The Description of Two New Micrometers. By Mr. Ramsden, Optician; Communicated by Joseph Banks, Esq. P. R. S.

XXVII. The Description of Two new Micrometers. By Mr. Ramsden, Optician; communicated by Joseph Banks, Esq. P. R. S. Read March 25, 1779: WHEN I offer the description of a new micrometer to the learned members of the Royal Society, I do not flatter myself that mere novelty will entitle it to their patronage. Sensible how much the theory of astronomy is limited by the imperfection of instruments, I always incline to improve rather than invent, except when repeated examinations convince me, that the imperfections arise from defect in principle as well as in the construction. In considering micrometers, when an observer finds, that with the micrometer, which depends on moveable parallel wires, he cannot measure any diameter of a planet, except that which is at right angles to the direction of its apparent motion, he cannot withhold his preference to that construction which measures the angle by the separation of the images. It appeared therefore to me a matter of some importance, to investigate the causes of the uncertainty which has been found in the observations made with the micrometer with a divided object-glass. The result of my examination convinced me, that were it possible to execute the construction of that micrometer, with the degree of accuracy required, it must still be subject to inaccuracy from its principle. By the position of the micrometer every error of its glass is magnified by the telescope; and if each surface of the micrometer glass has not, in every part, precisely the same radius (which opticians must allow to be exceedingly difficult) there will be a considerable error in the angle to be measured, and the eye applied to the different parts of the pencil will, without moving the micrometer, see the images of the object in the telescope fluctuating, sometimes appearing to overlap, and sometimes to separate from each other. But supposing the glass itself to be perfect in its substance and in its curvature, there will yet remain imperfections which arise from its principle. A micrometer glass applied to a telescope causes a very considerable aberration. If the focus of the glass is positive, the extreme aberration will be within the geometrical focus; if negative, it will be beyond it: and the aberration not only affects affects the distinctness of the image, but also the angle measured by the micrometer. At the time I took up this subject, the divided object-glass micrometer was the only one which measured angles by the separation of two images. Since that time, a very ingenious application of the prism to this purpose has been invented by the rev. Dr. Maskelyne, Astronomer Royal; and although experience has not yet ascertained the extent of its merit, it will always deserve great consideration from its ingenuity; but the more I considered the subject, I became more fully convinced, that the principle of reflection applied to micrometers would have great advantages over those hitherto constructed on the principle of refraction; and the catoptric micrometer I have the honour to describe, besides the advantage it derives from the principle of reflection, of not being disturbed by the heterogeneity of light, avoids every defect of other micrometers, and can have no aberration, nor any defect which arises from the imperfection of materials, or of execution, as the extreme simplicity of its construction requires no additional mirrors or glasses to those required for the telescope: and the separation of the image being effected by the inclination of the two specula, and not depending on the focus of any lens or mir- Mr. Ramsden's Description of ror, any alteration in the eye of an observer cannot affect the angle measured. It has, peculiar to itself, the advantages of an adjustment to make the images coincide in a direction perpendicular to that of their motion; and also of measuring the diameter of a planet on both sides the zero, which will appear no inconsiderable advantage to observers who know how much easier it is to ascertain the contact of the external edges of two images than their perfect coincidence. A short explanation of the annexed drawings will make the construction and the properties of this micrometer obvious. I divided the small speculum of a reflecting telescope, of Cassegrain's construction, into two equal parts, by a plane across its center; and by inclining the halves of the speculum to each other on an axis at right angles to the plane that separated them, I obtained two distinct images. The satisfaction I received on the first trial was checked by the apparent impossibility of reducing this principle to practice. The angular separation of the two images in this case being half the angular inclination of the two specula, it required an index of an unmanageable length, to allow the quantity of one second of a degree to become visible. Some time afterwards, on revising the principle, I considered, that if both the halves of the mir- ror turned on their center of curvature, there could be no alteration in their relative inclination to each other from their motion on this center; and that any extent of scale might be obtained, by fixing the center of motion at a proportional distance from the common center of curvature. This will be better understood from the annexed drawing. A (fig. 1.) represents the small speculum divided into two equal parts; one of which is fixed on the end of the arm B; the other end of the arm is fixed on a steel axis x, which crosses the end of the telescope c. The