of incidence; and also reversing the polarizer and analyser, so as to read the opposite sides of their scales. The following definitions will explain the sense in which I use certain terms. The Azimuth of a beam of plane-polarized light is the angle which its plane of polarization makes with the plane of incidence. The Index of Refraction is the ratio which the sine of the angle of incidence bears to the sine of the angle of refraction. The Coefficient of Refraction is the tangent of the Principal Incidence. The Principal Incidence is that angle of incidence at which rays polarized in any azimuth have the major axis of the reflected elliptic light in the plane of incidence; or at which the components of the reflected beam, in and perpendicular to the plane of incidence, differ by $90^\circ$ in phase. This angle is nearly the same as Brewster's Angle of Polarization or Maximum Polarization. The Coefficient of Reflexion is the Cotangent of the Azimuth of an incident beam of plane-polarized light, which after reflexion at the principal incidence becomes circularly polarized. The Principal Components of the incident and reflected light are the components in and perpendicular to the plane of incidence. The following preliminary investigation will serve to show the principles on which I have tabulated the results of my experiments: Let the elliptically polarized reflected beam be represented, as in the annexed figure, inscribed in a rectangle, whose sides are parallel to OI and OP, the plane of incidence and perpendicular plane. Let Ox be the diagonal of the circumscribed rectangle, and Oy the axis of the ellipse; it is required, from the difference of phase of the light in the planes OI and OP, and knowing the direction of the line Ox, to find the direction of Oy and the ratio of the axes of the ellipse. The angle $xOI = \alpha'$ is the azimuth of the reflected beam, measured by the analyser, after it has lost its elliptic polarization in the compensator; and the difference of phase of OI and OP is measured in the compensator itself, by the displacement necessary to reduce the elliptically-polarized to plane-polarized light. We may imagine, to aid our conception, but without hypothesis, that a material point traverses the ellipse, and that its coordinates are $$\xi = A \sin (kt + e),$$ $$\eta = B \sin (kt + e'),$$ where $e' - e$ is the difference of phase between the beams OI and OP, and A, B are the lines OI and OP. Eliminating $t$, we find $$\frac{\xi^2}{A^2} + \frac{\eta^2}{B^2} - 2 \cos(\epsilon' - \epsilon) \frac{\xi \eta}{AB} = \sin^2(\epsilon' - \epsilon). \quad \ldots \ldots \ldots (1.)$$ In this ellipse, the angle $\phi$ made by the axis with the plane of incidence is found from the well-known expression $$\tan 2\phi = \frac{2E}{D-F},$$ belonging to the ellipse $$Dx^2 + 2Exy + Fy^2 = \text{const.}$$ Substituting for $D$, $E$, $F$ their values from (1.), we find $$\tan 2\phi = \tan 2\alpha' \cos(\epsilon' - \epsilon); \quad \ldots \ldots \ldots \ldots (2.)$$ $\phi$ denoting the angle $yOI$, and $\alpha'$ the angle $xOI$. But if $a$ and $b$ denote the axes of the ellipse, it can be proved that $$\frac{b^2}{a^2} = \frac{(D+F) + (D-F) \sec 2\phi}{(D+F) - (D-F) \sec 2\phi},$$ or substituting from (1.) and (2.), $$\frac{a}{b} = \sqrt{-\cot(\phi + \alpha') \cot(\phi - \alpha')} \quad \ldots \ldots \ldots \ldots (3.)$$ From equations (2.) and (3.), I calculate the position of the elliptic axes and their ratio. The angle $\alpha'$ is obtained by direct measurement with the analysing prism; and $\epsilon' - \epsilon$ may be found, as follows, from the compensator. In the compensator made for me by M. Duboscq, I find that 39·43 represents the zero, i.e. the position in which the compensator affects equally the light in and perpendicular to the plane of incidence; the number of graduations corresponding to a difference of half a wave (180°) I found to be Red lamplight (colza oil) . . . . 15·43 Red sunlight . . . . . . . . . . 15·37 White lamplight (colza oil) . . . . 13·29 If, therefore, $C$ denote the reading of the compensator in any experiment, the difference of phase of the two principal beams will be expressed for red sunlight, in degrees, by the expression $$(C - 39·43) \times \frac{180°}{15·37},$$ and by a corresponding formula for the other kinds of light. The angle thus measured by the compensator is not the difference of phase between the principal components of the reflected light until it is increased by 180°, because experiment shows that in the act of reflexion there is this constant difference between the two components, in addition to the varying difference of phase, depending on incidence, azimuth, and nature of polished surface. We therefore use the formula \[ e' - e = 180^\circ + \left( C - 39.43 \right) \times \frac{180^\circ}{i} \] where \( i \) denotes the interval corresponding to 180° for the light used. In tabulating my experiments, I give the original measurements of the analyser and compensator, and use the equations (2.), (3.), and (4.) to calculate the other columns. I. Munich Glass (a). The first experiments I shall record were made with glass procured from Munich by the late Professor McCullagh. I have four rhombs made of it, whose index of refraction I determined by the following experiments: | Rhomb. | Angle | Minimum deviation* of red light | Refractive index | |--------|-------|---------------------------------|------------------| | No. 1. | 44° 56' 6" | 31° 43' 30" | 1.6229 | | No. 2. | 54° 28' 30" | 41° 28' 0" | 1.6230 | | No. 3. | 39° 50' 0" | 27° 17' 0" | 1.6227 | | No. 4. | 59° 58' 30" | 48° 22' 0" | 1.6221 | Mean ...... 1.6227 Calculated Angle of Polarization = 58° 21'. I also found the refractive indices of No. 2 for the extreme red and violet rays to be 1.6190 and 1.6555, which indicates a dispersive power in the glass of 0.0573. This glass was found to contain the following constituents: - Silica . . . . . . . . 42.25 - Oxide of Lead . . . . 46.35 - Lime . . . . . . . . 0.45 - Alkalies (by diff.) . . 10.95 Total 100.00 The following Tables contain my observations on this glass: * In all my experiments the red light used was passed through the same piece of red glass, which was very homogeneous. TABLE II.—Munich Glass (a). (September 20, 1854.) Azimuth of Polarizer = 20°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e = 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | \( \tan^{-1}\left(\frac{J}{I}\right) \) | |-----------|-------------|----------|-----------------|--------|--------|----------------| | 34° 30' | 39.69 | 11° 35' | 2° 41' | +11° 34' | 89.66 | 29° 23' | | 52° 30' | 42.55 | 2° 5' | 36° 30' | +1° 40' | 45.80 | 5° 42' | | 53° 30' | 44.09 | 2° 0' | 54° 31' | +1° 10' | 35.25 | 5° 29' | | 54° 30' | 45.81 | 2° 0' | 74° 38' | +0° 32' | 29.71 | 5° 29' | | 55° 30' | 48.68 | 2° 6' | 108° 13' | -0° 39' | 28.68 | 5° 45' | | 56° 30' | 49.86 | 2° 37' | 122° 2' | -1° 24' | 25.89 | 7° 9' | | 73° 30' | 53.88 | 11° 45' | 169° 4' | -11° 34' | 26.93 | 29° 45' | The principal incidence is therefore 54° 57'. The last column of this Table is thus found: Let the principal components of the incident polarized beam, in and perpendicular to the plane of incidence, be \( \cos \alpha \) and \( \sin \alpha \) (unity denoting the incident beam); and let \( I \) and \( J \) denote what a unit of light becomes after reflexion, in and perpendicular to the plane of incidence respectively; then the principal components of the reflected beam are \( I \cos \alpha \) and \( J \sin \alpha \), and therefore \[ \frac{J}{I} = \tan \alpha' \cot \alpha; \quad \ldots \ldots \ldots \ldots \ldots \ldots . \] (5.) and the angle \( \tan^{-1}\left(\frac{J}{I}\right) \) may be found from this equation without any difficulty. According to the theory of Fresnel, \[ \frac{J}{I} = \frac{\cos(i+r)}{\cos(i-r)}, \] an expression which vanishes at the polarizing angle \( (i+r=90^\circ) \), and therefore \( \tan^{-1}\left(\frac{J}{I}\right) \) ought at this angle of incidence to vanish also; but we find, not only in this experiment, but in those which follow, that it does not vanish, but only reaches a minimum, the tangent of which is sensibly equal to what I have called the Coefficient of Reflexion*. In fact, let \( \lambda \) denote the angle whose cotangent is this coefficient. Then \( I \cos \lambda, J \sin \lambda \) are the principal components of the reflected light, which by definition is circularly polarized, and therefore \( I \cos \lambda = J \sin \lambda \), and \[ \cot \lambda = \frac{J}{I}. \] The coefficients of Refraction and Reflexion, as determined by this experiment, are therefore Coefficient of Refraction \( = \tan 54° 57' = 1.4255 \). Coefficient of Reflexion \( = \cot 84° 31' = 0.0960 \). * Strictly speaking the angle of incidence at which the maximum is reached is found to be somewhat less than the Principal Incidence. **Table III.—Munich Glass (a). (June 26, 1854.)** Azimuth of Polarizer = 45°. White lamplight (Colza oil). | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\left(\frac{J}{I}\right) \) | |-----------|-------------|----------|--------------------------|---------|-------------|------------------| | 43° 37' | 39·54 | 18° 30' | 3° 11' | +18° 28' | 47·79 | 18° 30' | | 48° 37' | 40·07 | 10° 55' | 10° 17' | +10° 45' | 29·42 | 10° 55' | | 50° 45' | 40·61 | 8° 10' | 17° 36' | +7° 48' | 23·37 | 8° 10' | | 51° 45' | 41·11 | 6° 45' | 24° 22' | +6° 10' | 20·70 | 6° 45' | | 52° 45' | 42·67 | 6° 10' | 45° 29' | +4° 21' | 13·03 | 6° 10' | | 53° 52' | 43·15 | 5° 22' | 50° 21' | +3° 27' | 13·86 | 5° 22' | | 54° 20' | 44·46 | 5° 1' | 69° 44' | +1° 45' | 12·15 | 5° 1' | | 55° 20' | 46·30 | 5° 36' | 94° 38' | -0° 27' | 10·23 | 5° 36' | | 56° 20' | 48·18 | 6° 15' | 120° 6' | -3° 10' | 10·58 | 6° 15' | | 57° 40' | 50·07 | 7° 35' | 145° 41' | -6° 19' | 13·52 | 7° 35' | | 58° 40' | 51·00 | 9° 39' | 158° 16' | -9° 0' | 16·16 | 9° 39' | | 60° 35' | 51·60 | 11° 10' | 166° 24' | -10° 53' | 22·34 | 11° 10' | | 65° 40' | 51·98 | 18° 11' | 171° 33' | -18° 2' | 22·84 | 18° 11' | | 75° 35' | 52·50 | 30° 25' | 178° 40' | -30° 25' | ∞ | 30° 25' | The principal incidence is therefore 55° 8', and the minimum value of tan\(^{-1}\left(\frac{J}{I}\right)\) is 5° 1', or Circular limit = 84° 59'. Therefore the Coefficient of Refraction = 1·4352. Coefficient of Reflexion = 0·0877. **Table IV.—Munich Glass (a). (July 28, 1854.)