Ixvl InTRODUCTION TO THE MAKERSTOUN OBSERVATIONS, 1843. 
where f” is the force opposed to the magnetic force. Fora horizontal force X’, which 
would alone have brought the magnet into this position the equation would have 
been 
m X' cos Av=f" 
whence 
ig 
v 
and 
BOD. ANOS Bil os 7° tan wu 
mm DD. Ce a oD, ne By as) 
u being the deflection of a freely suspended magnet produced by placing the deflect- 
ing bar at right angles to the magnetic meridian, with its centre at a distance 7, 
from the centre of the suspended magnet. 
As kis the value of “= for one seale division 
_ 72 tan u* 
— 7 On 
120. The results of the experiments made on two days, and at a different dis- 
tance on each day, are, 
First day, £=0:0001021. 
Second day, =0:0001025. 
The value of & from the formula, =a cot v, being k=0°000125. This difference is 
very considerable, so much so, that even though again delaying the publication of 
the Observations for 1843, I have determined to go over the various reductions in 
the abstracts, with the coefficients derived from the above in the following manner :— 
k being the coefficient given in Table 11, the coefficient used in the reductions in 
the abstracts of results is obtained from it in multiplying by 1923 =0-8184; 0-0001023 
being the mean value of & obtained by deflections, and 0-0001250 the value of & 
obtained from the formula k=a cot v. The coefficients used are therefore as follow : 
Jan. 14—April 274 1843, s=0-0001021, 
April 28 —Nov. 8 1843, s=0-0000986, 
Nov. 10 —Dec. 31 1843, s=0-0001064. 
* It is obvious that the investigation for the balance magnet might be made in this way with ad- 
vantage, the final equation in the note, p. xxxvi, would then stand thus— 
tan wu 
r> ° QntanO 
Maxerstoun, August 1846. 
