Royal Society. 71 



duced by Ampere, namely an attraction of the strength 



cii r ds ds f ( — 9 — |- r L. ). 



ds ds'* 



This Amperian formula, however, cannot be proved by ex- 

 periment for two single elements of current, but the experi- 

 mental proof always refers to cases in which at least one of the" 

 currents is closed. Hence other forces may be regarded as 

 admissible between two current-elements, if, for the case in 

 which one current is closed, they only give the same result 

 that was given by Ampere's calculation. Such forces are ob- 

 tained when various values are given to the constant n in the 

 above expressions ; for the term affected by the factor n, occur- 

 ring in each of the three expressions, which is a differential 

 coefficient of the second order according to s and /, becomes in 

 the integration over a closed current zero, and consequently 

 cannot have any influence on the force which a closed current 

 exerts on a current-element. 



Hence, if we admit as certain only that which has been con^ 

 firmed by experiment, we can provisionally consider n a con- 

 stant yet to be determined. Theoretically, however, that value 

 is the most probable which makes the fundamental equations 

 simplest, viz. the value 0, by which those equations are trans- 

 formed into 



x^la-wcos^Jgf), 



Y=£(l-Wcose) + *!(JJ> 

 Z^ld-WcoseH^f). 



XL Proceedings of Learned Societies. 



ROYAL SOCIETY. 



June 17, 1875. — Joseph Dalton Hooker, C.B., President, in 

 the Chair. 



THE following Papers were read: — 

 " On a new Form of Dynamo-Magneto-Electric Machine." 

 By S. C. Tisley. 



In the first machines constructed by Siemens and Wheatstone in 



