Determinations of the Magnetic Inclination and Force in the British Provinces of Nova Scotia and New Brunswick, in the Summer of 1847

XIV. Determinations of the Magnetic Inclination and Force in the British Provinces of Nova Scotia and New Brunswick, in the Summer of 1847. By Professor George W. Keely, of Waterville College, Maine, United States. Communicated by Lieut.-Colonel Sabine, For. Sec. R.S. Received March 1,—Read April 6, 1848. In an excursion in the provinces of Nova Scotia and New Brunswick in August and September 1847, I took with me some magnetical instruments, with which I made a few observations for determining the magnetic intensity. The observations were of two kinds; those for the relative total force, made with a pair of Lloyd needles, which I shall designate L(1) and L(2), and an inclination circle, seven inches in diameter, with two verniers reading to single minutes, constructed by Barrow, successor to Robinson; and those for the absolute horizontal force, made with a unifilar magnetometer by Jones. The positions of the needles in the inclination circle are determined by two reading microscopes with micrometer scales. The unifilar has a theodolite base and circle of six inches, divided on silver, and reading to twenty seconds. Both instruments are described in Captain Riddell's "Supplement" to his "Magnetical Instructions." Observations to determine the temperature coefficients of the Lloyd needles were made in a small building fastened with nothing but copper, and containing a copper stove. For the weights sent by the maker with these needles, which were inconvenient, I substituted two platinum weights, which have never been removed from the holes in which they were placed before my observations commenced. Using $t$, $t'$, $v$, $v'$, $\theta$, $\theta'$, $\phi$, $\phi'$ for the temperatures, the angles of deflection, the inclinations, and the relative forces, respectively, at low and high temperatures, the following Table exhibits the observations and results by the well-known formula $\phi = \frac{\cos v}{\sin (\theta + v)}$. I find the results the same whether the mean values of $t$, $v$, and $\theta$, &c. are used to obtain $\phi$ and $\phi'$, or a mean of the daily results is taken. ### Table I. Observations for the Temperature Coefficient of L(2). Waterville Mean Time. | Low temperatures | High temperatures | |------------------|-------------------| | **1847.** | | | Feb. 10 | Feb. 10 | | d h | d h | | Feb. 10 | Feb. 10 | | 26-1 | 73-1 | | 26 26 33 | 26 59 46 | | 75 55 57 | 75 55 57 | | 0-9166800 | 0-9142133 | | Feb. 10 | Feb. 10 | | 20 00-5 | 70-0 | | 27 11 41 | 75 56 45 | | 0-9177840 | 0-9133754 | | Feb. 10 | Feb. 10 | | 21 23-7 | 64-5 | | 27 15 33 | 75 56 17 | | 0-9173431 | 0-9130579 | | Feb. 10 | Feb. 10 | | 22 23-7 | 60-5 | | 27 09 20 | 76 00 58 | | 0-9157335 | 0-9138112 | | Feb. 10 | Feb. 10 | | 23 23-7 | 84-2 | | 27 50 06 | 75 55 26 | | 0-9171375 | 0-9140202 | | Feb. 10 | Feb. 10 | | 26 00-3 | 80-6 | | 27 38 39 | 75 56 16 | | 0-9141865 | 0-9113319 | | Feb. 10 | Feb. 10 | | 27 00 | 73-3 | | 27 38 46 | 75 57 38 | | 0-9147465 | 0-9114102 | | Feb. 10 | Feb. 10 | | 28 23-7 | 69-7 | | 27 27 59 | 76 00 01 | | 0-9143125 | 0-9123667 | | Feb. 10 | Feb. 10 | | Mar. 1 | 23-5 | | 67-7 | 75 57 30 | | 0-9144437 | 0-9123912 | | Feb. 10 | Feb. 10 | | 26 56 56 | 75 57 30 | | 0-9145187 | 0-9142698 | | Means........... | 24-51 | | 26 41 27 | 75 57 54 | | 0-9156886 | 0-9126578 | | Calculated value from means of t, v, and θ ... | 0-9156908 | | Calculated value from means