** Azimuth of Polarizer = 80°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\left(\frac{J}{I}\right) \) | |-----------|-------------|----------|--------------------------|---------|-------------|------------------| | 34° 30' | 39·72 | 7° 4' | 3° 23' | +7° 1' | 88·20 | 31° 35' | | 43° 30' | 40·13 | 61° 45' | 8° 11' | +61° 53' | 16·90 | 18° 10' | | 48° 30' | 40·76 | 49° 15' | 15° 34' | +49° 24' | 7·62 | 11° 34' | | 50° 30' | 42° 15' | 38° 0' | 31° 49' | +36° 49' | 3·62 | 7° 51' | | 51° 30' | 42·80 | 33° 30' | 39° 26' | +30° 36' | 3·09 | 6° 40' | | 52° 30' | 43·85 | 28° 0' | 51° 42' | +21° 17' | 2·70 | 5° 22' | | 53° 30' | 45·41 | 25° 45' | 69° 57' | +11° 39' | 2·38 | 4° 52' | | 54° 30' | 47·20 | 26° 34' | 90° 54' | -0° 36' | 1·99 | 5° 2' | | 55° 30' | 48·80 | 28° 45' | 109° 37' | -13° 53' | 2·02 | 5° 31' | | 56° 30' | 50·30 | 34° 0' | 127° 10' | -28° 7' | 2·26 | 6° 47' | | 57° 30' | 51·20 | 40° 0' | 137° 42' | -38° 18' | 2·64 | 8° 25' | | 58° 30' | 51·21 | 42° 30' | 137° 49' | -41° 38' | 2·82 | 9° 10' | | 60° 30' | 52·14 | 53° 45' | 148° 42' | -55° 8' | 3·76 | 13° 31' | | 65° 30' | 52·77 | 66° 30' | 156° 4' | -67° 47' | 6·59 | 22° 5' | | 70° 45' | 53·18 | 75° 15' | 160° 52' | -75° 56' | 12·30 | 33° 49' | Principal Incidence = 54° 27'. Tan\(^{-1}\left(\frac{J}{I}\right)\) = 4° 57', or Circular limit = 85° 3'. Coeff. of Refraction = 1·3993. Coeff. of Reflexion = 0·0866. ### Table V.—Munich Glass (a). (August 7, 1854.) Azimuth of Polarizer = 85°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180^\circ$ | $\phi$ | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|---------------------|-------|-------------|----------------------------------| | 34° 30' | 39·68 | 80° 12' | 2° 55' | +80° 13' | 98·30 | 26° 52' | | 52° 30' | 43·37 | 44° 30' | 46° 5 | +44° 17' | 2° 37' | 4° 55' | | 53° 30' | 44·33 | 39° 54' | 57° 19 | +35° 47' | 1° 86' | 4° 11' | | 54° 30' | 46·12 | 38° 24' | 78° 16 | +20° 28' | 1° 36' | 3° 58' | | 55° 30' | 48·13 | 41° 50' | 101° 47 | -30° 44' | 1° 26' | 4° 28' | | 56° 30' | 49·45 | 44° 0 | 117° 13 | -42° 49' | 1° 64' | 4° 50' | | 57° 30' | 50·42 | 51° 0 | 138° 34 | -54° 24' | 2° 15' | 6° 10' | | 73° 30' | 53·62 | 81° 0 | 166° 1 | -81° 15' | 26° 76' | 28° 55' | Principal Incidence = 54° 59'. $\tan^{-1}\left(\frac{J}{I}\right) = 3° 58'$, or Circular limit = 86° 2'. Coeff. of Refraction = 1·4272. Coeff. of Reflexion = 0·0693. ### Table VI.—Munich Glass (a). (September 27, 1854.) Azimuth of Polarizer = 85° 45'. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180^\circ$ | $\phi$ | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|---------------------|-------|-------------|----------------------------------| | 54° 30' | 46·05 | 43° 26' | 77° 23' | +37° 56' | 1° 25' | 4° 2' | | 54° 45' | 46·75 | 43° 20' | 85° 38' | +26° 18' | 1° 09' | 4° 1' | | 55° 0 | 46·90 | 43° 8 | 87° 24' | +17° 24' | 1° 08' | 3° 59' | | 55° 15' | 47·53 | 43° 15' | 94° 46' | -26° 49' | 1° 11' | 4° 0' | | 55° 30' | 48·05 | 45° 30' | 100° 51' | -47° 39' | 1° 21' | 4° 20' | Principal Incidence = 55° 6'. $\tan^{-1}\left(\frac{J}{I}\right) = 3° 59'$, or Circular limit = 86° 1'. Coeff. of Refraction = 1·4334. Coeff. of Reflexion = 0·0696. ### Table VII.—Munich Glass (a). (September 27, 1854.) Azimuth of Polarizer = 85° 55'. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180^\circ$ | $\phi$ | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|---------------------|-------|-------------|----------------------------------| | 54° 30' | 45·96 | 45° 30' | 76° 24' | +47° 7' | 1° 27' | 4° 16' | | 54° 45' | 46·65 | 45° 12' | 84° 28' | +47° 4' | 1° 10' | 4° 7' | | 55° 0 | 47·00 | 45° 5 | 88° 34' | +48° 19' | 1° 02' | 4° 6' | | 55° 15' | 47·72 | 45° 40' | 96° 59' | -50° 25' | 1° 13' | 4° 11' | | 55° 30' | 48·00 | 46° 30' | 100° 16' | -53° 12' | 1° 20' | 4° 18' | Principal Incidence = 55° 7'. $\tan^{-1}\left(\frac{J}{I}\right) = 4° 6'$, or Circular limit = 85° 54'. Coeff. of Refraction = 1·4343. Coeff. of Reflexion = 0·0717. ### Table VIII.—Munich Glass (a). (September 26, 1854.) Azimuth of Polarizer = 86°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|--------------|-------------------------------| | 34° 30 | 39·77 | 83° 20 | 3° 58 | +83° 21 | 120·50 | 30° 53 | | 52° 30 | 43·03 | 53° 30 | 42° 7 | +56° 16 | 2·73 | 5° 24 | | 53° 30 | 44·67 | 47° 0 | 61° 18 | +49° 8 | 1·70 | 4° 17 | | 54° 0 | 45·25 | 46° 20 | 68° 5 | +48° 34 | 1·48 | 4° 11 | | 54° 30 | 46·13 | 46° 11 | 78° 23 | +50° 48 | 1·23 | 4° 10 | | 54° 45 | 46·48 | 46° 0 | 82° 28 | +52° 28 | 1·14 | 4° 8 | | 55° 0 | 46·91 | 45° 45 | 87° 30 | +60° 29 | 1·06 | 4° 6 | | 55° 15 | 47·33 | 47° 0 | 92° 25 | −74° 27 | 1·08 | 4° 17 | | 55° 30 | 48·07 | 48° 20 | 101° 5 | −60° 39 | 1·25 | 4° 30 | | 56° 0 | 48·86 | 50° 15 | 111° 30 | −58° 25 | 1·53 | 4° 48 | | 56° 30 | 49·40 | 51° 30 | 116° 38 | −58° 37 | 1·71 | 5° 2 | | 57° 30 | 50·20 | 57° 0 | 126° 0 | −63° 34 | 2·26 | 6° 9 | | 73° 30 | 53·69 | 83° 15 | 166° 50 | −83° 25 | 37·96 | 30° 35 | Principal Incidence = 55° 8′. Tan$^{-1}\left(\frac{J}{I}\right) = 4° 6′$, or Circular limit = 85° 54′. Coeff. of Refraction = 1·4352. Coeff. of Reflexion = 0·0717. ### Table IX.—Munich Glass (a). (September 21, 1854.) Azimuth of Polarizer = 87°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|--------------|-------------------------------| | 34° 30 | 39·48 | 84° 50 | 0° 27 | +84° 50 | ∞ | 30° 6 | | 52° 30 | 42·87 | 60° 0 | 40° 14 | +63° 33 | 3·27 | 5° 11 | | 53° 30 | 44·06 | 55° 0 | 54° 10 | +60° 56 | 2·16 | 4° 17 | | 54° 0 | 44·93 | 54° 20 | 64° 21 | +63° 59 | 1·78 | 4° 11 | | 54° 30 | 45·82 | 54° 0 | 74° 45 | +70° 30 | 1·52 | 4° 8 | | 54° 45 | 46·34 | 53° 54 | 80° 50 | +76° 48 | 1·43 | 4° 7 | | 55° 0 | 46·60 | 53° 55 | 83° 53 | +80° 50 | 1·40 | 4° 7 | | 55° 15 | 47·23 | 53° 34 | 91° 15 | −87° 59 | 1·35 | 4° 4 | | 55° 30 | 47·92 | 55° 30 | 99° 20 | −78° 33 | 1·48 | 4° 22 | | 56° 0 | 48·40 | 56° 30 | 104° 57 | −74° 21 | 1·64 | 4° 32 | | 56° 30 | 49·08 | 59° 30 | 112° 54 | −72° 28 | 1·97 | 5° 5 | | 57° 30 | 50·00 | 64° 30 | 123° 40 | −72° 48 | 2·72 | 6° 16 | | 73° 30 | 53·34 | 85° 0 | 165° 5 | −85° 10 | 44·50 | 30° 55 | Principal Incidence = 55° 13′. Tan$^{-1}\left(\frac{J}{I}\right) = 4° 4′$, or Circular limit = 85° 56′. Coeff. of Refraction = 1·4397. Coeff. of Reflexion = 0·0711. Collecting together the preceding results, and denoting by $\lambda$ the azimuth of the plane of polarization of the incident light, which on reflexion at the principal incidence will produce, on reflexion, circularly polarized light, and calling it the Circular Limit, we obtain TABLE X.—Constants of Munich Glass (a). | Azimuth of Polarizer | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |----------------------|--------------------|---------------|--------------------------|-------------------------| | 20° 0 | 54° 57' | 84° 31' | 1·4255 | 0·0960 | | 45° 0 | 55° 8 | 84° 59' | 1·4352 | 0·0877 | | 80° 0 | 54° 27' | 85° 3 | 1·3993 | 0·0866 | | 85° 0 | 54° 59' | 86° 2 | 1·4272 | 0·0693 | | 85° 45 | 55° 6 | 86° 1 | 1·4334 | 0·0696 | | 85° 55 | 55° 7 | 85° 54 | 1·4343 | 0·0717 | | 86° 0 | 55° 8 | 85° 54 | 1·4352 | 0·0717 | | 87° 0 | 55° 13 | 85° 56 | 1·4397 | 0·0711 | | Means........... | 55° 0' 37" | 85° 32' 30" | 1·4287 | 0·0780 | The movement of the axis of the reflected ellipse differs according as the azimuth of the incident light is less or greater than the circular limit. This is shown in Plate VIII. fig. A, on which the values of $\phi$ are laid down for different angles of incidence in the two cases in which the azimuth of the incident light is 80° and 87°. When the azimuth of the incident light is less than $\lambda$, the circular limit, the axis of the ellipse moves as in the annexed figure. Let POA be the azimuth of the incident light, and QOA equal to POA; PO is the position of the axis major corresponding to 0° incidence; OA is the position of the axis major in the plane of incidence, corresponding to the principal incidence; and OQ is the position of the axis corresponding to 90° incidence. When, however, the azimuth of the incident light is greater than the circular limit, the axis major moves from P to x, as in the annexed figure, then back from x to y, passing through B at the principal incidence, and finally from y to Q. Let POA be the azimuth of the incident light, and QOB equal to POB. At the incidence 0°, OP is the position of the axis major; as the incidence increases from 0° to the principal incidence, the axis major moves from OP to Ox and turns back, attaining the position OB at the principal incidence; and as the incident angle increases from the principal incidence to 90°, the axis major moves from OB to Oy, and back again to OQ. Having ascertained the truth of the preceding laws of the movement of the axis major of the elliptically polarized light, I made the following experiments. Having removed the compensator, I set the polarizer at 88° and 89°, and found that the analyser gave a minimum of light at 90°, showing that the axis major of the ellipse was perpendicular to the plane of incidence. All the experiments already given were made with the Munich glass (a) No. 1. I made the following experiment with (a) No. 2, in order to establish fully the identity of the pieces of glass with regard to reflexion, as they are certainly identical in their refractive indices. **Table XI.—Munich Glass (a). (October 11, 1854.)** Azimuth of Polarizer = 86°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( \frac{d}{l} \)) | |-----------|-------------|----------|-----------------|--------|--------|------------------| | 34° 30' | 39·70 | 83° 20' | 3° 8 | +83° 20' | ∞ | 30° 53' | | 52° 30' | 43·33 | 53° 30' | 45° 37 | +56° 48' | 2·53 | 5° 24' | | 53° 30' | 44° 70' | 50° 0 | 61° 39 | +55° 11' | 1·73 | 4° 46' | | 54° 0 | 45° 60' | 49° 0 | 72° 11 | +57° 20' | 1·41 | 4° 36' | | 54° 30' | 46° 30' | 47° 30' | 80° 22 | +58° 48' | 1·21 | 4° 22' | | 54° 45' | 46° 79' | 46° 45' | 85° 58 | +65° 30' | 1·10 | 4° 15' | | 55° 0 | 47° 81' | 46° 0 | 92° 11 | −66° 15' | 1·05 | 4° 9' | | 55° 15' | 47° 70' | 47° 30' | 96° 45 | −63° 20' | 1·16 | 4° 22' | | 55° 30' | 48° 00' | 48° 30' | 100° 16 | −62° 17' | 1·24 | 4° 31' | | 56° 0 | 48° 83' | 50° 30' | 109° 58 | −59° 50' | 1·50 | 4° 51' | | 56° 30' | 49° 10' | 52° 30' | 113° 8 | −62° 9 | 1·64 | 5° 12' | | 57° 30' | 49° 95' | 57° 0 | 123° 5 | −64° 32' | 2·15 | 6° 9' | | 73° 30' | 53·40 | 82° 30' | 163° 27 | −82° 48' | 26·98 | 27° 59' | Principal Incidence = 54° 53'. Coeff. of Refraction = 1·4220. Circular Limit = 85° 51'. Coeff. of Reflexion = 0·0725. The agreement of these values with those given for No. (1) in Table X. is sufficiently satisfactory. **II. Munich Glass (b).