other half of the mirror A is fixed on the arm D, which arm at the other end terminates in a socket y, that turns on the axis, x; both arms are prevented bending by the braces aa. G represents a double screw, having one part e cut into double the number of threads in an inch to that of the part g; the part e having 100 threads in one inch, and the part g 50 only. The screw e works in a nut f in the side of the telescope, while the part g turns in a nut h, which is attached to the arm B; the ends of the arms B and D, to which the mirrors are fixed, are separated from each other by the point of the double screw pressing against the stud b, fixed to the arm D, and turning in the nut h on the arm B. The two arms B and D are pressed against the direction of the double screw eg by a spiral a spiral spring within the part n, by which means all shake or play in the nut H, on which the measure depends, is entirely prevented. From the difference of the threads on the screw at e and g it is evident, that the progressive motion of the screw through the nut will be half the distance of the separation of the two halves of the mirror, and consequently the half mirrors will be moved equally in contrary directions from the axis of the telescope c. The wheel v fixed on the end of the double screw has its circumference divided into 100 equal parts, and numbered at every fifth division with 5, 10, &c. to 100, and the index I shews the motion of the screw with the wheel round its axis, while the number of revolutions of the screw is shewn by the divisions on the same index. The steel screw r may be turned by the key s, and serves to incline the small mirror at right angles to the direction of its motion. By turning the finger head t (fig. 2.) the eye tube p is brought nearer or farther from the small mirror, to adjust the telescope to distinct vision; and the telescope itself hath a motion round its axis for the convenience of measuring the diameter of a planet in any direction. The inclination of the diameter measured with the horizon is shewn in degrees and minutes by a level and vernier on a graduated circle, at the breech of the telescope. The method of adjusting and using the catoptric micrometer is too obvious to require any explanation: it is only necessary to observe that, besides the table for reducing the revolutions and parts of the screw to minutes, seconds, &c. it may require a table for correcting a very small error which arises from the excentric motion of the half mirrors. By this motion their centers of curvature will (when the angle to be measured is large) approach a little towards the large mirror; the equation for this purpose in small angles is insensible, but when angles to be measured exceed ten minutes, it should not be neglected. Or, the angle measured may be corrected by diminishing it in the proportion the versed sine of the angle measured, supposing the excentricity radius, bears to the focal length of the small mirror. The telescope to which the catoptric micrometer is applied is of the Cassegrain construction. The great speculum is about twenty-two inches focus, and bears an aperture of $5\frac{1}{2}$ inches, which is considerably larger than those of the same focal length are generally made: indeed, the apparent utility of this micrometer makes me wish to see the reflecting telescope meet with further improvements. I believe it would more tend to the advancement of the art of working mirrors; if writers on this subject, instead of giving us their methods of working ima- imaginary parabolas, would demonstrate the properties of curves for mirrors which, placed in a telescope, will shew images of objects perfectly free from aberration; or, what will yet be more useful in practice, of what forms specula might be made, that the aberration caused by one mirror may be corrected by that of the other. If mathematicians assume data which really exist, they must see, that when the two specula of a reflecting telescope are parabolas, they cause a very considerable aberration, which is negative, that is to say, the focus of the extreme rays is longer than those of the middle ones. If the large speculum is a parabola, the small one ought to be an ellipse; but when the small speculum is spherical, which is generally the case in practice, if concave, the figure of the large speculum ought to be an hyperbola; if convex, the large speculum ought to be an ellipse, to free the telescope from aberration. This will be easier understood by attending to the positions of the first and second images; when a curve is of such form that lines drawn from each image, and meeting in any part of the curve, make equal angles with the tangent to the curve at that point, it is evident, that such curve will be free from aberration. This is the property of a circle when the radiant and image are in the same place; but when they recede from each other, of an ellipse, of such form that the radiant and image are in the two foci, till one distance becoming infinite the ellipse changes into a parabola, and to an hyperbola when the focus is negative; that is to say, when reflected rays diverge, and the focus is on the opposite side of the mirror. These principles made me prefer Cassegrain's construction of the reflecting telescope to either the Gregorian or Newtonian. In the former, errors caused by one speculum are diminished by those in the other. From a property of the reflecting telescope (which has not been attended to) that the apertures of the two specula are to each other very nearly in the proportion of their focal lengths, it follows, that their