of t', v', and θ' ... | 0-9126596 | ### Observations for the Temperature Coefficient of L(1). Waterville Mean Time. | Feb. 7 20-5 | Feb. 8 03 | |-----------------|------------------| | 29-9 | 75-1 | | 35 55 26 | 36 11 41 | | 75 54 21 | 75 54 21 | | 0-8723502 | 0-8710132 | | Feb. 7 20-5 | Feb. 8 03 | | 31-9 | 9-02 | | 36 00 08 | 86-9 | | 75 57 55 | 36 23 47 | | 0-8723284 | 0-8703828 | | Feb. 7 20-5 | Feb. 8 03 | | 34-2 | 10-01 | | 35 59 36 | 78-3 | | 75 56 05 | 36 15 45 | | 0-8721856 | 0-8708558 | | Feb. 7 20-5 | Feb. 8 03 | | 32-6 | 10-23 | | 35 52 53 | 78-8 | | 75 58 51 | 36 16 50 | | 0-8720186 | 0-8710536 | | Feb. 7 20-5 | Feb. 8 03 | | 24-0 | 12-01 | | 35 51 37 | 74-8 | | 76 00 06 | 36 15 36 | | 0-8732486 | 0-8712842 | | Feb. 7 20-5 | Feb. 8 03 | | 25-9 | 13-00 | | 35 53 28 | 74-3 | | 75 58 32 | 36 13 11 | | 0-8729382 | 0-8713204 | | Feb. 7 20-5 | Feb. 8 03 | | 16-7 | 14-23 | | 35 44 27 | 63-0 | | 75 58 34 | 36 13 38 | | 0-8736786 | 0-8712866 | | Feb. 7 20-5 | Feb. 8 03 | | 15-0 | 15-23 | | 35 44 33 | 71-0 | | 75 58 24 | 36 18 04 | | 0-8736534 | 0-8709048 | | Feb. 7 20-5 | Feb. 8 03 | | 19-0 | 16-23 | | 35 54 58 | 75-7 | | 75 58 04 | 36 24 26 | | 0-8727674 | 0-8703360 | | Feb. 7 20-5 | Feb. 8 03 | | 15-0 | 19-00 | | 35 57 57 | 67-8 | | 76 02 14 | 36 29 45 | | 0-8729488 | 0-8703426 | | Feb. 7 20-5 | Feb. 8 03 | | 20-4 | 20-01 | | 35 55 41 | 81-0 | | 75 56 45 | 36 28 25 | | 0-8725744 | 0-8608804 | | Means........... | 23-33 | | 35 53 42 | 75 58 10 | | 0-8728811 | 0-8707882 | | Calculated value of φ from means of t, v, and θ ... | 0-8728810 | | Calculated value of φ' from means of t', v', and θ' ... | 0-8707881 | whence by the formula \( q = \frac{\phi - \phi'}{t' - t} \) we have for L(1) the coefficient '0000463; and for L(2) the coefficient '0000722. The values of \( \theta \) in the above observations were obtained by the two dipping-needles accompanying the Lloyd needles, and which I shall call A(1) and A(2). The observations were made in the usual way with poles direct and reversed, in each case the marked limb of the circle facing both east and west; each single reading being a mean of from four to eight, successively obtained by lifting the needle from its agate supports by the lifting frame. The mean of the whole is, for A(1), twenty complete observations, 75° 57' 03"; for A(2), nineteen complete observations, 75° 58' 50"; whence the mean dip for Waterville (lat. 44° 33' N., long. 293° 23"), Feb. 17, 1847, is 75° 57' 56½". Between June 14th and June 30th I made at the same place, with each of the needles, six complete observations, on as many days, and when, from the less variations of temperature, the adjustments were more under control; the results were for A(1), 75° 56' 27"; for A(2), 75° 59' 31"; mean dip for June 22nd, 75° 57' 59". In all my observations with these dipping-needles, up to the time of my excursion, I had observed far greater irregularities in A(2) than in A(1); in this last set, for instance, the greatest difference between any partial result by A(1) and the mean dip was 01'7, while for A(2) it was 03'2; the difference for A(1) indeed was, in two-thirds of the results, less than 1'. Though this might not affect the means of a great number of observations, it is evident that if the observer is limited to one observation with each of these needles, he is far more likely, setting aside the effects of carelessness, to obtain a truly comparable value of $\theta$ by needle A(1) alone, than by a mean of the two. I have therefore confined my observations for $\theta$, on