Ixvi Introduction to the Makerstoun Observations, 1843. 



where/' is tlie 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 A V =/' 



whence 



x- = x + l^ 



and 



X'-X _ aX c M _ /jS tan u 



X 



^3 



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 r^ 

 from the centre of the suspended magnet. 



As h is the value of -^ for one scale division 



_ r^ tan u* 



120. The results of the experiments made on two days, and at a difi'erent dis- 

 tance on each day, are, 



First day, A; =0-0001021. 



Second day, A; = 00001025. 



The value of h from the formula, Jc—a cot v^ being A;=0-000125. This difi'erence 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 : — 

 Ic 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 h obtained by deflections, and 0*0001250 the value of k 

 obtained from the formula h=a cot v. The coefficients used are therefore as follow : 



Jan. Id—April 27'^ 1843, X;= 0-0001021, 

 April 28 —Nov. 8 1843, A; =0-0000986, 

 Nov. 10 —Dec. 31 1843, A;=00001064. 



* 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 — 



r^ 2 n tan Q ' 

 Makeestoun, Av^ust 1846. 