** The glass now to be described is a rhomb which gave me the following values: Angle of rhomb . . . . . . . . . . . = 54° 30' Minimum deviation of standard red . . . 34° 2 Hence the refractive index of this red is 1·5244, and the angle of polarization 56° 44'. **Table XII.—Munich Glass (b). (October 10, 1854.)** Azimuth of Polarizer = 45°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( \frac{d}{l} \)) | |-----------|-------------|----------|-----------------|--------|--------|------------------| | 54° 15' | 39·43 | 1° 6 | 0° 0 | +1° 6 | ∞ | 1° 6 | | 54° 30' | 39·43 | 0° 43 | 0° 0 | +0° 43 | ∞ | 0° 43 | | 54° 45' | 39·43 | 0° 30 | 0° 0 | +0° 30 | ∞ | 0° 30 | | 55° 0 | 39·43 | 0° 10 | 0° 0 | +0° 10 | ∞ | 0° 10 | | 55° 15' | 54·13 | 2° 15 | 172° 0 | −2° 14 | 209·4 | 2° 15 | Principal Incidence = 55° 1'. Coeff. of Refraction = 1·4290. Circular Limit = 89° 50'. Coeff. of Reflexion = 0·0029. ### Table XIII.—Munich Glass (b). (September 29, 1854.) Azimuth of Polarizer = 80°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \over I \)) | |-----------|-------------|----------|--------------------------|----------|-------------|------------------| | 34° 30' | 39° 43' | 72° 30' | 0° 0° | +72° 30' | ∞ | 29° 13' | | 52° 30' | 39° 57' | 20° 15' | 1° 38' | +20° 15' | ∞ | 3° 38' | | 53° 30' | 39° 65' | 11° 30' | 2° 34' | +11° 29' | 127° 3' | 2° 3 | | 53° 45' | 39° 65' | 10° 15' | 2° 34' | +10° 14' | 135° 6' | 1° 49 | | 54° 0° | 39° 65' | 7° 30' | 2° 34' | +7° 29' | 160° 2' | 1° 20 | | 54° 15' | 39° 65' | 6° 0° | 2° 34' | +5° 59' | 179° 9' | 1° 4 | | 54° 30' | 39° 73' | 1° 20' | 3° 30' | +1° 20' | 171° 8' | 0° 13 | | 54° 45' | 54° 25' | 4° 15' | 173° 23' | -4° 13' | 114° 9' | 0° 45 | | 55° 0° | 54° 25' | 6° 0° | 173° 23' | -5° 57' | 80° 6' | 1° 4 | | 55° 15' | 54° 25' | 8° 30' | 173° 23' | -8° 27' | 54° 8' | 1° 30 | | 55° 30' | 54° 35' | 9° 37' | 174° 33' | -9° 34' | 62° 8' | 1° 43 | | 56° 30' | 54° 35' | 17° 30' | 174° 33' | -17° 26' | 37° 5' | 3° 11 | | 57° 30' | 54° 36' | 25° 25' | 174° 41' | -25° 21' | 28° 3' | 4° 47 | | 58° 30' | 54° 45' | 31° 0° | 175° 44' | -30° 58' | 30° 3' | 6° 3 | | 73° 30' | 54° 68' | 70° 0° | 178° 25' | -70° 0° | 90° 5' | 25° 51 | | 83° 30' | 54° 68' | 76° 30' | 178° 25' | -76° 30' | 164° 3' | 36° 18 | Principal Incidence = 54° 35'. Circular Limit = 89° 47'. Coeff. of Refraction = 1·4063. Coeff. of Reflexion = 0·0037. ### Table XIV.—Munich Glass (b). (October 10, 1854.) Azimuth of Polarizer = 87°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \over I \)) | |-----------|-------------|----------|--------------------------|----------|-------------|------------------| | 54° 15' | 39° 43' | 15° 40' | 0° 0° | +15° 40' | ∞ | 0° 51 | | 54° 30' | 39° 43' | 2° 15' | 0° 0° | +2° 15' | ∞ | 0° 7 | | 54° 45' | 54° 13' | 3° 45' | 172° 0° | -3° 43' | 114° 5' | 0° 12 | | 55° 0° | 54° 13' | 7° 40' | 172° 0° | -7° 36' | 56° 1' | 0° 24 | | 55° 15' | 54° 13' | 14° 20' | 172° 0° | -14° 13' | 30° 0' | 0° 46 | Principal Incidence = 54° 36'. Circular Limit = 89° 53'. Coeff. of Refraction = 1·4071. Coeff. of Reflexion = 0·0020. ### Table XV.—Munich Glass (b). (October 1, 1855.) Azimuth of Polarizer = 88°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \over I \)) | |-----------|-------------|----------|--------------------------|----------|-------------|------------------| | 33° 37' | 39° 43' | 86° 45' | 0° 0° | +86° 45' | ∞ | 31° 36' | | 43° 37' | 39° 43' | 83° 45' | 0° 0° | +83° 45' | ∞ | 17° 41' | | 53° 37' | 39° 43' | 37° 30' | 0° 0° | +37° 30' | ∞ | 1° 32 | | 54° 37' | 39° 43' | 359° 45' | 180° 0° | -0° 15' | ∞ | 0° 1 | | 55° 37' | 39° 43' | 332° 0° | 180° 0° | -38° 0° | ∞ | 1° 34 | | 56° 37' | 39° 43' | 301° 30' | 180° 0° | -58° 30' | ∞ | 3° 16 | | 63° 37' | 39° 43' | 278° 0° | 180° 0° | -82° 0° | ∞ | 13° 57 | | 73° 37' | 39° 43' | 274° 30' | 180° 0° | -85° 30' | ∞ | 23° 55 | Principal Incidence = 54° 37'. Circular Limit = 89° 59'. Coeff. of Refraction = 1·4080. Coeff. of Reflexion = 0·0001. TABLE XVI.—Munich Glass (b). (October 5, 1855.) Azimuth of Polarizer = 89°. Red Sunlight. | Incidence | Compensator | Analyser | $e - e - 180°.$ | ϕ | $\frac{a}{b}$ | Tan$^{-1} \left( \frac{J}{I} \right)$ | |-----------|------------|----------|----------------|----|--------------|-------------------| | 33° 37' | 39·43 | 88° 6 | 0° 0 | +88° 0 | 8 | 26° 34 | | 43° 37' | 39·43 | 85° 25 | 0° 0 | +85° 25 | 8 | 12° 17 | | 53° 37' | 39·43 | 55° 0 | 0° 0 | +55° 0 | ∞ | 1° 26 | | 54° 37' | 39·43 | 358° 0 | 180° 0 | −2° 0 | ∞ | 0° 2 | | 55° 37' | 39·43 | 307° 30 | 180° 0 | −52° 30 | 8 | 1° 2 | | 56° 37' | 39·43 | 292° 0 | 180° 0 | −68° 0 | ∞ | 2° 28 | | 63° 37' | 39·43 | 275° 0 | 180° 0 | −85° 0 | 8 | 11° 17 | | 73° 37' | 39·43 | 272° 15 | 180° 0 | −87° 45 | ∞ | 23° 57 | Principal Incidence = 54° 35'. Circular Limit = 0° 2'. Coeff. of Refraction = 1·4063. Coeff. of Reflexion = 0·0006. From this and the four preceding Tables the following results may be collected. TABLE XVII.—Constants of Munich Glass (b). | Azimuth of Polarizer. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |----------------------|---------------------|-----------------|---------------------------|--------------------------| | 45° | 55° 1° | 89° 50' | 1·4290 | 0·0029 | | 80° | 54° 35' | 89° 47' | 1·4063 | 0·0037 | | 87° | 54° 36' | 89° 53' | 1·4071 | 0·0020 | | 88° | 54° 37' | 89° 59' | 1·4080 | 0·0001 | | 89° | 54° 35' | 89° 58' | 1·4063 | 0·0006 | | Means........... | 54° 40' 48" | 89° 53' 24" | 1·4113 | 0·0019 | III. PARIS GLASS. This glass was supplied to me by M. Duboscq of Paris. Its refractive constants were found to be as follows: Angle of prism . . . . . . . . . . . . . . . . . . . . . . . 59° 55 Minimum deviation of extreme red . . . . . . . . . . . . . . 37° 35 Minimum deviation of extreme violet . . . . . . . . . . . . . 39° 13 Index of refraction of extreme red . . . . . . . . . = 1·5059 Index of refraction of extreme violet . . . . . . . . . = 1·5246 OF POLARIZED LIGHT FROM POLISHED SURFACES. TABLE XVIII.—Paris Glass. (October 1, 1855.) Azimuth of Polarizer = 88°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \)) | |-----------|-------------|----------|-----------------|--------|---------|------------------| | 33° 37' | 39·43 | 86° 20' | 0° 0' | +86° 20' | ∞ | 28° 35' | | 43° 37' | 39·43 | 84° 30' | 0° 0' | +84° 30' | ∞ | 19° 56' | | 53° 37' | 39·43 | 63° 45' | 0° 0' | +63° 45' | ∞ | 4° 3' | | 54° 37' | 40·19 | 50° 20' | 8° 53' | +50° 24' | 12°76' | 2° 25' | | 55° 37' | 42·43 | 25° 30' | 35° 6' | +23° 39' | 4°24' | 0° 57' | | 55° 52' | 44·44 | 19° 30' | 58° 36' | +11° 26' | 3°41' | 0° 43' | | 56° 7 | 46·75 | 17° 30' | 85° 38' | + 1° 32' | 3°18' | 0° 38' | | 56° 22 | 48·39 | 18° 45' | 104° 41' | -5° 30' | 3°07' | 0° 41' | | 56° 37 | 50·22 | 27° 30' | 126° 14' | -20° 5' | 2°65' | 1° 2' | | 57° 37 | 52·70 | 48° 0' | 155° 15' | -48° 18' | 4°59' | 2° 13' | | 58° 37 | 53·27 | 60° 0' | 161° 55' | -60° 38' | 7°32' | 3° 28' | | 63° 37 | 54·00 | 80° 0' | 170° 28' | -80° 7' | 36°85' | 11° 12' | | 73° 37 | 54·40 | 87° 0' | 175° 8' | -87° 1' | 180°90' | 33° 41' | Principal Incidence = 56° 10'. Circular Limit = 89° 22'. Coeff. of Refraction = 1·4919. Coeff. of Reflexion = 0·0110. The compensator was then set at 47°12', which corresponds with a difference of phase of 90°, between the principal components of the reflected light; and the compensator being thus set, the angle of incidence was determined by trial, for which the dark band was centrally placed. The incidence so found is the principal incidence. Having thus found the principal incidence, I changed the azimuth of the polarizer, and read the analyser, obtaining the following results. TABLE XIX.—Paris Glass. (October 1, 1855.) Compensator = 47°12' = 90°. Red Sunlight. | Polarizer | Analyser | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \)) | |-----------|----------|-----------------|------------------| | 89° 30' | 48° 0' | 1·110 | 0° 33' | | 89° 0 | 32° 0' | 1·600 | 0° 37' | | 88° 0 | 18° 0' | 3·077 | 0° 39' | | 87° 0 | 13° 20' | 4·219 | 0° 43' | | 86° 0 | 10° 0' | 5·671 | 0° 43' | | 85° 0 | 9° 0' | 6·314 | 0° 48' | | 80° 0 | 4° 30' | 12°706 | 0° 48' | | 70° 0 | 2° 45' | 20°819 | 1° 0' | | 60° 0 | 1° 40' | 34°367 | 0° 58' | | 50° 0 | 1° 10' | 49°103 | 0° 59' | | 40° 0 | 0° 54' | 63°656 | 1° 4' | | 30° 0 | 0° 47' | 73°139 | 1° 21' | | 20° 0 | 0° 37' | 92°908 | 1° 42' | | 10° 0 | 0° 24' | 143°237 | 2° 16' | Principal Incidence = 56° 7'. Circular Limit = 89° 24'. Coeff. of Refraction = 1·4891. Coeff. of Reflexion = 0·0104. The last column of this Table shows that the value of \( \frac{J}{I} \) increases slightly as the azimuth of the polarizer diminishes. Combining the preceding results, we find **Table XX.—Constants of Paris Glass.** | No. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-----|----------------------|-----------------|---------------------------|--------------------------| | XVIII. | 56° 10' | 89° 22' | 1·4919 | 0·0110 | | XIX. | 56° 7' | 89° 24' | 1·4891 | 0·0104 | | Means........... | 56° 8' 30'' | 89° 23' | 1·4905 | 0·9107 | **IV. Fluor-Spar.** The specimen of fluor-spar on which I made my experiments was transparent and blue. The following are the results I obtained. **Table XXI.—Fluor-Spar. (September 11, 1855.)** Azimuth of Polarizer = 80°. Red Sunlight. | Incidence. | Compensator. | Analyser. | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( \frac{J}{I} \)) | |------------|--------------|-----------|--------------------------|---------|--------|------------------| | 33° 37' | 39°43' | 73° 36' | 0° 0° | +73° 36' | ∞ | 30° 46' | | 43° 37' | 39°43' | 60° 45' | 0° 0° | +60° 45' | ∞ | 17° 29' | | 53° 37' | 39°43' | 10° 30' | 0° 0° | +10° 30' | ∞ | 1° 53' | | 54° 37' | 39°43' | 0° 30' | 0° 0° | +0° 30' | ∞ | 0° 5' | | 55° 37' | 39°43' | 351° 45' | 180° 0° | -8° 15' | ∞ | 1° 28' | | 58° 37' | 39°43' | 327° 0' | 180° 0° | -33° 0' | ∞ | 6° 32' | | 63° 37' | 39°43' | 305° 0' | 180° 0° | -55° 0' | ∞ | 14° 8' | | 73° 37' | 39°43' | 288° 15' | 180° 0° | -71° 45' | ∞ | 28° 8' | Principal Incidence = 54° 40'. Circular Limit = 89° 55'. Coeff. of Refraction = 1·4106. Coeff. of Reflexion = 0·0014. Table XXII.