my tour, with one exception, to A(1). The direction of the meridian has always been obtained with A(1), by considering the meridian as 90° from a mean of the positions of the vertical limb of the circle, when the needle resting on its supports had an inclination of 90° with its marked face alternately north and south. Moreover, in all my observations with the dipping or force needles, whenever the instrument was newly placed, the adjustments for correct position of the microscopes, the axis, the level, and the planes of support, were duly made if necessary. Table II. gives the details of the observations made in the provinces for $v$ and $\theta$ with the logs of $\phi$, by each needle reduced to 50° Fahr. ### Table II. | No. for reference | Place | Date, 1847 | Latitude to nearest minute | Longitude to nearest minute | Needle | Poles direct. | Poles reversed. | $\theta$ | Observations with Lloyd needles | Logarithms of $\phi$. | |-------------------|------------------------|------------|----------------------------|-----------------------------|--------|---------------|-----------------|---------|--------------------------------|----------------------| | | | | | | | | | | Needle. Temp. Fahr. | $v$. | | 1. Halifax, N.S. | Aug. 20 | 44 39 | 296 23 | A(1) | 75 37 | 75 37-1 | 75 37 | L(1) | 77-3 39 32-1 | Means used. | | | | | | | | | | | L(1) 77-5 39 32-5 | | | | | | | | | | | | L(2) 76-9 32 15-1 | | | 2. Hiltz's, N.S. | 23. 44 57 | 295 9 | A(1) | 75 37 | 75 37 | 75 37 | L(1) | 74-0 39 36-5 | | | 3. Windsor, N.S. | 24. 45 10 | 295 44 | A(1) | 75 40-6 | 75 42-2 | 75 41-4 | L(1) | 76-8 39 38 | | | 4. Kentville, N.S.| 25. 45 12 | 295 14 | A(1) | 75 45-1 | 75 46-3 | 75 45-7 | L(1) | 52-1 39 09-6 | | | 5. Bridgetown, N.S.| 26. 44 51 | 294 22 | A(1) | 75 40-9 | 75 41-9 | 75 41-4 | L(1) | 75-3 39 05-2 | | | 6. Annapolis, N.S.| 27. 44 45 | 294 04 | A(1) | 75 41-7 | 75 41-2 | 75 41-5 | L(1) | 68-5 38 58-8 | | | | | | | | | | | | L(2) 70-3 31 41-2 | | | 7. St. John, N.B. | Sept. 1 | 45 14 | 293 57 | A(1) | 75 55-7 | 75 55-7 | 75 55-7 | L(1) | 59-9 38 22-2 | | | 8. Fredericton, N.B.| 2. | | | | | | | | L(1) 72-0 39 19-7 | | | 9. Woodstock, N.B.| 4. 46 09 | 292 25 | A(1) | {77 12} | 77 10-2 | 77 11-1 | 77 11-4 | L(1) | 73-2 39 14-8 | | | | | | | | | | | | L(2) 63-2 30 56-1 | | | | | | | | | | | | L(2) 45-3 30 37-8 | | | 10. Riviere des Chutes | 6. 46 36 | 292 16 | A(1) | 77 11-1 | 77 11-7 | 77 11-4 | L(1) | 69-0 38 54-3 | | | | | | | | | | | | L(2) 45-3 30 37-8 | | | 11. Grand Falls of St. John | 7. 47 03 | 292 15 | A(1) | 77 28-1 | 77 31 | 77 29-5 | L(1) | 70-7 39 29-1 | | | | | | | | | | | | L(2) 59-0 31 09 | | | 12. Grand River | 8. 47 11 | 292 03 | A(1) | 77 36-4 | 77 34-8 | 77 35-6 | L(1) | 49-2 38 51-4 | | | | | | | | | | | | L(2) 61-4 31 01-6 | | | 13. Madawaska | 9. 47 22 | 291 41 | A(1) | 77 44-9 | 77 44-8 | 77 44-8 | L(1) | 65-1 39 09-3 | | | | | | | | | | | | L(2) 77-6 31 08-7 | | | | | | | | | | | | L(2) 77-6 31 08-7 | | Remarks on Table II. 1. This station was on the east side of Citadel Hill, in an enclosure surrounded with a picket fence, and as much as forty or fifty rods from the N.E. outer line of the works. There were no iron stores in the works, and only two or three guns mounted, which were on the S.W. side. To ascertain if there was local attraction, I took the dip again in the plain on the west side of the hill, at least 100 rods from the works, and found it did not vary by one minute. 2. On the hill, back of Hiltz’s Tavern, half-way from Halifax to Windsor. 