the Intensity of the Earth's Magnetic Force. .541 



i-3 \mM'- I {M.M + MM\) ;^ + 1^ {M,M' + 2M,M\ + ilfJi',) 1 + &c. j, 



or tI/J/' C/, in which 



1 L 3/3/3 .il/'aN 1 15(M, M,M'.M'\ 1 _^ . j 



M M 



Now it is to be observed, that the variations of the ratios -r^, ^, &c., 



M M ' 



arising from the variations of /i, are of a lower order of magnitude than that of 

 M, and may be disregarded in their effect upon the value of U.* On the sup- 

 position that the quantity of free magnetism, at any point of a magnet, is pro- 

 portional to the distance from the centre, or that fi = kr, we have 



M= IM\ M3 = §kl', 1/5 = f H', 



and when k becomes k — Ik, these values will all be altered proportionally, and 



31 M 

 consequently the ratios -,y, ~, &c., will be absolutely unchanged ; and the 



same thing is manifestly true, if the quantity of free magnetism be supposed to 

 vary as any simple power of the distance, whether integer or fractional. 



This is a point of considerable importance in reference to the method now 

 proposed. For it follows that, at a given distance between the two needles, the 

 function U may be regarded as constant ; and, therefore, that, even when U is 

 unknown, the value of R will be relatively determined, by a process which is 

 independent of the changes induced by time in the magnetic moments of the 

 needles employed. Accordingly, if the value of the force be found at any one 

 place, by any independent means, it will be absolutely known at all ; and it is 

 only necessary that the observer should include in his series an observation at 

 some base-station, at which the absolute value of the force is determined simul- 

 taneously by the ordinary method. 



I now proceed to show, however, that the value of the constant U may be 

 found by deflection, by the instrument itself, and without any subsidiary appa- 

 ratus ; and that the method may therefore be rendered rigorously absolute. It 

 is obvious that the ordinary process is inapplicable in this case, owing to the 

 large number of terms which acquire a sensible value, in the value of the func- 



* This circumstance was first pointed out by Dr. L.uiont. 

 VOL. XXIII 4 B 



