xxxiv Introduction to the Makerstoun Observations, 1843. 
or adaj)ting the first constant to logarithmic computation 
9 • (3 
J sin— . q C0S (v + (3) 
N = cos ( v + — ) + n * ^- + t a 1 
a cos v \ 2 / cos v 
= A + n B + tq' 
(3 is considered negative when v is diminished, n is negative when the reading is 
below the zero, and t is the temperature of the magnet minus 26°. 
42. It was necessary to turn the arms of the torsion circle once only in 1843, 
namely, on 
May 6 d 10 h 45 m , when vernier B was turned from 287° 44' to 291° 45', whence 
/3=-4° 1', A=234-7 scale divisions, B = 1\L9, v being=69° 46'. 
May 6 d 13 h 45 m , the arms of the torsion circle were turned from B 291° 45' to 
B 287° 41', as this was 3' different from the original reading, 3 scale divisions were 
subtracted from the abstracts of the observations from April 28 d 2 h till May 6 d 10 h , 
the two hourly and extra observations are, however, affected to that amount. 
43. The effect of the balance needle upon the readings of the bifilar was deter- 
mined, September 4 d 1843, to be —4*03 scale divisions ; no correction has been ap- 
plied ; the effect of the declination magnet is zero, and the effect of the copper ring 
or damper has not been determined, but it is supposed to be small. 
44. Time of vibration of the bifilar magnet. 
S. 
Feb. 22. Mean of 38 vibrations, 1 vibration = 26-18 
March 1. Mean of 28 vibrations, 1 vibration = 26 25 
June 1. Mean of 27 vibrations, 1 vibration = 27 - 08 
Oct. 25. Mean of 8 vibrations, 1 vibration = 26-99 
Oct. 25. Another series, . . . 27-03 
45. The natural arc of vibration is generally very small, and when considerable 
the time of vibration is found different from that determined by artificial vibrations 
(Introd. 1841-2, p. xxix), namely, about 25 seconds, which has been used in the 
observations. The observations are made as follows : — the point of the scale coin- 
ciding with the vertical wire of the fixed telescope is estimated to a tenth of a divi- 
sion at 25 s before the minute of observation, at the minute, and 25 s after it ; the 
mean reading is deduced from the three readings by the formula (7 + ^ + c , a, b, 
and c being the three readings. The mean thus obtained is corrected to the tempe- 
rature of 2G° Fahr., this being below the lowest temperature which occurred within 
the Observatory in 1843 ; a constant quantity of 300*0 has been added to all the cor- 
rected means. Tables weir formed giving the temperature correction for every 
tenth of a degree above 2G° from the formula (t~ 2G) ^' + 300*0. 
4G. The temperature of the magnet was obtained till November 27 d 18 h from 
the thermometer by lloss, after that time from the thermometer by Messrs Adie 