3. McBride’s Garden, one-fifth of a mile N. of the Catholic Chapel. 4. Garden, back of Terrey’s Hotel. 5. Forty rods S.E. of Quirk’s Tavern. 6. An open field back of Hall’s Tavern, and about forty rods S. of Catholic Chapel. 7. On the sea-side E. of the Barracks. 8. River-side in front of the Province House. 9. In an open field, a few rods, say thirty, N. of the Woodstock Hotel. On examining my notes at home, I found that a somewhat thick pencil-mark, in noting the azimuths for meridian, had caused the observations for $\theta$ and $v$ on the 4th to be made just $10^\circ$ out of it: calling those angles $\theta'$ and $v'$, $\theta'$ was reduced to the meridian by the formula $\cot \theta = \cot \theta' - \cos 10^\circ$; I then obtained the value $\phi'$ from $\theta'$ and $v'$, as if rightly observed; and then obtained $\phi$ from the equation $\phi = \phi' \frac{\sin \theta'}{\sin \theta}$, which, I believe, will be found a correct process. 10. In the road near Woolverton’s. 11. Near the Barracks; needles unsteady on the 7th. 12. On the lower cape, at the junction with the St. John. Observations with L(1) disturbed. 13. On the lower cape, at the junction of the Madawaska with the St. John. In regard to the latitudes and longitudes, I am indebted to Major Graham for those of Nos. 9, 10, 11, 12 and 13. Messrs. Crauford and Agnew, chronometer raters at Halifax and St. John respectively, furnished me with those for Nos. 1 and 7; the rest were obtained from the best authorities of books or maps that I could procure. Table III. exhibits the change in force of needles L(1) and L(2); the results are reduced to a temperature of $50^\circ$. | Year | No. of observations | $\phi$ for L(1) | Difference | Year | No. of observations | $\phi$ for L(2) | Difference | |------|-------------------|----------------|------------|------|-------------------|----------------|------------| | 1847 | February 13 | 22 | .8718039 | 1847 | February 23 | 21 | .9140079 | | | June ……17 | 10 | .8707137 | | June ……30 | 10 | .9070629 | | | August …16 | 5 | .8707129 | | August …16 | 5 | .9068502 | From the above Table it is obvious that both needles lost considerable force between February and June, and that after that time $L(2)$ continued to lose, while $L(1)$ retained its force. I have therefore reduced all observations made with $L(2)$ to the 30th of June, by considering the loss as proportional to the time, the coefficient of reduction being $(1 + 0.00005 \cdot d)$, $d$ being the number of days after the 30th of June. Column (3.) in Table IV. contains the logarithms corrected in this manner for $L(2)$, and those of $L(1)$ as originally found. The numbers '8707137 and '9070629 are the values of $\phi$ at Waterville on the 30th of June by $L(1)$ and $L(2)$ respectively; if the factor 1'04175 which connects them is compared with the corresponding factors in column (4.) (omitting that for Grand River for a reason already stated), these factors will all be found to exceed it by a small quantity: waiving discussion, at present, on the cause of this difference, I shall assign half the difference between the mean of these factors and 1'04175, or 0'00036 as a correction common to both, positive for $L(1)$ and negative for $L(2)$, which, while it leaves the mean determinations where both needles were used unaltered, will secure a more just comparison for stating where but one needle was used. I believe the difference, however, has hitherto been considered wholly within the errors of observation. Column (5.) contains the corrected logarithms, that