266 ON THE DETERMINATION OF THE TOTAL 



of free magnetism, at any point of a magnet, is proportional to 

 the distance from the centre, or that /u = AT, we have 



* = A-/ 3 , z 3 = | A-/ 3 , w 5 - 1 M\ 



and when & becomes k + SA-, these values will all be altered 

 proportionally, and consequently the ratios '-, , &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 V 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 inde- 

 pendent 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 simultaneously 

 by the ordinary method. 



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

 V may be found by deflection, by the instrument itself, and 

 without any subsidiary apparatus ; 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 function U, and the consequent difficulty and uncertainty of 

 the elimination : moreover, the position which has been adopted 

 for the deflecting needle will not admit of the required alteration 

 of distance. 



Now here I premise, that it is not necessary that the usual 

 deflection distance should be one of the series employed in 

 deducing the coefficients of the inverse powers of the distance in 

 the value of U: it is not even requisite that the relative positions 

 of the two magnets should be the same in the two cases. For if 

 the value of the corresponding function be found, for any other 

 position, and at any distance, that of U will be known by a 

 comparison of the deflections produced. Accordingly, 1 propose 



