﻿368 Prof. Challis on a Theory of Mutual Action 



possess analogous properties, provided that in the latter the con- 

 dition 



d ( bf—ce \_ d / be — af \ ,,,. 



dy\ac-bV~ dx\ac-b*) * . ." * " V } 



is satisfied. When all the coefficients of the quotoid are constant, 

 then (11) is satisfied, and the critical functions and the criticoids 

 have the same forms and values. In other cases they, in general, 

 are of different forms and values. When the group (3) holds 

 both for quotic and quotoid, and the coefficients of the latter are 

 constant, the critical and criticoidal functions are substantially 

 identical. When such coefficients are variable, and a, b, and e 

 are equal, then the critical and criticoidal functions have the 

 same form, though not the same value. When (9) is satisfied, 

 the criticoid is definite. When (9) is not satisfied, the criticoid 

 contains an arbitrary function, which should be so assigned as 

 to give the simplest or most useful transformations. The name 

 fractional criticoids sufficiently marks the criticoids discussed in 

 this paper. 



" Oakwal," near Brisbane, Queensland, 

 Australia, January 11, 1871. 



XLIX. On a Theory of the Mutual Action between Electrified and 

 Magnetized Bodies. By Professor Challis, M.A., F.R.S., 

 F.R.A.S* 



I HAVE given a theory of Electric Force in the Number of 

 the Philosophical Magazine for October 1860, a theory of 

 Galvanic Force in that for December 1860, and a theory of Mag- 

 netic Force in the Numbers for January and February 1861. 

 The same theories are reproduced, with corrections and amplifi- 

 cations, in my work ' On the Principles of Mathematics and 

 Physics/ It is known from experiment that these three kinds 

 of physical force are distinctly separated from each other in re- 

 spect to the conditions under which they are generated. For 

 the generation of electric force it is necessary to employ friction ; 

 galvanic force has its origin in the chemical action between two 

 dissimilar substances in contact, or in a tendency to such action ; 

 and magnetic force is due either to the natural condition of sub- 

 stances like the loadstone, or to artificial magnetization. The 

 experimental evidence of the reality of these forces is derived, 

 as in the case of the force of gravity, from the motions, and ac- 

 celerations of motion, which they are observed to impress on 

 visible or tangible substances. 



Now, according to the above-mentioned theories, the three 

 * Communicated by the Author. 