is, the values of $\phi$ for $L(1)$ increased in the ratio of 1 to 1'00036, and those of $\phi$ for $L(2)$ reduced in the same ratio. Column (7.) contains the total forces for both needles, considering '8707137, or the number expressing the relative force by $L(1)$ on the 30th of June at Waterville, as the unit of force; and column (8.) contains the means. ### Table IV. | Station | Needle | Logarithms corrected for change of force in L(2) | Factors connecting the numbers corresponding to the logarithms (in col. 3) for L(1) and L(2) | Logarithms corrected for factor connecting L(1) and L(2). | Logarithms reduced to Waterville as unit. | Forces to Waterville unit. | Means | |------------------|--------|-------------------------------------------------|------------------------------------------------------------------------------------------|----------------------------------------------------------|------------------------------------------|----------------------------|-------| | Halifax | L(1) | 1·9310218 | 1·04387 | 1·9311781 | 1·9913028 | 98017 | | | Halifax | L(2) | 1·9496683 | | 1·9495120 | 1·9918746 | 98146 | 98081 | | Hiltz's | L(1) | 1·9307381 | | 1·9308944 | 1·9910191 | 97953 | 97953 | | Windsor | L(1) | 1·9309837 | | 1·9311400 | 1·9912647 | 98009 | 98009 | | Kentville | L(1) | 1·9320107 | | 1·9321670 | 1·9922917 | 98241 | 98241 | | Bridgetown | L(1) | 1·9323155 | | 1·9324718 | 1·9925965 | 98310 | 98310 | | Annapolis | L(1) | 1·9325703 | | 1·9327266 | 1·9928513 | 98367 | | | Annapolis | L(2) | 1·9509458 | 1·04322 | 1·9507895 | 1·9931521 | 98436 | 98401 | | St. John | L(1) | 1·9348103 | | 1·9349666 | 1·9950913 | 98876 | 98876 | | Fredericton | L(1) | 1·9364098 | | 1·9365661 | 1·9966908 | 99241 | 99241 | | Woodstock | L(1) | 1·9377287 | | 1·9378850 | 1·9980097 | 99543 | | | Woodstock | L(2) | 1·9555509 | 1·04189 | 1·9553946 | 1·9977572 | 99485 | 99514 | | Riviere des Chutes| L(1) | 1·9381584 | | 1·9383147 | 1·9984394 | 99641 | | | Riviere des Chutes| L(2) | 1·9561010 | 1·04218 | 1·9559447 | 1·9983073 | 99611 | 99626 | | Grand Falls | L(1) | 1·9379492 | | 1·9381055 | 1·9982302 | 99593 | | | Grand Falls | L(2) | 1·9526088 | 1·04308 | 1·9561125 | 1·9984751 | 99649 | 99621 | | Grand River | L(1) | 1·9392578 | | 1·9394141 | 1·9995388 | 99894 | | | Grand River | L(2) | 1·9567205 | 1·04102 | 1·9565642 | 1·9989268 | 99753 | 99823 | | Madawaska | L(1) | 1·9395932 | | 1·9397495 | 1·9998742 | 99971 | | | Madawaska | L(2) | 1·9574700 | 1·04202 | 1·9573137 | 1·9996763 | 99925 | 99948 | | Waterville | L(1) | | | 1·9398753 | 10· | 1· | | | Waterville | L(2) | | | 1·9576374 | 10· | 1· | 1·0000 | Logarithmic factors used in the above changes: | Needle | Logarithm | Logarithm | |--------|-----------|-----------| | L(1) | +0·001563 | +0·0601247| | L(2) | -0·001563 | +0·0423626| ### Observations with the Unifilar. At Halifax, Kentville, Annapolis and Fredericton, I made observations with the unifilar; the magnet vibrated, and used also as a deflector, was marked H(10) and was a cylinder 2·953 inches in length; the deflected magnet was marked I(14), a cylinder 2·414 inches in length. The magnet H(10) being suspended,—by turning the telescope through arcs of three or four degrees, and applying a correction for torsion, observed at the same times,—I obtained on the 27th of March for a scale division 10·0999, and on the 29th 10·0963; the value used is 10·1. Table V. exhibits the results of observations to determine the temperature coeffi- cient of magnet H(10); and Table VI. shows the values of P from the formula \[ P = \frac{r^2 r^5 \sin u' - r^2 r^5 \sin u}{r^5 \sin u' - r^5 \sin u} \] using the distances 1 foot and 1.4 foot. **Table V.