450 Prof. Challis on the Hydrodynamical 



along a rectilinear axis. The assumption was required for 

 satisfying that condition. 



(3) In the statement of the fundamental principles of the 

 general theory of the physical forces, one of the adopted hy- 

 potheses is that atoms are spheres admitting of no change of 

 form or magnitude. At the same time it was asserted that 

 this hypothesis is one of those which require to be verified by 

 comparisons of deductions from them with experimental facts. 

 I did not, however, refer to certain theoretical results I had 

 obtained which actually afford such verification. These results 

 are given in a dissertation entitled " The Hydrodynamical 

 Theory of the action of a Galvanic Coil on an external small 

 Magnet/' which is divided into three parts, contained respec- 

 tively in the Numbers of the Philosophical Magazine for Sep- 

 tember, November, and December 1874. The hypotheses on 

 which the theory rests are stated in art. 1 of the dissertation, 

 and are identical with the fundamental principles referred to 

 above. In a postscript to the article in the November 

 Number two sets of numerical comparisons of the theory with 

 observation are exhibited ; and at the end of the dissertation 

 in the December Number (art. 76) a summary is given of the 

 grounds on which the whole theory may be regarded as satis- 

 factory. What I am now concerned with is to state that this 

 theory depends essentially on the hypothesis that atoms are 

 spherical in form and of constant magnitude, and that the 

 satisfactory conclusions to which it leads are confirmatory of 

 this hypothesis. 



(4) Since in the above-mentioned dissertation there are 

 some remarks which might be supposed to imply that the 

 hydrodynamical theory is not in complete accordance with 

 the formula obtained experimentally by Ampere for the mu- 

 tual action between a galvanic element and a magnetic ele- 

 ment, I take occasion to say that I have since seen reason to 

 conclude that the accordance is quite satisfactory. I have 

 adverted to this point because in Clerk Maxwell's i Treatise on 

 Electricity and Magnetism' (vol. ii. p. 16) that mutual action 

 is expressed in four different forms, and the formula of Ampere 

 is considered to be the best. It is evident that on such a ques- 

 tion there should be no uncertainty, and that a good theory 

 ought to be capable of deciding whether or not a proposed 

 formula is true. According to the hydrodynamical theory 

 which I have advocated, Ampere's is the true formula. 



(5) To the " few results " obtained under Parts II. and III. 

 of the general hydrodynamical theory, which are cited in the 

 January Number (p. 31), and considered to be confirmatory 

 of that theory, I might have added the explanations it is 



