Action of a Galvanic Coil on an external small Magnet. 435 



the intensities and lengths of the original elements of currents ; 

 and accordingly V sin 6 ds and V cos 6 ds will be like products for 

 the resolved parts of one of the original elements, and V sin & 

 cos e ds', V' cos 6' ds 1 , and V sin e ds those for the resolved parts of 

 the other. It is important to remark that these several pro- 

 ducts represent elementary moments of currents, and that the. 

 stresses required for maintaining these moments are, in fact, 

 those to which has hitherto been ascribed the generation of the 

 motions of the aether by the hydrodynamical operation of which 

 an element of one rheophore acts upon an element of another. 

 Now, according to what is said in art. 59, the original elemen- 

 tary currents and their resolved parts must all be supposed to 

 partake of the characteristic type of a galvanic current ; and 

 hence it may be shown, by arguing just as in arts. 55 and 56, 

 that an element of a rheophore acts upon an element of another 

 rheophore only by means of those motions due to the resolved 

 parts of the respective elementary currents which within the limits 

 of the element acted upon are parallel to each other. Hence 

 the velocities V cos 6, V' cos ff, and Y f sin e are excluded from 

 consideration. Respecting the exclusion of the first two more 

 will be said subsequently. 



63. From these preliminaries we may proceed to obtain a 

 formula for the action of either of the elements on the other. It 

 will, at first, be supposed that the element whose action is in- 

 vestigated is that to which the velocity V belongs. At the 

 distance r from the middle of this element, in the direction of 

 the line joining the middle points of the two elements, the 

 velocity transverse to that line may, according to the law ob- 

 tained in art. 43 and the argument of art. 62, be expressed as 



aV 



— sin 0, fjb being a constant factor depending on the dimensions 



and atomic constitution of the element whose action the formula 



is intended to express. The parallel velocity within the other 



element is V sin 6' cos e ; and as the action on the latter element 



will cceteris paribus be proportional to the number of its atoms, 



and that number is in some fixed proportion to ds*, the expression 



required may be supposed to contain the factor p' ds 1 , p' being a 



constant dependent on the constitution of the element acted 



upon. It must also contain ds as a factor, because the action 



of the elementary current is in a certain proportion not simply 



to the velocity V, but, as explained in art. 62, to the moment 



represented by Yds. Hence, by reference to the formula for 



d j) 



*£* obtained in art. 56, it will be seen that the complete expression 



required., inasmuch as the total action has a constant ratio to 



o ]? o. 