** | April 29th and 30th | Mean | |---------------------|------| | -0.000160 | | | -0.000169 | | | -0.000158 | | | -0.000168 | | | Mean...... | -0.000164 | **Table VI.** | Date | Values of P. | |------------|--------------| | July 28 | -0.00042 | | July 29 | -0.00091 | | Sept. 25 | -0.00157 | | Nov. 27 | -0.00162 | | Dec. 8 | -0.00102 | | Mean ... | -0.00111 | Lamont's method was adopted of obtaining the moment of inertia of cylinder H(10) by means of a brass ring accompanying the instrument, whose dimensions were, - External diameter . . 0.2153 ft. - Internal diameter . . 0.1667 ft. - Weight* . . . . . . Whence log \( k' = 0.5489695 \). The cylinder H(10) had on it, at the ends, two small brass rings, the contour of which I shortened by filing, so as to bear conveniently the metal ring in vibration. Twenty-one sets of vibrations without the ring, and eight sets with it, made between the 2nd and 6th of October, varying, in number of vibrations, from 340 to 466 each, and corrected for temperature, arc, torsion and rate of chronometer, all observed at the same times, gave for log \( \pi^2 k \) at a mean temperature of 63°3, 1.3320923. Observing, however, that the cylinder suspended seemed very slightly depressed at the N. end, I shifted the little ring there to the S. end, putting it in contact with the other ring, and at such a distance from the end of the cylinder as I had calculated would give the same moment of inertia; and then on the 8th and 9th of October made more observations for \( \pi^2 k \), the particulars of which are in Table VII. **Table VII.** | Date. Civil reckoning. | Whole time. | Number of vibrations. | Time of one vibration. | Commencing arc. | Final arc. | Temperature. | Torsion for 90° in scale divisions. | Rate chron. | \( k \) | |------------------------|-------------|-----------------------|-----------------------|-----------------|------------|---------------|-----------------------------------|-------------|-------| | Oct. 8 | 9 33 A.M. | 1448:3572 | 330 | 4:38896 | 3:0 | 4 | 50:5 | 8725 | -6:5 | | | 10 21 A.M. | 2091:8929 | 294 | 7:11528 | 3:0 | 9 | 54:5 | 1:1800 | -6:5 | | | 18 P.M. | 1500:8215 | 342 | 4:38836 | 2:9 | 7 | 65:4 | 76 | -6:5 | | | 32 P.M. | 2103 | 296 | 7:10473 | 2:8 | 1 | 65:75 | 1:065 | -6:5 | | | 17 P.M. | 1490:7857 | 340 | 4:38466 | 3:0 | 6 | 64:0 | 69 | -6:5 | | | 00 P.M. | 1501 | 342 | 4:38889 | 2:9 | 7 | 59:5 | 55 | -6:5 | | | 55 P.M. | 2217:2643 | 312 | 7:10662 | 2:9 | 1 | 59:3 | 945 | -6:5 | | | 53 P.M. | 1499:0357 | 342 | 4:38314 | 2:9 | 4 | 56:0 | 6875 | -6:5 | | | 47 | 2228:8857 | 314 | 7:09836 | 2:7 | 9 | 56:1 | 1:0925 | -6:5 | | | 33 | 1523:4785 | 348 | 4:37781 | 3:0 | 6 | 50:5 | 795 | -6:5 | * Weight not stated in the MSS.—E. S. These observations gave for the mean value of log $k$, 3377587, at a mean temperature of 58°2, and hence $\pi^2 k = 1.3320584$. If this value of $\pi^2 k$ is reduced to the temperature of 63°3, by the formula $1 + 2e(t' - t)$, it gives 1.3320885, differing from the former observed value only 0.000038. Where in the table three observations are included in one set, the mean of the true corrected values of $T$ for the first and third was taken and combined with $T'$, so as in some degree to eliminate changes of force. Table VIII. contains the uncorrected particulars of my observations of vibrations and deflections at Halifax, Annapolis and Fredericton, and those of