Ixvi Introduction to the Makerstoun Observations, 1843. 
where/' is the force opposed to the magnetic force. For a horizontal force X', which 
would alone have brought the magnet into this position the equation would have 
been 
m X' cos Av=f f 
whence 
X' = X + ^ 
and 
X'-X_aX c M tan u 
~X ~XT" ^X ~ W ~2~ 
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 i\ 
from the centre of the suspended magnet. 
A X 
As k is the value of for one scale division 
_ r i tan u* 
120. The results of the experiments made on two days, and at a different dis- 
tance on each day, are, 
First day, k =0-0001021. 
Second day, A =0-0001025. 
The value of k from the formula, k=a cot v, being £=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 i§§§ =0-8184; 0*0001023 
being the mean value of k obtained by deflections, and 0*0001250 the value of h 
obtained from the formula k=a cot v. The coefficients used are therefore as follow : 
Jan. l d — April 27 d 1843, k= 0-0001021, 
April 28 —Nov. 8 1843, k =0-0000986, 
Nov. 10 —Dec. 31 1843, £ = 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 tho note, p. xxxvi, would then stand thus — 
, 3 tan u 
k = 
" 3 2 n tan 6 
Makeustoun, August 1840. 
