268 Prof. Kelland's Reply to some Objections against the 



But in his Memoire sur la Dispersion de la Lumiere (Prague), 

 he gives the value of F as 



^ f2mfr . 2 &rcos&\ . n \ 



S \—f— cos z 3 cos y sin • — 2 — J" ^ p " * 



Had Mr. Earnshaw seen this last value, he would hardly have 

 conceived that it could be made zero by the symmetry of the 

 axes : he would have been convinced that the relative values 

 of /3, y, and 8, i, e. the relative directions of transmission and 

 of the axes, alone could effect that object. The fact is, that if 

 any one of the axes of coordinates coincide with that of trans- 

 mission, the three quantities do vanish ; in other cases they 

 do not. Mr. Earnshaw's oversight consists, then, in assigning 

 to an axis of symmetry a property which belongs only to the 

 axis of transmission. It is remarkable that Mr. Earnshaw did 

 not inquire into the cause of difference between his equations 

 and mine, for in form they are identical. [See Phil. Mag., 

 May, 1837, p. 388, and various other places.] I say it is re- 

 markable, for Mr. Earnshaw perceived that the cause of differ- 

 ence lay in the dependence or want of dependence of the equa- 

 tions of motion on the direction of transmission. All the 

 argument he offers in support of his view is contained in the 

 following words: — "Again, by referring to my former com- 

 munication, it will be seen that the equations of motion do not 

 depend upon the position of the front of the waves traversing 

 the medium" (p. 47). And this is in reality all the reasoning 

 on which he founds his remarks subversive of so many of my 

 conclusions. One word will serve to answer it. Mr. Earn- 

 shaw's former communication did not contain the equations of 

 motion on which his arguments are founded. These are to 

 be found only in the latter communication, and in a form 

 which does depend on the position of the front of the wave. 

 Having then shown that Mr. Earnshaw's argument is founded 

 in a mistake, I will adopt his language (p. 48), modified to 

 suit my own purpose : — 



I consider it therefore as proved incontestably, that according 

 to the finite-interval theory there is a connexion between the 

 directions of the vibrations and the law of molecular force. Hence, 

 then, I have established the transversality of vibrations on that 

 theory on a basis which defies opposition. 



Having thus shown that an error lies at the foundation of 

 all Mr. Earnshaw's objections, it might be deemed unneces- 

 sary to refute them in detail : yet since they are so plainly and 

 prominently brought forward as opposed to my conclusions, I 

 owe it to myself briefly to do so. They are, — 



1. "The vibrations have no necessary reference to the di- 