vibration only at Kentville; with the nearest observations, before and after my tour, at Waterville. Table IX. contains $m$, X, and the total force; a mean for the value of $m$ at Kentville having been taken from the values at Halifax and Annapolis. Table X. contains the total forces at the four stations obtained by the unifilar reduced to Waterville by the observations of the Lloyd needle L(1) at the same stations, in order to test the accuracy of the observations; an additional column shows the same comparison for the only two stations where the two Lloyd needles and unifilar were all used; in other words, having obtained the total force at, say, Halifax by the unifilar, and also the relative force by the Lloyd needles, and knowing also the relative force at Waterville by the Lloyd needles, and therefore the ratio of the force at Halifax to the force at Waterville by the Lloyd needles, I multiply the aforesaid total force at Halifax got by the unifilar by this ratio, and obtain the total unifilar force at Waterville, and so with the rest. ### Table VIII. | Station | Date | Magnet. | $u$ | Temperature | $u'$ | Temperature | Time of one vibration | Number of vibrations | Temperature | Commencing arc | Final arc | Rate of chron. | Torsion for 90° in sec. divisions | |-------------|--------|---------|-----|-------------|-----|-------------|----------------------|---------------------|-------------|---------------|----------|--------------|----------------------------------| | Waterville | July 29 | H(10) | 12 21:3 | 63:8 | 4 28:5 | 64:1 | 4:35021 | 548 | 66:4 | 6:5 | 1:1 | ... | 8925 | | Waterville | Aug. 30 | H(10) | 12 21:6 | 67:6 | ... | ... | 4:35277 | 460 | 72:0 | 5:25 | 0:75 | ... | 1:009 | | Halifax | Aug. 21 | H(10) | ... | ... | ... | ... | 4:34901 | 338 | 71:5 | 5:0 | 1:0 | ... | 69 | | Kentville | Aug. 24 | H(10) | ... | ... | ... | ... | 4:36005 | 238 | 61:9 | 5:0 | 1:0 | ... | 8:5 | 6018 | | Annapolis | Sept. 27 | H(10) | ... | ... | ... | ... | 4:35008 | 344 | 68:5 | 5:5 | 0:8 | ... | 8:0 | 52 | | Fredericton | Sept. 25 | H(10) | ... | ... | ... | ... | 4:53733 | 344 | 72:5 | 4:9 | 0:7 | ... | 7:0 | 7225 | | Waterville | Sept. 25 | H(10) | 12 10:9 | 61 | 4 24:9 | 60:4 | 4:37520 | 356 | 56:0 | 8:4 | 1:4 | ... | 6:2 | 1:01 | In this Table $u$ and $u'$ are given to the nearest tenth of a minute, but in the calculations the value in seconds was employed. ### Table IX. | Station | Date | Corrected angles of defection | Time of one vibration | m | X | Total force | |---------------|-----------|-------------------------------|-----------------------|-----------|-----------|-------------| | Waterville | July 29 | 12° 23' 02.5" | 4:34798 | '34928 | 3:2536 | 13:4174 | | Waterville | 29 | 4 29 04.8 | | '34926 | 3:2538 | 13:4181 | | Waterville | 30 | 12 23 43.9 | 4:34901 | '34937 | 3:2515 | 13:4086 | | Halifax | Aug. 21 | 4 26 41.2 | 4:34457 | '34799 | 3:2710 | 13:1757 | | Kentville | 24 | | 4:35914 | * | 3:2493 | 13:2112 | | Annapolis | 27 | 4 26 54 | 4:34777 | '34787 | 3:2672 | 13:2198 | | Fredericton | Sept. 2 | 4 49 58.7 | 4:53242 | '34780 | 3:0071 | 13:3491 | | Waterville | 25 | 12 12 15.6 | 4:27832 | '34437 | 3:2544 | 13:4207 | | Waterville | 25 | 4 25 19.8 | | '34441 | 3:2540 | 13:4192 | ### Table X. | Station | Reduced to Waterville | Value | |--------------------------|-----------------------|-------| | Halifax | | 13:442| | Kentville | | 13:448| | Annapolis | | 13:439| | Fredericton | | 13:451| | | | 13:445| |----------------------|-----------------------|-------| | | | 13:436|