—Fluor-Spar. (September 20, 1855.) Azimuth of Polarizer = 88°. Red Sunlight. | Incidence | Compensator | Analyser | \(e' - e - 180^\circ\) | \(a/b\) | Tan\(^{-1}\)(\(J/\bar{I}\)) | |-----------|-------------|----------|------------------------|---------|--------------------------| | 53° 37' | 39·43 | 43° 30' | 0° 0' | +43° 30' | ∞ | | 54° 7 | 39·43 | 31° 0 | 0° 0' | +31° 0 | ∞ | | 54° 37' | 39·43 | 15° 0 | 0° 0' | +15° 0 | ∞ | | 55° 7 | 39·43 | 344° 30' | 180° 0 | -15° 30' | ∞ | | 55° 37' | 39·43 | 331° 0 | 180° 0 | -29° 0 | ∞ | Principal Incidence = 54° 52'. Circular Limit = 89° 28'. Coeff. of Refraction = 1·4211. Coeff. of Reflexion = 0·0093. From the preceding results combined, we obtain the following constants of fluor-spar. Table XXIII.—Constants of Fluor-Spar. | No. | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |-----|---------------------|---------------|--------------------------|--------------------------| | XXI.| 54° 46 | 89° 55 | 1·4106 | 0·0014 | | XXII.| 54° 52 | 89° 28 | 1·4211 | 0·0093 | | Means...........| 54° 46 | 89° 41' 30'' | 1·4158 | 0·0053 | V. Glass of Antimony. The specimen of this glass with which I experimented was given to me by Professor Apjohn. Table XXIV.—Glass of Antimony. (October 5, 1855.) Azimuth of Polarizer = 80°. Red Sunlight. | Incidence | Compensator | Analyser | \(e' - e - 180^\circ\) | \(a/b\) | Tan\(^{-1}\)(\(J/\bar{I}\)) | |-----------|-------------|----------|------------------------|---------|--------------------------| | 33° 37' | 39·43 | 75° 0 | 0° 0' | +75° 0 | ∞ | | 43° 37' | 39·43 | 66° 20 | 0° 0' | +66° 20 | ∞ | | 53° 37' | 39·82 | 38° 50 | 4° 33' | +38° 49 | 27° 43 | | 55° 37' | 40·16 | 25° 10 | 8° 32' | +25° 1 | 17° 84 | | 57° 37' | 41·90 | 10° 30 | 28° 54' | +8° 50 | 9° 89 | | 58° 7 | 43·14 | 8° 30 | 43° 24' | +6° 16 | 9° 86 | | 58° 37' | 46·19 | 6° 20 | 79° 5' | +1° 13 | 9° 18 | | 59° 7 | 49·50 | 7° 30 | 117° 48' | -3° 34 | 8° 62 | | 59° 37' | 51·18 | 10° 15 | 137° 22' | -7° 41 | 8° 30 | | 61° 37' | 53·21 | 26° 30 | 161° 13' | -25° 46 | 7° 77 | | 63° 37' | 53·70 | 39° 30 | 166° 57' | -39° 21 | 13° 92 | | 73° 37' | 54·25 | 68° 20 | 173° 33' | -63° 25 | 27° 04 | Principal Incidence = 58° 44'. Circular Limit = 88° 53'. Coeff. of Refraction = 1·6468. Coeff. of Reflexion = 0·0195. Table XXV.—Glass of Antimony. (October 5, 1855.) Azimuth of Polarizer = 89°. Red Sunlight. | Incidence | Compensator | Analyser | \( e' - e - 180^\circ \) | \( \phi \) | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \over I \)) | |-----------|-------------|----------|-----------------|--------|---------|------------------| | 33° 37' | 39°43 | 89° 0 | 0° 0 | +89° 0 | ∞ | 45° 6 | | 43° 37' | 39°43 | 87° 45 | 0° 0 | +87° 45| ∞ | 23° 57 | | 53° 37' | 39°65 | 83° 20 | 2° 34 | +83° 20| ∞ | 8° 30 | | 55° 37' | 39°91 | 80° 0 | 5° 36 | +80° 3 | 56°19 | 5° 39 | | 57° 37' | 41°25 | 64° 30 | 21° 17 | +65° 30| 6°93 | 2° 6 | | 58° 7 | 42°43 | 55° 40 | 35° 6 | +57° 46| 3°44 | 1° 28 | | 58° 37' | 45°72 | 48° 0 | 73° 35 | +55° 12| 1°36 | 1° 7 | | 58° 47' | 47°00 | 47° 0 | 88° 34 | +72° 11| 1°09 | 1° 4 | | 59° 7 | 48°76 | 49° 30 | 109° 9 | −67° 26| 1°24 | 1° 10 | | 59° 37' | 50°35 | 60° 0 | 127° 45 | −60° 23| 9°36 | 1° 44 | | 61° 37' | 52°80 | 78° 30 | 156° 26 | −79° 22| 12°75 | 6° 9 | | 63° 37' | 53°68 | 82° 15 | 166° 43 | −82° 27| 32°36 | 7° 19 | | 73° 37' | 54°10 | 88° 45 | 171° 38 | −88° 46| 281°50 | 38° 40 | Principal Incidence = 58° 50'. Circular Limit = 88° 56'. Coeff. of Refraction = 1·6533. Coeff. of Reflexion = 0·0186. Table XXVI.—Glass of Antimony. (October 5, 1855.) Compensator = 47°12 = 90°. Red Sunlight. | Polarizer | Analyser | \( \frac{a}{b} \) | Tan\(^{-1}\)(\( J \over I \)) | |-----------|----------|-----------------|------------------| | 89° | 50° 0 | 1·192 | 1° 11' | | 88° | 28° 45 | 1·823 | 1° 6 | | 87° | 21° 15 | 2·571 | 1° 10 | | 85° | 12° 40 | 4·449 | 1° 9 | | 80° | 6° 25 | 8·892 | 1° 8 | | 70° | 3° 10 | 18°075 | 1° 9 | | 50° | 1° 35 | 36°177 | 1° 20 | | 30° | 0° 52 | 66°105 | 1° 30 | | 10° | 0° 37 | 92°908 | 3° 29 | Mean = 1° 28' 0"' Principal Incidence = 58° 52'. Circular Limit = 88° 46'. Coeff. of Refraction = 1·6555. Coeff. of Reflexion = 0·0215. It is to be remarked, that in Table XXV., in which the azimuth of the polarizer is greater than the circular limit, the movement of the axis of the ellipse follows the same law as that of the Munich glass already described. From the foregoing Tables, the optical constants of Glass of Antimony may be thus inferred:— ### Table XXVII.—Constants of Glass of Antimony. | No. | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |-----|---------------------|----------------|--------------------------|--------------------------| | XXIV. | 58° 44' | 88° 53' | 1·6468 | 0·0195 | | XXV. | 58° 50' | 88° 56' | 1·6533 | 0·0186 | | XXVI. | 58° 52' | 88° 46' | 1·6555 | 0·0215 | | Means ...... | 58° 48' 40'' | 88° 51' 40'' | 1·6519 | 0·0199 | VI. Quartz (a). Natural surface. Plane of incidence perpendicular to optical axis. ### Table XXVIII.—Quartz (a). (October 13, 1855.) Azimuth of Polarizer = 88°. Red Sunlight. | Incidence. | Compensator. | Analyser. | \(e'-e-180^\circ\) | \(a/b\) | Tan\(^{-1}(J/I)\) | |------------|--------------|-----------|-------------------|--------|------------------| | 33° 37' | 39·43 | 87° 10' | 0° 0' | +87° 10' | ∞ | 35° 12' | | 43° 37' | 39·43 | 84° 20' | 0° 0' | +84° 20' | ∞ | 19° 23' | | 53° 37' | 39·90 | 67° 45' | 3° 9' | +67° 45' | 59·16 | 4° 52' | | 55° 37' | 41·02 | 42° 0' | 18° 36' | +41° 50' | 6° 09 | 1° 48' | | 56° 7 | 43·40 | 32° 0' | 46° 27' | +27° 21' | 2° 70 | 1° 15' | | 56° 37' | 46·82 | 24° 30' | 86° 27' | +4° 4' | 2° 20 | 0° 55' | | 57° 7 | 50·53 | 35° 0' | 129° 52' | -30° 12' | 2° 34 | 1° 16' | | 57° 37' | 51·28 | 48° 0' | 138° 38' | -49° 0' | 2° 65 | 2° 13' | | 58° 37' | 52·10 | 63° 15' | 148° 14' | -65° 31' | 4° 50 | 3° 58' | | 63° 37' | 53·30 | 80° 45' | 162° 16' | -81° 10' | 20° 52 | 12° 6' | | 73° 37' | 53·50 | 86° 30' | 164° 36' | -86° 37' | 63° 78 | 29° 43' | Principal Incidence = 56° 40'. Coeff. of Refraction = 1·5204. Circular Limit = 89° 5'. Coeff. of Reflexion = 0·0160. ### Table XXIX.—Quartz (a). (October 15, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer. | Analyser. | \(a/b\) | Tan\(^{-1}(J/I)\) | |------------|-----------|---------|------------------| | 89° 30' | 64° 0' | 2·050 | 1° 1' | | 89° 0 | 48° 0' | 1·110 | 1° 7' | | 88° 0 | 28° 0' | 1·881 | 1° 4' | | 85° 0 | 11° 10' | 5·066 | 1° 0' | Mean = 1° 3' 0" Principal Incidence = 56° 40'. Coeff. of Refraction = 1·5204. Circular Limit = 88° 51'. Coeff. of Reflexion = 0·0200. Hence we obtain **TABLE XXX.—Constants of Quartz (a).** | No. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-----|----------------------|-----------------|---------------------------|--------------------------| | XXVIII. | 56° 40' | 89° 5' | 1·5204 | 0·0160 | | XXIX. | 56° 40' | 88° 51' | 1·5204 | 0·0200 | | Means ...... | 56° 40' | 88° 58' | 1·5204 | 0·0180 | **VII. QUARTZ (b). Natural surface. Plane of incidence contains optical axis.** **TABLE XXXI.—Quartz (b). (October 16, 1855.)** Azimuth of Polarizer = 88°. Red Sunlight. | Incidence. | Compensator. | Analyser. | \(e' - e - 180^\circ\). | \(a\) | \(b\) | Tan\(^{-1}(J)\) | |------------|--------------|-----------|------------------------|------|------|----------------| | 33° 37' | 39·43 | 86° 36' | 0° 0' | +86° 36' | ∞ | 29° 43' | | 43° 37' | 39·43 | 84° 30' | 0° 0' | +84° 30' | ∞ | 19° 56' | | 53° 37' | 39·90 | 66° 0' | 5° 30' | +66° 4' | 27° 85' | 4° 29' | | 55° 37' | 40·72 | 45° 15' | 15° 5' | +45° 16' | 5° 57' | 2° 1' | | 56° 7' | 41·82 | 36° 30' | 27° 57' | +35° 27' | 4° 22' | 1° 29' | | 56° 37' | 43·87 | 23° 30' | 51° 57' | +16° 44' | 3° 15' | 0° 52' | | 57° 7' | 48·14 | 27° 30' | 101° 54' | −8° 12' | 1° 99' | 1° 2' | | 57° 37' | 50·97 | 39° 0' | 135° 0' | −36° 39' | 2° 47' | 1° 37' | | 63° 37' | 53·85 | 79° 30' | 168° 42' | −82° 34' | 7° 17' | 10° 40' | | 73° 37' | 54·27 | 86° 50' | 173° 37' | −86° 51' | 17° 20' | 32° 15' | Principal Incidence = 56° 57'. Circular Limit = 89° 8'. Coeff. of Refraction = 1·5369. Coeff. of Reflexion = 0·0151. **TABLE XXXII.—Quartz (b). (October 16, 1855.)** Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer. | Analyser. | \(a\) | \(b\) | Tan\(^{-1}(J)\) | |------------|-----------|------|------|----------------| | 89° 30' | 44° 30' | 1·017 | 0° 30' | | 89° 0' | 41° 10' | 1·143 | 0° 52' | | 88° 0' | 26° 20' | 2·020 | 0° 59' | | 85° 0' | 13° 20' | 4·219 | 1° 11' | Mean = 0° 53' 0"' Principal Incidence = 56° 52'. Circular Limit = 89° 34'. Coeff. of Refraction = 1·5320. Coeff. of Reflexion = 0·0076. From which we obtain **TABLE XXXIII.—Constants of Quartz (b).** | No. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-----|----------------------|-----------------|---------------------------|--------------------------| | XXXI.| 56° 57' | 89° 8' | 1·5369 | 0·0151 | | XXXII.| 56° 52' | 89° 34' | 1·5320 | 0·0076 | | Means | 56° 54' 30" | 89° 21' | 1·5344 | 0·0108 | The following experiments were made on the metallic bodies. **VIII. Speculum Metal.** **TABLE XXXIV.—Speculum Metal. (July 29, 1854.)** Azimuth of Polarizer = 45°. Red Lamplight. | Incidence. | Compensator. | Analyser. | \(e' - e - 180^\circ\). | \(a\) | \(b\) | Tan \(-1\)\(\frac{J}{I}\) | |------------|--------------|-----------|-------------------------|------|------|------------------------| | 35° 7 | 40·25 | 42° 30' | 9° 42' | +42° 27' | 10·06 | 42° 30' | | 44° 7 | 40·73 | 42° 45' | 15° 12' | +42° 40' | 7·42 | 42° 45' | | 49° 7 | 41·19 | 41° 30' | 20° 35' | +41° 16' | 5·58 | 41° 30' | | 51° 7 | 41·46 | 40° 50' | 23° 45' | +40° 27' | 4·78 | 40° 50' | | 53° 7 | 41·62 | 40° 20' | 25° 36' | +39° 50' | 4·45 | 40° 20' | | 55° 7 | 41·89 | 40° 3 | 28° 46' | +39° 22' | 3·96 | 40° 3 | | 57° 7 | 42·10 | 39° 20' | 31° 14' | +38° 24' | 3·65 | 39° 20' | | 59° 7 | 42·63 | 39° 6 | 37° 26' | +37° 38' | 3·03 | 39° 6 | | 61° 7 | 43·06 | 39° 20' | 42° 28' | +37° 24' | 2·64 | 39° 20' | | 64° 7 | 43·68 | 38° 50' | 49° 42' | +35° 40' | 2·24 | 38° 50' | | 69° 7 | 44·96 | 37° 45' | 64° 42' | +29° 25' | 1·69 | 37° 45' | | 74° 7 | 46·90 | 37° 45' | 87° 24' | +4° 58' | 1·29 | 37° 45' | Principal Incidence = 75° 27'(?). Circular Limit = 52° 15'(?). In this experiment the angle of incidence was not made at any time equal to the principal incidence. **TABLE XXXV.—Speculum Metal. (August 30, 1855.)