aberrations will be to each other in the same proportion, and these aberrations are in the same direction, if the two specula are both concave; or in contrary directions, if one speculum is concave, and the other convex. In the Gregorian construction, both specula being concave, the aberration at the second image will be the sum of the aberrations of the two mirrors; but in the Cassegrain construction, one mirror being concave, and the other convex, the aberration at the second image will be the difference between their aberrations. By assuming such proportions for the foci of the specula as are gene- Mr. Ramsden's Description of rally used in the reflecting telescope, which is about as 1 to 4, the aberration in the Cassegrain construction will be to that in the Gregorian as 3 to 5. I have mentioned these circumstances in hopes of recommending the demonstration of curves suited to the purposes of optics to the attention of mathematicians, which would be of great use to artists. I shall conclude this paper with the description of a new micrometer suited to the principle of refraction; being sensible that both principles have their peculiar advantages. Though the former part of this paper proves my partiality to the principle of reflection applied to micrometers, yet the very favourable opinion I have of the refracting telescope made me attentively consider some means of applying a micrometer to it, which might obviate the errors complained of in the former part of this paper. The application of any lens or medium between the object glass and its focus must inevitably destroy the distinctness of the image; I therefore have employed for the micrometer glass one of the eye glasses requisite in the common construction of the telescope; but if it should be found necessary to apply an additional eye glass for the convenience of enlarging the scale, I am able thereby to cor- rect both the colours and spherical aberration of the first eye glass. This micrometer is applied to the erect eye tube of a refracting telescope, and is placed in the conjugate focus of the first eye glass: hence arises its great superiority to the object glass micrometer. It has been before observed, that if a micrometer is applied at the object glass, the imperfections of its glass are magnified by the whole power of the telescope; but in this position, the image being considerably magnified before it comes to the micrometer, any imperfection in its glass will be magnified only by the remaining eye glasses, which in any telescope seldom exceeds five or six times. By this position the size of the micrometer glass will not be the $\frac{1}{100}$th part of the area which would be required if it was placed at the object glass; and, notwithstanding this great disproportion of size, which is of great moment to the practical optician, the same extent of scale is preserved, and the images are uniformly bright in every part of the field of the telescope. Fig. 4th, represents the glasses of a refracting telescope; $xy$ the principal pencil of rays from the object glass $o$; $tt$ and $uu$ the axis of two oblique pencils; $a$ the first eye glass; $m$ its conjugate focus, or the place of the micrometer; $b$ the second eye glass, $c$ the third, and $d$ the fourth. fourth, or that which is nearest the eye. Let $p$ be the diameter of the object glass, $e$ the diameter of a pencil at $m$, and $f$ the diameter of the pencil at the eye; it is evident, that the axis of the pencils from every part of the image will cross each other at the point $m$, and $e$, the width of the micrometer glass, is to $p$ the diameter of the object glass as $ma$ is to $go$, which is the proportion of the magnifying power at the point $m$, and the error caused by an imperfection in the micrometer glass placed at $m$ will be to the error, had the micrometer been at $o$, as $m$ is to $p$. Fig. 3d, represents the micrometer; $a$ a convex or concave lens divided into two equal parts by a plane across its center; one of these semi-lenses is fixed in a frame $b$, and the other in the frame $e$. Which two frames slide on a plate $h$, and are pressed against it by thin plates $aa$: the frames $b$ and $e$ are moved in contrary directions by turning the button $d$; $l$ is a scale of equal parts on the frame $b$; it is numbered from each end towards the middle with $10, 20, \&c.$ There are two verniers on the frame $e$, one at $m$, and the other at $n$, for the conveniency of measuring the diameter of a planet, &c. on both sides the zero. The first division on both these verniers coincides at the same time with the two zero's on the scale $l$, and, and, if the frame is moved towards the right, the relative motion of the two frames is shewn on the scale L by the vernier M; but if the frame B be moved towards the left, the relative motion is shewn by the vernier N. This micrometer has a motion round the axis of vision, for the conveniency of measuring the diameter of a planet, &c. in any direction, by turning an endless screw F, and the inclination of the diameter measured with the horizon is shewn on the circle g by a vernier on the plate v. The telescope may be adjusted to distinct vision by means of an adjusting screw, which moves the whole eye tube with the micrometer nearer or farther from the object glass, as telescopes are generally made; or the same effect may be produced in a better manner, without moving the micrometer, by sliding the part of the eye tube m on the part n, by help of a screw or pinion. The micrometer is made to take off occasionally from the eye tube, that the telescope may be used without it.