** Azimuth of Polarizer = 50°. Red Sunlight. | Incidence. | Compensator. | Analyser. | \(e' - e - 180^\circ\). | \(a\) | \(b\) | Tan \(-1\)\(\frac{J}{I}\) | |------------|--------------|-----------|-------------------------|------|------|------------------------| | 33° 37' | 40·00 | 47° 15' | 6° 40' | +47° 16' | 16·48 | 42° 53' | | 43° 37' | 40·95 | 45° 40' | 17° 47' | +45° 42' | 6·40 | 40° 39' | | 53° 37' | 41·80 | 43° 0 | 27° 44' | +42° 45' | 4·13 | 38° 3 | | 63° 37' | 43·34 | 40° 15' | 45° 44' | +38° 16' | 2·42 | 35° 24' | | 68° 37' | 44·60 | 39° 40' | 60° 29' | +34° 32' | 1·77 | 34° 50' | | 73° 37' | 46·26 | 39° 0 | 79° 59' | +19° 38' | 1·32 | 34° 12' | | 74° 37' | 46·40 | 39° 32' | 81° 33' | +18° 38' | 1·27 | 34° 42' | | 75° 37' | 46·56 | 40° 15' | 83° 18' | +17° 26' | 1·23 | 35° 24' | | 76° 37' | 47·03 | 39° 20' | 87° 30' | +6° 8 | 1·23 | 34° 40' | | 77° 37' | 47·50 | 39° 43' | 94° 25' | -11° 13' | 1·22 | 34° 53' | | 78° 37' | 48·00 | 39° 45' | 100° 16' | -21° 56' | 1·29 | 34° 55' | | 83° 37' | 50·85 | 43° 0 | 133° 36' | -42° 6 | 2·34 | 38° 2 | | 88° 37' | 53·50 | 49° 45' | 164° 37' | -49° 55' | 7·65 | 44° 45' | Principal Incidence = 75° 51'. Coeff. of Refraction = 3·9665. Circular Limit = 55° 48'. Coeff. of Reflexion = 0·6796. **Table XXXVI.—Speculum Metal. (August 28, 1855.)** Azimuth of Polarizer =60°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|--------------|-------------------------------| | 33° 37' | 40·17 | 57° 30' | 8° 39' | +57° 38' | 14·20 | 42° 11 | | 43° 37' | 40·76 | 55° 15' | 15° 33' | +55° 36' | 7·89 | 39° 46 | | 53° 37' | 41·76 | 53° 30' | 27° 15' | +54° 30' | 4·31 | 37° 58 | | 63° 37' | 43·40 | 52° 10' | 46° 27' | +55° 10' | 2·44 | 36° 38 | | 68° 37' | 44·60 | 51° 0 | 60° 29' | +56° 40' | 1·79 | 35° 29 | | 73° 37' | 46·13 | 49° 30' | 78° 23' | +64° 6 | 1·29 | 34° 3 | | 74° 37' | 46·30 | 49° 30' | 80° 22' | +66° 43' | 1·26 | 34° 3 | | 75° 37' | 46·55 | 48° 45' | 83° 18' | +69° 14' | 1·19 | 33° 22 | | 76° 37' | 46·91 | 49° 15' | 87° 30' | +81° 52' | 1·17 | 33° 49 | | 77° 37' | 47·36 | 48° 55' | 92° 47' | −80° 17' | 1·16 | 33° 31 | | 78° 37' | 48·25 | 51° 0 | 103° 11' | −66° 30' | 1·37 | 35° 29 | | 83° 37' | 50·86 | 54° 30' | 133° 43' | −58° 14' | 2·53 | 38° 59 | | 88° 37' | 54·00 | 60° 0 | 170° 28' | −60° 10' | 14·13 | 45° 0 | Principal Incidence =75° 57'. Circular Limit =56° 38'. Coeff. of Refraction =3·9959. Coeff. of Reflexion =0·6585. In this Table, the polarizer having been set at an angle exceeding the circular limit, the axis major of the ellipse passes through 90° at the principal incidence, and behaves exactly as in the transparent bodies. **Table XXXVII.—Speculum Metal. (June 29, 1855.)** Azimuth of Polarizer =80°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|--------------|-------------------------------| | 33° 37' | 40·14 | 80° 0 | 8° 18' | +80° 6 | 39·78 | 45° 0 | | 43° 37' | 40·97 | 79° 15' | 18° 1 | +79° 44' | 17·57 | 42° 53 | | 53° 37' | 41·81 | 77° 30' | 27° 50' | +78° 48' | 10·02 | 38° 30 | | 63° 37' | 43·28 | 76° 30' | 45° 2 | +80° 6 | 6·06 | 36° 18 | | 68° 37' | 44·44 | 76° 0 | 58° 36' | +82° 16' | 4·78 | 35° 16 | | 73° 37' | 46·00 | 76° 0 | 76° 52' | +86° 33' | 4·13 | 35° 16 | | 74° 37' | 46·32 | 75° 47' | 80° 36' | +87° 28' | 4·01 | 34° 50 | | 75° 37' | 46·57 | 75° 50' | 83° 32' | +88° 16' | 3·99 | 34° 56 | | 76° 37' | 46·94 | 76° 0 | 87° 52' | +89° 26' | 4·01 | 35° 16 | | 77° 37' | 47·21 | 75° 55' | 91° 1 | −89° 44' | 3·99 | 35° 6 | | 78° 37' | 48·15 | 76° 30' | 102° 1 | −86° 58' | 4·27 | 36° 18 | | 81° 37' | 49·38 | 77° 30' | 116° 24' | −84° 9 | 5·45 | 38° 30 | | 83° 37' | 50·20 | 77° 45' | 126° 0 | −82° 30' | 5·89 | 39° 5 | | 85° 37' | 51·30 | 79° 20' | 128° 53' | −81° 48' | 8·24 | 43° 7 | | 88° 37' | 54·19 | 80° 0 | 172° 41' | −80° 4 | 47·68 | 45° 0 | Principal Incidence =76° 7'. Circular Limit =55° 10'. Coeff. of Refraction =4·0458. Coeff. of Reflexion =0·6959. TABLE XXXVIII.—Speculum Metal (fresh polished with rouge). (Sept. 11, 1855.) Compensator = 47°12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 75 40 | 3·732 | 34° 37' | | 70 | 62 45 | 1·942 | 35° 15' | | 60 | 49 45 | 1·181 | 34° 18' | | 50 | 38 0 | 1·279 | 33° 15' | | 40 | 29 30 | 1·767 | 33° 57' | | 30 | 21 45 | 2·506 | 34° 39' | | 20 | 14 10 | 3·961 | 34° 43' | | 10 | 7 30 | 7·596 | 36° 45' | Mean = 34° 41' 7" Principal Incidence = 78° 7'. Circular Limit = 55° 19'. Coeff. of Refraction = 4·7522. Coeff. of Reflexion = 0·6920. This experiment shows that the fresh polishing of the surface affected the coefficient of refraction more than the coefficient of reflexion, on which the elliptic polarization altogether depends. The angle tan$^{-1}\left(\frac{J}{I}\right)$ is not constant, but attains a minimum at the circular limit. Additional direct experiments with speculum metal, such as setting the compensator at 90°, making the incidence 76°, setting the analyser at 45°, and then determining the azimuth of the polarizer, gave for the circular limit 54° 45'. Combining all together, we find TABLE XXXIX.—Constants of Speculum Metal. | No. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-------|----------------------|-----------------|----------------------------|---------------------------| | XXXV. | 75 51 | 55 48 | 3·9665 | 0·6796 | | XXXVI.| 75 57 | 56 38 | 3·9959 | 0·6585 | | XXXVII.| 76 7 | 55 10 | 4·0458 | 0·6959 | | XXXVIII.| 78 7 | 55 19 | 4·7522 | 0·6920 | | Direct Ex.| ........ | 54 45 | ....... | 0·7067 | | Means | 76 33 | 55° 32' 0'' | 4·1901 | 0·6865 | IX. Silver. I examined three descriptions of silver,— (a) Fine silver, rolled. (b) Fine silver, cast. (c) Standard silver, rolled. Table XL.—Silver (a). (September 3, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{d}{l}\right)$ | |-----------|----------|---------------|----------------------------------| | 80 | 79 36 | 5.395 | 43 34 | | 70 | 69 0 | 2.605 | 43 29 | | 60 | 56 40 | 1.520 | 41 17 | | 50 | 46 15 | 1.044 | 41 14 | | 40 | 36 10 | 1.368 | 41 3 | | 30 | 27 15 | 1.941 | 41 44 | | 20 | 18 0 | 3.077 | 41 45 | | 10 | 9 40 | 5.870 | 44 1 | Mean = 42° 15' 52" Principal Incidence = 72° 37'. Circular Limit = 48° 46'. Coeff. of Refraction = 3.1942. Coeff. of Reflexion = 0.8765. Table XLI.—Fine Silver (a) (newly polished). (September 7, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{d}{l}\right)$ | |-----------|----------|---------------|----------------------------------| | 80 | 79 40 | 5.484 | 44 2 | | 70 | 68 15 | 2.506 | 42 23 | | 60 | 54 45 | 1.415 | 39 15 | | 50 | 46 15 | 1.045 | 41 14 | | 45 | 42 45 | 1.082 | 42 45 | | 40 | 38 0 | 1.280 | 42 57 | | 30 | 27 40 | 1.907 | 42 15 | | 20 | 19 0 | 2.904 | 43 25 | | 10 | 9 20 | 6.084 | 42 59 | Mean = 43° 28' 20" Principal Incidence = 71° 37'. Circular Limit = 48° 13'. Coeff. of Refraction = 3.0090. Coeff. of Reflexion = 0.8936. Having set the angle of incidence at 72° 37', the compensator at 47° 12' = 90°, and the analyser at 45°, I found, by trial, the polarizer or circular limit to be 48° 0'. Table XLII.—Silver (b). (September 6, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|--------------|----------------------------------| | 80 | 79 35 | 5.439 | 43° 48' | | 70 | 69 5 | 2.616 | 43° 36' | | 60 | 58 40 | 1.642 | 43° 29' | | 50 | 47 50 | 1.104 | 42° 49' | | 45 | 42 45 | 1.082 | 42° 45' | | 40 | 37 30 | 1.303 | 42° 27' | | 30 | 28 10 | 1.867 | 42° 51' | | 20 | 18 40 | 2.960 | 42° 52' | | 10 | 9 50 | 5.769 | 44° 31' | Mean = 43° 14' 13" Principal Incidence = 78° 7'. Circular Limit = 47° 13'. Coeff. of Refraction = 4.7522. Coeff. of Reflexion = 0.9255. Table XLIII.—Silver (c). (September 7, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|--------------|----------------------------------| | 80 | 79 30 | 5.395 | 43° 34' | | 70 | 68 30 | 2.538 | 42° 44' | | 60 | 57 30 | 1.570 | 42° 11' | | 50 | 47 15 | 1.082 | 42° 14' | | 45 | 42 30 | 1.091 | 42° 30' | | 40 | 37 0 | 1.327 | 41° 55' | | 30 | 28 0 | 1.881 | 42° 39' | | 20 | 19 25 | 2.837 | 44° 5 | | 10 | 9 50 | 5.769 | 44° 30' | Mean = 42° 55' 47" Principal Incidence = 78° 22'. Circular Limit = 47° 38'. Coeff. of Refraction = 4.8573. Coeff. of Reflexion = 0.9120. By direct experiment, as before described, I found the circular limit to be 46° 45'. On the day preceding that on which the experiments were made on Silver (c), I examined it before polishing, when evidently tarnished with sulphuret, and found Principal Incidence = 67° 37'. Circular Limit = 52° 30'. Coeff. of Refraction = 2.4282. Coeff. of Reflexion = 0.7673. Combining the preceding results into one Table, we find, ### Table XLIV.—Constants of Silver. | Silver (a). | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-------------|----------------------|-----------------|---------------------------|--------------------------| | XL. | 72° 37' | 48° 46' | 3·1942 | 0·8765 | | XLI. | 71° 37' | 48° 13' | 3·0090 | 0·8936 | | Direct exp. | …… | 48° 0' | …… | 0·9004 | | Means …….. | 72° 7' | 48° 19' 40" | 3·1016 | 0·8901 | | Silver (b). | XLII. | | | | | XLII. | 78° 7' | 47° 13' | 4·7522 | 0·9255 | | Silver (c). | XLIII. | | | | | XLIII. | 78° 22' | 47° 38' | 4·8573 | 0·9120 | | Direct exp.| …… | 46° 45' | …… | 0·9407 | | Means …….. | 78° 22' | 47° 11' 30" | 4·8573 | 0·9263 | **Note.**—In all the experiments on silver, the minimum value of \( \tan^{-1}\left(\frac{J}{I}\right) \), corresponding to the circular limit, is apparent, although, if the surface were mathematically smooth, it ought to be constant, being a function of the incidence only. ### X. Gold (Standard). #### Table XLV.—(September 20, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer. | Analyser. | \( \frac{a}{b} \) | Tan\(^{-1}\)\(\left(\frac{J}{I}\right)\) | |------------|-----------|-------------------|----------------------------------------| | 80° | 79° 45' | 5·530 | 44° 17' | | 70° | 68° 45' | 2·571 | 43° 6 | | 60° | 58° 15' | 1·616 | 43° 0 | | 50° | 47° 0' | 1·072 | 42° 38 | | 45° | 42° 30' | 1·091 | 42° 30 | | 40° | 37° 45' | 1·291 | 42° 42 | | 30° | 28° 0' | 1·881 | 42° 39 | | 20° | 19° 10' | 2·876 | 43° 41 | | 10° | 9° 40' | 5·870 | 44° 1 | Mean = 43° 10' 26" Principal Incidence = 75° 37'. Circular Limit = 47° 47'. Coeff. of Refraction = 3·8994. Coeff. of Reflexion = 0·9073. The minimum value of \( \tan^{-1}\left(\frac{J}{I}\right) \) is here also evident. XI. Mercury (Distilled). Table XLVI.—(November 1, 1860.) Compensator = 47° 12' = 90°. Red Lamplight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|--------------|----------------------------------| | 80° | 76° 0 | 4·011 | 35° 16 | | 70 | 62° 42 | 1·937 | 35° 11 | | 60 | 51° 35 | 1·260 | 36° 3 | | 50 | 41° 0 | 1·150 | 36° 6 | | 40 | 32° 2 | 1·598 | 36° 43 | | 30 | 23° 25 | 2·309 | 36° 53 | | 20 | 14° 49 | 3·780 | 36° 1 | | 10 | 7° 19 | 7·788 | 36° 4 | | 0 | 0 | ∞ | | Mean = 36° 2' 7" Principal Incidence = 81° 4'. Circular Limit = 53° 46'. Coeff. of Refraction = 6·3616. Coeff. of Reflexion = 0·7328. By a direct experiment, I obtained, as before described, Circular Limit = 53° 52'. Coeff. of Reflexion = 0·7301. The value of tan$^{-1}\left(\frac{J}{I}\right)$ appears to be constant in mercury: can this be due to its being a liquid? XII. Platinum. Table XLVII.—(September 21, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|--------------|----------------------------------| | 80° | 76° 10 | 4·061 | 35° 36 | | 70 | 63° 0 | 1·962 | 35° 32 | | 60 | 52° 15 | 1·291 | 36° 43 | | 50 | 40° 10 | 1·185 | 35° 19 | | 40 | 32° 0 | 1·600 | 36° 41 | | 30 | 22° 15 | 2·444 | 35° 19 | | 20 | 14° 45 | 2·798 | 35° 53 | | 10 | 8° 0 | 7·115 | 38° 33 | Mean = 36° 12' 0" Principal Incidence = 76° 37'. Circular Limit = 54° 0'. Coeff. of Refraction = 4·2030. Coeff. of Reflexion = 0·7265. XIII. Palladium. Table XLVIII.—(September 21, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 75 15 | 3.798 | 33 49 | | 70 | 65 40 | 2.211 | 38 50 | | 60 | 50 10 | 1.199 | 34 41 | | 50 | 40 15 | 1.181 | 35 23 | | 40 | 29 30 | 1.631 | 33 59 | | 30 | 22 50 | 2.375 | 36 6 | | 20 | 15 0 | 3.732 | 36 21 | | 10 | 8 0 | 7.115 | 38 33 | Mean = 35° 57' 45"" Principal Incidence = 77° 37'. Circular Limit = 54° 47'. Coeff. of Refraction = 4.5546. Coeff. of Reflexion = 0.7058. XIV. Copper. Table XLIX.—Copper. (October 6, 1857.) Azimuth of Polarizer = 46° 15'. Red Sunlight. | Incidence | Compensator | Analyser | $e'-e-180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|-------------|--------|---------------|-----------------------------------| | 63 30 | 44.96 | 42 40 | 64 42 | +39 35 | 1.589 | 41 25 | | 68 30 | 46.19 | 42 30 | 79 0 | +32 41 | 1.236 | 41 15 | | 69 30 | 46.49 | 42 45 | 82 36 | +29 17 | 1.164 | 41 30 | | 70 30 | 46.77 | 42 25 | 85 52 | +19 17 | 1.123 | 41 10 | | 71 30 | 47.17 | 42 16 | 90 34 | -2 57 | 1.101 | 41 5 | | 72 30 | 47.25 | 42 20 | 91 30 | -7 50 | 1.102 | 41 5 | | 73 30 | 47.63 | 42 15 | 95 57 | -23 33 | 1.152 | 41 4 | | 74 30 | 47.81 | 42 32 | 98 4 | -29 12 | 1.180 | 41 17 | | 75 30 | 48.54 | 43 50 | 106 35 | -37 34 | 1.174 | 42 35 | | 76 30 | 48.76 | 43 1 | 109 9 | -39 2 | 1.416 | 41 46 | | 78 30 | 49.84 | 43 20 | 121 48 | -41 51 | 1.804 | 42 5 | | 83 30 | 51.74 | 45 24 | 144 2 | -45 30 | 3.000 | 44 9 | Principal Incidence = 71° 21'. Circular Limit = 48° 55'. Coeff. of Refraction = 2.9629. Coeff. of Reflexion = 0.8718. ### Table I.—Copper. (October 6, 1857.) Azimuth of Polarizer = $47^\circ 45'$. Red Sunlight. | Incidence | Compensator | Analyser | $\epsilon' - \epsilon - 180^\circ$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------------------------|-------|-------------|---------------------| | 63° 30' | 44·93 | 45° 10' | +45° 23' | 1·593 | 42° 25' | | 68° 30' | 46·17 | 44° 20' | +41° 34' | 1·218 | 41° 35' | | 69° 30' | 46·38 | 44° 25' | +41° 10' | 1·166 | 41° 40' | | 70° 30' | 46·67 | 42° 45' | +24° 47' | 1·129 | 40° 1' | | 71° 30' | 47·15 | 43° 50' | -7° 58' | 1·043 | 41° 6' | | 72° 30' | 47·68 | 43° 20' | -31° 27' | 1·137 | 40° 36' | | 73° 30' | 47·85 | 43° 20' | -34° 16' | 1·174 | 40° 36' | | 74° 30' | 48·23 | 43° 45' | -39° 29' | 1·261 | 41° 1' | | 75° 30' | 48·45 | 43° 45' | -40° 22' | 1·320 | 41° 1' | | 76° 30' | 48·84 | 43° 45' | -41° 23' | 1·435 | 41° 1' | | 78° 30' | 49·71 | 44° 45' | -44° 30' | 1·732 | 42° 0' | | 83° 30' | 51·85 | 45° 50' | -46° 1' | 3·177 | 43° 5' | Principal Incidence = $71^\circ 27'$. Circular Limit = $49^\circ 59'$. Coeff. of Refraction = 2·9800. Coeff. of Reflexion = 0·8396. ### Table LI.—Copper. (October 6, 1857.) Azimuth of Polarizer = $55^\circ$. Red Sunlight. | Incidence | Compensator | Analyser | $\epsilon' - \epsilon - 180^\circ$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------------------------|-------|-------------|---------------------| | 63° 30' | 44·72 | 50° 15' | +55° 40' | 1·734 | 40° 7' | | 68° 30' | 45·93 | 50° 15' | +63° 46' | 1·362 | 40° 7' | | 69° 30' | 46·17 | 50° 0' | +66° 11' | 1·301 | 39° 51' | | 70° 30' | 46·68 | 50° 20' | +77° 12' | 1·231 | 40° 11' | | 71° 30' | 46·90 | 50° 7' | +82° 57' | 1·204 | 39° 58' | | 72° 30' | 47·24 | 50° 26' | -86° 27' | 1·226 | 40° 16' | | 73° 30' | 47·59 | 49° 30' | -74° 29' | 1·203 | 39° 21' | | 74° 30' | 47·77 | 49° 28' | -70° 1' | 1·228 | 39° 19' | | 75° 30' | 48·23 | 49° 30' | -62° 38' | 1·320 | 39° 21' | | 76° 30' | 48·67 | 49° 47' | -59° 15' | 1·282 | 39° 38' | | 78° 30' | 49·33 | 51° 20' | -58° 39' | 1·683 | 41° 11' | | 83° 30' | 51·37 | 53° 45' | -56° 14' | 2·896 | 43° 41' | Principal Incidence = $71^\circ 6'$. Circular Limit = $50^\circ 40'$. Coeff. of Refraction = 2·9207. Coeff. of Reflexion = 0·8194. Table LII.—Copper. (September 21, 1855.) Compensator = $47^\circ 12' = 90^\circ$. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1} \left( \frac{3}{1} \right)$ | |-----------|----------|---------------|----------------------------------------| | 80 | 79 50 | 5.576 | 44° 31' | | 70 | 69 15 | 2.639 | 43° 51' | | 60 | 59 30 | 1.697 | 44° 25' | | 50 | 48 0 | 1.110 | 42° 59' | | 45 | 43 0 | 1.072 | 43° 0' | | 40 | 37 30 | 1.303 | 42° 27' | | 30 | 28 40 | 1.829 | 42° 47' | | 20 | 19 30 | 2.924 | 44° 13' | | 10 | 9 50 | 5.769 | 44° 31' | Mean = $43^\circ 38' 13''$ Principal Incidence = $73^\circ 37'$. Circular Limit = $47^\circ 0'$. Coeff. of Refraction = $3.4013$. Coeff. of Reflexion = $0.9325$. Combining the preceding results, we obtain Table LIII.—Constants of Copper. | No. | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |-----|--------------------|----------------|---------------------------|--------------------------| | XLIX.| 71° 21' | 48° 55' | 2.9629 | 0.8718 | | L. | 71° 27' | 49° 59' | 2.9800 | 0.8396 | | LI. | 71° 6' | 50° 40' | 2.9207 | 0.8194 | | LII. | 73° 37' | 47° 0' | 3.4013 | 0.9325 | | Means | 71° 52' 45'' | 49° 8' 30'' | 3.0662 | 0.8656 | XV. Zinc. Table LIV.—Zinc. (April 22, 1858.) Azimuth of Polarizer = 53°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|-------------|----------------------------------| | 63° 30 | 43·71 | 47° 0 | 50° 4 | 48° 7 | 2·143 | 38° 57 | | 68° 30 | 44·58 | 46° 0 | 60° 15 | 47° 1 | 1·723 | 37° 58 | | 75° 30 | 46·93 | 45° 45 | 87° 45 | 61° 51| 1·048 | 37° 43 | | 76° 30 | 46·98 | 45° 0 | 88° 20 | +45° 0| 1·000 | 37° 0 | | 77° 30 | 47·19 | 45° 30 | 90° 47 | −70° 56| 1·022 | 37° 29 | | 78° 30 | 47·84 | 45° 45 | 98° 23 | −50° 5 | 1·161 | 37° 43 | | 79° 30 | 48·49 | 45° 30 | 106° 0 | −46° 49| 1·327 | 37° 29 | | 80° 30 | 48·65 | 46° 0 | 107° 52 | −48° 15| 1·375 | 37° 58 | | 81° 30 | 49·20 | 46° 0 | 114° 12 | −47° 26| 1·548 | 37° 58 | | 83° 30 | 50·47 | 46° 30 | 129° 10 | −47° 22| 2·114 | 38° 27 | | 88° 30 | 54·15 | 52° 0 | 172° 13 | −52° 4 | 13·078 | 43° 58 | Principal Incidence = 77° 11'. Circular Limit = 53° 0'. Coeff. of Refraction = 4·3956. Coeff. of Reflexion = 0·7535. Table LV.—Zinc. (May 7, 1858.) Azimuth of Polarizer = 57°. Red Sunlight. | Incidence | Compensator | Analyser | $e' - e - 180°$ | $\phi$ | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|-------------|----------|----------------|-------|-------------|----------------------------------| | 63° 30 | 43·37 | 53° 6 | 46° 6 | +56° 14| 2·485 | 40° 45 | | 68° 30 | 44·43 | 50° 30 | 58° 30 | +55° 12| 1·849 | 38° 14 | | 73° 30 | 45·94 | 48° 30 | 76° 9 | +58° 35| 1·315 | 36° 17 | | 75° 30 | 46·49 | 49° 30 | 82° 36 | +70° 26| 1·227 | 37° 15 | | 76° 30 | 46·95 | 49° 0 | 87° 58 | +82° 55| 1·169 | 36° 46 | | 77° 30 | 47·49 | 50° 0 | 94° 18 | −78° 29| 1·224 | 37° 44 | | 78° 30 | 47·74 | 50° 0 | 97° 13 | −72° 16| 1·244 | 37° 44 | | 79° 30 | 48·34 | 49° 30 | 104° 14 | −61° 5 | 1·354 | 37° 15 | | 80° 30 | 48·79 | 50° 30 | 109° 30 | −60° 6 | 1·491 | 38° 14 | | 81° 30 | 49·32 | 50° 30 | 115° 42 | −57° 4 | 1·658 | 38° 14 | | 83° 30 | 50·17 | 52° 0 | 125° 39 | −56° 35| 2·048 | 39° 44 | | 88° 30 | 54·06 | 54° 0 | 171° 10 | −54° 5 | 14·983 | 41° 48 | Principal Incidence = 76° 49'. Circular Limit = 53° 29'. Coeff. of Refraction = 4·2691. Coeff. of Reflexion = 0·7404. Table LVI.—Zinc. (September 20, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}(\frac{J}{I})$. | |-----------|----------|--------------|-------------------------| | 80 | 75 | 3·732 | 33° 21' | | 70 | 62 | 1·881 | 34° 23' | | 60 | 49 | 1·171 | 34° 3' | | 50 | 39 | 1·202 | 34° 54' | | 40 | 29 | 1·785 | 33° 43' | | 30 | 22 | 2·414 | 35° 39' | | 20 | 15 | 3·732 | 36° 21' | | 10 | 7 | 7·596 | 36° 45' | Mean = 34° 53' 37" Principal Incidence = 78° 7'. Circular Limit = 55° 23'. Coeff. of Refraction = 4·7522. Coeff. of Reflexion = 0·6903. Combining the preceding results, we obtain the following Table for zinc. Table LVII.—Constants of Zinc. | No. | Principal Incidence. | Circular Limit. | Coefficient of Refraction. | Coefficient of Reflexion. | |-----|----------------------|-----------------|----------------------------|---------------------------| | LIV.| 77° 11 | 53° 6 | 4·3956 | 0·7535 | | LV. | 76° 49 | 53° 29 | 4·2691 | 0·7404 | | LVI.| 78° 7 | 55° 23 | 4·7522 | 0·6903 | | Means | 77° 22' 20'' | 53° 57' 20'' | 4·4723 | 0·7281 | XVI. Lead (polished). Table LVIII. (September 20, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}(\frac{J}{I})$. | |-----------|----------|--------------|-------------------------| | 80 | 64 | 2·050 | 19° 52' | | 70 | 40 | 1·171 | 17° 16' | | 60 | 29 | 1·750 | 18° 16' | | 50 | 22 | 2·414 | 19° 10' | | 40 | 15 | 3·732 | 17° 43' | | 30 | 10 | 5·671 | 16° 59' | | 20 | 7 | 7·861 | 19° 16' | | 10 | 2 | 22·903 | 13° 54' | Mean = 17° 48' 15" Principal Incidence = 69° 37'. Circular Limit = 71° 55'. Coeff. of Refraction = 2·6913. Coeff. of Reflexion = 0·3265. OF POLARIZED LIGHT FROM POLISHED SURFACES. XVII. BISMUTH. Table LIX. (September 25, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|----------------------------------| | 80 | 76 15 | 4·086 | 35° 43' | | 70 | 60 45 | 1·785 | 33° 1 | | 60 | 50 25 | 1·209 | 34° 56 | | 50 | 39 30 | 1·213 | 34° 40 | | 40 | 30 30 | 1·697 | 35° 4 | | 30 | 21 0 | 2·605 | 33° 37 | | 20 | 14 25 | 3·890 | 35° 14 | | 10 | 6 30 | 8·777 | 32° 52 | Mean = 34° 23' 22"' Principal Incidence = 73° 37'. Circular Limit = 55° 2'. Coeff. of Refraction = 3·4013. Coeff. of Reflexion = 0·6993. XVIII. TIN. Table LX. (September 25, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|----------------------------------| | 80 | 76 30 | 4·165 | 36° 18 | | 70 | 64 10 | 2·065 | 36° 56 | | 60 | 52 35 | 1·307 | 37° 2 | | 50 | 40 30 | 1·171 | 35° 38 | | 40 | 32 0 | 1·600 | 36° 40 | | 30 | 22 30 | 2·414 | 35° 40 | | 20 | 15 20 | 3·647 | 36° 59 | | 10 | 8 10 | 6·968 | 39° 8 | Mean = 36° 47' 37"' Principal Incidence = 75° 7'. Circular Limit = 53° 43'. Coeff. of Refraction = 3·7627. Coeff. of Reflexion = 0·7341. XIX. IRON. TABLE LXI.—Hard Steel. (September 29, 1855.) Compensator =47·12=90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 72 15 | 3·124 | 28° 51' | | 70 | 55 30 | 1·455 | 27° 54' | | 60 | 42 35 | 1·088 | 27° 57' | | 50 | 33 0 | 1·540 | 28° 36' | | 40 | 24 35 | 2·186 | 28° 36' | | 30 | 17 30 | 3·171 | 28° 39' | | 20 | 11 50 | 4·773 | 29° 57' | | 10 | 6 15 | 9·131 | 31° 51' | Mean = 29° 2' 37" Principal Incidence =78° 7'. Circular Limit =61° 52'. Coeff. of Refraction =4·7522. Coeff. of Reflexion =0·5347. TABLE LXII.—Soft Steel. (September 29, 1855.) Compensator =47·12=90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 70 45 | 2·863 | 26° 48' | | 70 | 55 50 | 1·473 | 28° 12' | | 60 | 41 45 | 1·120 | 27° 16' | | 50 | 31 45 | 1·616 | 27° 27' | | 40 | 23 30 | 2·300 | 27° 24' | | 30 | 17 50 | 3·108 | 29° 7' | | 20 | 11 20 | 4·989 | 28° 50' | | 10 | 6 0 | 9·514 | 30° 48' | Mean = 28° 14' 0" Principal Incidence =77° 7'. Circular Limit =63° 13'. Coeff. of Refraction =4·3721. Coeff. of Reflexion =0·5048. Swedish Iron (cut perpendicular to the grain). Table LXIII. (September 29, 1855.) Compensator = 47° 12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 71° 35' | 3·003 | 27° 54' | | 70 | 55° 10' | 1·437 | 27° 37' | | 60 | 40° 45' | 1·160 | 26° 27' | | 50 | 32° 0 | 1·600 | 27° 40' | | 40 | 22° 45' | 2·385 | 26° 33' | | 30 | 17° 0 | 3·271 | 27° 54' | | 20 | 11° 0 | 5·144 | 28° 6 | | 10 | 5° 30' | 10·385 | 28° 38' | Mean = 27° 36' 7" Principal Incidence = 76° 7'. Circular Limit = 62° 57'. Coeff. of Refraction = 4·0458. Coeff. of Reflexion = 0·5106. Swedish Iron (cut parallel to the grain). Table LXIV. (September 29, 1855.) | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 71° 45' | 3·032 | 28° 8 | | 70 | 55° 20' | 1·446 | 27° 46' | | 60 | 41° 40' | 1·124 | 27° 12' | | 50 | 32° 0 | 1·600 | 27° 40' | | 40 | 24° 0 | 2·246 | 27° 57' | | 30 | 17° 30' | 3·171 | 28° 39' | | 20 | 11° 0 | 5·144 | 28° 6 | | 10 | 5° 35' | 10·229 | 29° 0 | Mean = 28° 3' 30" Principal Incidence = 76° 7'. Circular Limit = 62° 26'. Coeff. of Refraction = 4·0458. Coeff. of Reflexion = 0·5220. Combining the preceding results, we find Table LXV.—Constants of Steel and Iron. | No. | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |-----------|---------------------|----------------|---------------------------|--------------------------| | LXI. Hard steel. | 78° 7' | 61° 52' | 4·7522 | 0·5347 | | LXII. Soft steel. | 77° 7' | 63° 13' | 4·3721 | 0·5048 | | LXIII. Iron (a). | 76° 7' | 62° 57' | 4·0458 | 0·5106 | | LXIV. Iron (b). | 76° 7' | 62° 26' | 4·0458 | 0·5220 | XX. Aluminium. Table LXVI. (May 10, 1856.) Compensator = 47°12' = 90°. Red Sunlight. | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}(\frac{J}{I})$ | |-----------|----------|---------------|------------------------| | 80° | 75° 45' | 3·937 | 34° 46' | | 70° | 60° 30' | 1·767 | 32° 45' | | 60° | 48° 0' | 1·110 | 32° 40' | | 50° | 37° 30' | 1·303 | 32° 47' | | 40° | 28° 15' | 1·861 | 32° 38' | | 30° | 20° 30' | 2·674 | 32° 56' | | 20° | 13° 45' | 4·086 | 33° 55' | | 10° | 7° 10' | 7·953 | 35° 30' | Mean = 33° 29' 37"" Principal Incidence = 77° 7'. Circular Limit = 57° 9'. Coeff. of Refraction = 4·3721. Coeff. of Reflexion = 0·6457. By a direct experiment I found the circular limit to be 57° 15'. XXI. Alloys of Copper and Zinc. The following experiments were made on fourteen alloys of copper and zinc prepared by Mr. Robert Mallet, in atomic proportions, as follow: - No. 1 . . . 10Cu + Zn - No. 2 . . . 9Cu + Zn - No. 3 . . . 8Cu + Zn - No. 4 . . . 7Cu + Zn - No. 5 . . . 6Cu + Zn - No. 6 . . . 5Cu + Zn - No. 7 . . . 4Cu + Zn - No. 8 . . . 3Cu + Zn - No. 9 . . . 2Cu + Zn - No. 10 . . . Cu + Zn - No. 11 . . . Cu + 2Zn - No. 12 . . . Cu + 3Zn - No. 13 . . . Cu + 4Zn - No. 14 . . . Cu + 5Zn The chemical and physical properties of these alloys are fully described by Mr. Mallet in his "Report on the Action of Air and Water upon Iron" to the British Association for the Advancement of Science for the year 1840, p. 306. In all the experiments red sunlight was used, and the compensator was placed at 47°12' = 90°. **Table LXVII.—Alloys of Copper and Zinc, No. 1. (September 16, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80 | 79 6 | 5·144 | 42° 13' | | 70 | 66 45 | 3·237 | 40° 16' | | 60 | 56 10 | 1·492 | 40° 45' | | 50 | 45 30 | 1·017 | 40° 30' | | 40 | 35 30 | 1·402 | 40° 22' | | 30 | 27 0 | 1·962 | 41° 26' | | 20 | 18 15 | 3·032 | 42° 11' | | 10 | 9 25 | 6·029 | 43° 15' | Mean = 41° 22' 15"" Principal Incidence = 72° 5'. Circular Limit = 49° 32'. Coeff. of Refraction = 3·0930. Coeff. of Reflexion = 0·8531. **Table LXVIII.—Alloys of Copper and Zinc, No. 2. (September 16, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80 | 79 40 | 5·484 | 44° 3' | | 70 | 67 35 | 2·424 | 41° 25' | | 60 | 58 0 | 1·600 | 42° 44' | | 50 | 45 35 | 1·020 | 40° 35' | | 40 | 35 25 | 1·406 | 40° 17' | | 30 | 27 30 | 1·921 | 42° 2' | | 20 | 17 40 | 3·140 | 41° 11' | | 10 | 9 30 | 5·976 | 43° 30' | Mean = 41° 58' 22"" Principal Incidence = 72° 15'. Circular Limit = 49° 32'. Coeff. of Refraction = 3·1240. Coeff. of Reflexion = 0·8531. **Table LXIX.—Alloys of Copper and Zinc, No. 3. (September 18, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 10' | 5·225 | 42° 40' | | 70° | 67° 20' | 2·394 | 41° 4' | | 60° | 54° 0 | 1·376 | 38° 28' | | 50° | 46° 0 | 1·035 | 40° 59' | | 40° | 34° 50' | 1·437 | 39° 40' | | 30° | 27° 15' | 1·941 | 41° 44' | | 20° | 17° 35' | 3·155 | 41° 2' | | 10° | 9° 15' | 6·140 | 42° 43' | Mean = 41° 2' 30" Principal Incidence = 73° 10'. Circular Limit = 49° 6'. Coeff. of Refraction = 3·3052. Coeff. of Reflexion = 0·8662. **Table LXX.—Alloys of Copper and Zinc, No. 4. (September 18, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 78° 30' | 4·915 | 40° 55' | | 70° | 67° 45' | 2·444 | 41° 40' | | 60° | 57° 0 | 1·540 | 41° 38' | | 50° | 46° 0 | 1·035 | 40° 59' | | 40° | 35° 30' | 1·402 | 40° 22' | | 30° | 27° 0 | 1·962 | 41° 26' | | 20° | 18° 0 | 3·077 | 41° 45' | | 10° | 8° 50' | 6·435 | 41° 23' | Mean = 41° 16' 0" Principal Incidence = 73° 8'. Circular Limit = 49° 3'. Coeff. of Refraction = 3·2983. Coeff. of Reflexion = 0·8677. **Table LXXI.—Alloys of Copper and Zinc, No. 5. (September 18, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 10' | 5·225 | 42° 40' | | 70° | 67° 0 | 2·356 | 40° 37' | | 60° | 56° 15' | 1·496 | 40° 50' | | 50° | 45° 55' | 1·032 | 40° 55' | | 40° | 35° 52' | 1·383 | 40° 45' | | 30° | 26° 50' | 1·977 | 41° 13' | | 20° | 18° 15' | 3·032 | 42° 11' | | 10° | 9° 45' | 5·819 | 44° 16' | Mean = 41° 45' 52" Principal Incidence = 74° 5'. Circular Limit = 49° 5'. Coeff. of Refraction = 3·5066. Coeff. of Reflexion = 0·8667. **Table LXXII.—Alloys of Copper and Zinc, No. 6. (September 19, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 25' | 5.352 | 43° 20' | | 70° | 68° 30' | 2.538 | 42° 44' | | 60° | 57° 55' | 1.595 | 42° 39' | | 50° | 47° 40' | 1.098 | 42° 39' | | 40° | 36° 30' | 1.351 | 41° 24' | | 30° | 28° 15' | 1.861 | 42° 57' | | 20° | 18° 12' | 3.041 | 42° 5 | | 10° | 9° 45' | 5.819 | 44° 16' | Mean = 42° 45' 39" Principal Incidence = 74° 8'. Circular Limit = 47° 37'. Coeff. of Refraction = 3.5183. Coeff. of Reflexion = 0.9126. **Table LXXIII.—Alloys of Copper and Zinc, No. 7. (September 19, 1856.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 10' | 5.225 | 42° 39' | | 70° | 67° 30' | 2.414 | 41° 18' | | 60° | 57° 0 | 1.540 | 41° 39' | | 50° | 45° 40' | 1.023 | 40° 39' | | 40° | 35° 0 | 1.428 | 39° 51' | | 30° | 26° 10' | 2.035 | 40° 24' | | 20° | 17° 45' | 3.124 | 41° 20' | | 10° | 9° 25' | 6.029 | 43° 15' | Mean = 41° 48' 7" Principal Incidence = 73° 16'. Circular Limit = 49° 23'. Coeff. of Refraction = 3.3261. Coeff. of Reflexion = 0.8576. **Table LXXIV.—Alloys of Copper and Zinc, No. 8. (July 13, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 77° 30' | 4.511 | 38° 30' | | 70° | 65° 10' | 2.161 | 38° 11' | | 60° | 55° 40' | 1.464 | 40° 13' | | 50° | 43° 50' | 1.041 | 38° 51' | | 40° | 33° 5 | 1.535 | 37° 49' | | 30° | 24° 40' | 2.177 | 38° 30' | | 20° | 15° 40' | 3.565 | 37° 37' | | 10° | 8° 20' | 6.827 | 39° 43' | Mean = 38° 46' 36" Principal Incidence = 73° 12'. Circular Limit = 50° 53'. Coeff. of Refraction = 3.3121. Coeff. of Reflexion = 0.8132. **Table LXXV.—Alloys of Copper and Zinc, No. 9. (October 5, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 6 | 5·144 | 42° 13 | | 70° | 67° 30 | 2·414 | 41° 18 | | 60° | 54° 55 | 1·424 | 39° 25 | | 50° | 46° 20 | 1·047 | 41° 19 | | 40° | 35° 35 | 1·397 | 40° 27 | | 30° | 26° 0 | 2·050 | 40° 11 | | 20° | 17° 0 | 3·271 | 40° 2 | | 10° | 8° 40 | 6·560 | 40° 50 | Mean = 40° 43' 7" Principal Incidence = 72° 18'. Circular Limit = 48° 46'. Coeff. of Refraction = 3·1334. Coeff. of Reflexion = 0·8764. **Table LXXVI.—Alloys of Copper and Zinc, No. 10. (October 5, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 79° 0 | 5·144 | 42° 13 | | 70° | 65° 0 | 2·144 | 37° 58 | | 60° | 54° 20 | 1·393 | 38° 49 | | 50° | 43° 45 | 1·044 | 38° 46 | | 40° | 34° 35 | 1·450 | 39° 35 | | 30° | 25° 15 | 2·120 | 39° 15 | | 20° | 16° 30 | 3·375 | 39° 9 | | 10° | 8° 45 | 6·497 | 41° 7 | Mean = 39° 36' 30" Principal Incidence = 72° 15'. Circular Limit = 51° 11'. Coeff. of Refraction = 3·1240. Coeff. of Reflexion = 0·8045. **Table LXXVII.—Alloys of Copper and Zinc, No. 11. (October 5, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | $\tan^{-1}\left(\frac{J}{I}\right)$ | |-----------|----------|---------------|-------------------------------------| | 80° | 78° 30 | 4·915 | 40° 55 | | 70° | 65° 30 | 2·194 | 38° 37 | | 60° | 54° 0 | 1·376 | 38° 28 | | 50° | 43° 0 | 1·072 | 38° 3 | | 40° | 33° 30 | 1·511 | 38° 16 | | 30° | 24° 30 | 2·194 | 38° 17 | | 20° | 16° 15 | 3·431 | 38° 41 | | 10° | 8° 35 | 6·025 | 40° 34 | Mean = 38° 58' 52" Principal Incidence = 72° 15'. Circular Limit = 51° 49'. Coeff. of Refraction = 3·1240. Coeff. of Reflexion = 0·7864. **Table LXXVIII.—Alloys of Copper and Zinc, No. 12. (October 5, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{T}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 74 40 | 3·647 | 32° 45 | | 70 | 58 45 | 1·648 | 30° 57 | | 60 | 48 0 | 1·110 | 32° 40 | | 50 | 37 45 | 1·291 | 33° 1 | | 40 | 28 10 | 1·867 | 31° 57 | | 30 | 20 0 | 2·747 | 32° 14 | | 20 | 13 20 | 4·219 | 33° 4 | | 10 | 6 30 | 8·776 | 32° 56 | Mean = 32° 26' 45" Principal Incidence = 76° 7'. Circular Limit = 57° 5'. Coeff. of Refraction = 4·0458. Coeff. of Reflexion = 0·6473. **Table LXXIX.—Alloys of Copper and Zinc, No. 13. (October 6, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{T}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 76 15 | 4·086 | 35° 46 | | 70 | 60 50 | 1·792 | 33° 7 | | 60 | 49 45 | 1·181 | 34° 18 | | 50 | 39 10 | 1·227 | 34° 21 | | 40 | 29 15 | 1·785 | 33° 43 | | 30 | 20 40 | 2·651 | 33° 10 | | 20 | 13 30 | 4·165 | 33° 25 | | 10 | 6 40 | 8·555 | 33° 32 | Mean = 33° 55' 15" Principal Incidence = 73° 52'. Circular Limit = 55° 31'. Coeff. of Refraction = 3·4570. Coeff. of Reflexion = 0·6868. **Table LXXX.—Alloys of Copper and Zinc, No. 14. (October 6, 1857.)** | Polarizer | Analyser | $\frac{a}{b}$ | Tan$^{-1}\left(\frac{T}{I}\right)$ | |-----------|----------|---------------|-----------------------------------| | 80 | 75 45 | 3·937 | 34° 46 | | 70 | 61 45 | 1·861 | 34° 7 | | 60 | 48 40 | 1·136 | 33° 17 | | 50 | 39 0 | 1·235 | 34° 12 | | 40 | 28 40 | 1·829 | 33° 5 | | 30 | 20 50 | 2·628 | 33° 23 | | 20 | 13 55 | 4·036 | 34° 15 | | 10 | 7 10 | 7·953 | 35° 30 | Mean = 34° 4' 22" Principal Incidence = 76° 0'. Circular Limit = 56° 12'. Coeff. of Refraction = 4·0108. Coeff. of Reflexion = 0·6694. The alloys from 1 to 11 are all yellowish, and from 12 to 14 are whitish. The following Table shows that the Coefficients of Refraction from 1 to 11 increase gradually, reaching a maximum at No. 6 (5Cu+Zn), and then diminish to No. 11, in passing from which to No. 12 the coefficient suddenly increases. The Coefficient of Reflexion follows an order somewhat similar, but suddenly decreases in passing from 11 to 12, which is the limit at which the zinc begins to preponderate over the copper, in producing the optical properties of the alloy. In Plate VIII. fig. B, I have tabulated the coefficients of refraction and reflexion of the alloys of copper and zinc, showing the progression of these constants, as just described. **Table LXXXI.—Optical Constants of all the Substances examined.** | Substance | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | Refractive Index | |----------------------------|---------------------|----------------|---------------------------|--------------------------|------------------| | **(A.) Transparent.** | | | | | | | I. Munich Glass (a) | 55° 0' 37" | 85° 32' 30" | 1·4287 | 0·0780 | 1·6227 | | II. Munich Glass (b) | 54° 40' 48" | 89° 53' 24" | 1·4113 | 0·0019 | 1·5244 | | III. Paris Glass | 56° 8' 30" | 89° 23' 0" | 1·4905 | 0·0107 | 1·5100 | | IV. Fluor-Spar | 54° 46' 0" | 89° 41' 30" | 1·4158 | 0·0053 | | | V. Glass of Antimony | 58° 48' 40" | 88° 51' 40" | 1·6519 | 0·0199 | | | VI. Quartz (a) | 56° 40' 0" | 88° 58' 0" | 1·5204 | 0·0180 | | | VII. Quartz (b) | 56° 54' 30" | 89° 21' 0" | 1·5344 | 0·0108 | | | **(B.) Metals.** | | | | | | | VIII. Speculum | 76° 33' 0" | 55° 32' 0" | 4·1901 | 0·6865 | | | IX. Silver (a) | 72° 7' 0" | 48° 19' 40" | 3·1016 | 0·8901 | | | — Silver (b) | 78° 7' 0" | 47° 13' 0" | 4·7522 | 0·9255 | | | — Silver (c) | 78° 22' 0" | 47° 11' 30" | 4·8573 | 0·9263 | | | X. Gold | 75° 37' 0" | 47° 47' 0" | 3·8994 | 0·9073 | | | XI. Mercury | 81° 4' 0" | 53° 49' 0" | 6·3616 | 0·7315 | | | XII. Platinum | 76° 37' 0" | 54° 0' 0" | 4·2030 | 0·7265 | | | XIII. Palladium | 77° 37' 0" | 54° 47' 0" | 4·5546 | 0·7058 | | | XIV. Copper | 71° 52' 45" | 49° 8' 30" | 3·0662 | 0·8656 | | | XV. Zinc | 77° 22' 20" | 53° 57' 20" | 4·4723 | 0·7281 | | | XVI. Lead | 69° 37' 0" | 71° 55' 0" | 2·6913 | 0·3265 | | | XVII. Bismuth | 73° 37' 0" | 55° 2' 0" | 3·4013 | 0·6993 | | | XVIII. Tin | 75° 7' 0" | 53° 43' 0" | 3·7627 | 0·7341 | | | XIX. Iron | 76° 7' 0" | 62° 41' 30" | 4·0458 | 0·5163 | | | — Steel | 77° 37' 0" | 62° 32' 30" | 4·5621 | 0·5197 | | | XX. Aluminium | 77° 7' 0" | 57° 9' 0" | 4·3721 | 0·6457 | | | XXI. Alloys of Copper and Zine:— | | | | | | | No. 1 | 72° 5' 0" | 49° 32' 0" | 3·0930 | 0·8531 | | | No. 2 | 72° 15' 0" | 49° 32' 0" | 3·1240 | 0·8531 | | | No. 3 | 73° 10' 0" | 49° 6' 0" | 3·3052 | 0·8662 | | | No. 4 | 73° 8' 0" | 49° 3' 0" | 3·2983 | 0·8677 | | | No. 5 | 74° 5' 0" | 49° 5' 0" | 3·5066 | 0·8667 | | | No. 6 | 74° 8' 0" | 47° 37' 0" | 3·5183 | 0·9126 | | | No. 7 | 73° 16' 0" | 49° 23' 0" | 3·3261 | 0·8576 | | | No. 8 | 73° 12' 0" | 50° 53' 0" | 3·3121 | 0·8132 | | | No. 9 | 72° 18' 0" | 48° 46' 0" | 3·1334 | 0·8764 | | | No. 10 | 72° 15' 0" | 51° 11' 0" | 3·1240 | 0·8045 | | | No. 11 | 72° 15' 0" | 51° 49' 0" | 3·1240 | 0·7864 | | | No. 12 | 76° 7' 0" | 57° 5' 0" | 4·0458 | 0·6473 | | | No. 13 | 73° 52' 0" | 55° 31' 0" | 3·4570 | 0·6868 | | | No. 14 | 76° 0' 0" | 56° 12' 0" | 4·0108 | 0·6694 | | In the preceding Table there are twelve pure metals; if we arrange these in two Tables, according to the magnitude of the Coefficients of Refraction and Reflexion, we obtain the following. **Table LXXXII.—Coefficient of Refraction of pure Metals.** | Metal | Coefficient of Refraction | |-------------|--------------------------| | I. Mercury | 6·3616 | | II. Silver | 4·8047 | | III. Palladium | 4·5546 | | IV. Zine | 4·4723 | | V. Aluminium | 4·3721 | | VI. Iron | 4·3039 | | VII. Platinum | 4·2030 | | VIII. Gold | 3·8994 | | IX. Tin | 3·7627 | | X. Bismuth | 3·4013 | | XI. Copper | 3·0662 | | XII. Lead | 2·6913 | **Table LXXXIII.—Coefficient of Reflexion of pure Metals.** | Metal | Coefficient of Reflexion | |-------------|--------------------------| | I. Silver | 0·9259 | | II. Gold | 0·9073 | | III. Copper | 0·8656 | | IV. Tin | 0·7341 | | V. Mercury | 0·7315 | | VI. Zinc | 0·7281 | | VII. Platinum | 0·7265 | | VIII. Palladium | 0·7058 | | IX. Bismuth | 0·6993 | | X. Aluminium | 0·6457 | | XI. Iron | 0·5180 | | XII. Lead | 0·3265 | The **brilliancy** of a metallic surface depends on the coefficient of refraction, and there is, doubtless, some sensible quality, not yet clearly defined, which corresponds to the coefficient of reflexion, which indicates the power of the surface to form elliptically polarized light from incident plane-polarized light. This quality might be provisionally named **lustre**. It is very remarkable that gold, silver, and copper, which from time immemorial have pleased the eye of man, and been used as coins, should head the list of bodies possessing a high coefficient of reflexion. Mercury, which has so brilliant a surface, and therefore heads the list in Table LXXXII., occupies a comparatively low place in Table LXXXIII., probably owing to its being a liquid, and its surface, therefore, in a less favourable condition than that of a solid for imparting elliptic polarization to an incident beam. M. Jamin has examined optically several of the substances mentioned in the preceding Tables—the metallic bodies by the methods of equal intensities and multiple reflexions, and the transparent bodies by the method employed in this paper, and originally used by him. I have deduced from his original observations, the optical constants of the substances common to him and myself, and have recorded them for the purpose of comparison, in the two following Tables, LXXXIV. and LXXXV.* **Table LXXXIV.—Optical Constants of Metals, deduced from Jamin’s experiments.** | Substance | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflection | |----------------------------|---------------------|----------------|---------------------------|--------------------------| | Steel (1) | 76° 6 | 59° 6 | 4·0108 | 0·5985 | | Steel (2) | 77° 4 | 61° 27 | 4·3546 | 0·5441 | | I. Means | 76° 32' 0" | 60° 16' 30" | 4·1827 | 0·5713 | | Silver (3) | 71° 40 | 54° 0 | 3·0178 | 0·7265 | | Silver (4) | 75° 0 | 47° 1 | 3·7320 | 0·9320 | | II. Means | 73° 20' 0" | 50° 30' 30" | 3·3747 | 0·8292 | | Zinc (5) | 77° 0 | ..... | 4·3314 | ..... | | Zinc (5) | 79° 13 | ..... | 5·2505 | ..... | | Zinc (6) | 75° 11 | 60° 57 | 3·7804 | 0·5554 | | III. Means | 77° 8' 0" | 60° 57' 0" | 4·4541 | 0·5554 | | Copper (7) | 70° 9 | 50° 36 | 2·7700 | 0·8214 | | Copper (8) | 71° 21 | 53° 41 | 2·9629 | 0·7350 | | IV. Means | 70° 45' 0" | 52° 8' 30" | 2·8664 | 0·7782 | | Speculum metal (9) | 75° 50 | 56° 45 | 3·9616 | 0·6556 | | Speculum metal (10) | ..... | 56° 40 | ..... | 0·6577 | | Speculum metal (11) | 76° 14 | 53° 33 | 4·0815 | 0·7386 | | V. Means | 76° 2' 0" | 55° 39' 20" | 4·9215 | 0·6839 | | VI. Brass (12) | 71° 31 | 52° 57 | 2·9916 | 0·7549 | * These Tables were added during the printing of the paper. Table LXXXV.—Optical Constants of Transparent Bodies, from Jamin’s experiments. | Substance | Principal Incidence | Circular Limit | Coefficient of Refraction | Coefficient of Reflexion | |--------------------|---------------------|----------------|---------------------------|--------------------------| | I. Glass of Antimony (13) | 63° 34' | 88° 26' | 2·0115 | 0·0290 | | II. Quartz (13) | 56° 50 | 89° 25 | 1·5301 | 0·0102 | | III. Fluor-Spar (13)| 55° 15 | 89° 31 | 1·4415 | 0·0084 | (1) Ann. de Chim. et de Phys. (sér. 3) vol. xix. p. 304. From the two Tables in this page, I find at 75° incidence, $I = 0·946$, and $J = 0·566$, from which it follows that $$\tan^{-1}\left(\frac{J}{I}\right) = 30° 54'.$$ (2) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 316 (mean red). The azimuths given in this and the following page are arcs such that $$\tan(\text{azimuth}) = k^2$$ $$k = \tan^{-1}\left(\frac{J}{I}\right).$$ From this consideration the coefficient of reflexion is deduced. (3) Ann. de Chim. et de Phys. (sér. 3) vol. xix. p. 315. (4) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 316 (mean red). (5) Ann. de Chim. et de Phys. (sér. 3) vol. xix. p. 320. (6) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 316 (mean red). (7) Ann. de Chim. et de Phys. (sér. 3) vol. xix. p. 337. I have calculated the value of the circular limit and coefficient of refraction from the experiment recorded as made with two reflexions. (8) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 317 (red light). (9) Ann. de Chim. et de Phys. (sér. 3) vol. xix. pp. 305, 306. The ratio of $J$ to $I$ at the principal incidence is found to be, from the Tables of these two pages, as 623 to 950, from which the circular limit is deduced. (10) Ann. de Chim. et de Phys. (sér. 3) vol. xix. p. 330. (11) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 316 (red light). (12) Ann. de Chim. et de Phys. (sér. 3) vol. xxii. p. 317 (red light). (13) Ann. de Chim. et de Phys. (sér. 3) vol. xxix. p. 303.