48 Mr. Earnshaw on the Motion of Luminous Waves. 



dium *. They show that a particle may vibrate in any di- 

 rection, and that the vibrations have no necessary reference 

 to the direction of transmission. And it is to be kept in 

 mind that we have found our equations without the aid of 

 any hypothesis respecting arrangement ; and therefore it 

 is impossible by means of arrangement to affect our results. 

 And, again, we have assumed no particular law as the law 

 of molecular action. I have elsewhere shown that there 

 are laws under which the motion of the aethereal particles 

 would not be a vibratory but a translatory motion : we have 

 rejected these laws in assuming that k 1 h 2 k 3 are all possi- 

 ble : but of all the laws which would give vibratory motions 

 and satisfy the known conditions of transmission we have re- 

 jected none : all possible cases are therefore included in our 

 results. I consider it therefore as proved incontestably, that 

 according to the finite-interval theory there can be no con- 

 nexion between the directions of the vibrations and the law of 

 molecular force. Hence, then, the transversality of vibrations 

 never can be established on that theory, and is therefore op- 

 posed to it. Perhaps it is proper to remark here, that I have 

 not taken account of the direct action of matter upon the aether; 

 but as my results are independent of arrangement, it is ob- 

 vious that the indirect effect of matter is included in them. 

 Consequently the indirect effect of matter never can assist us 

 in accounting either for the transversality of vibrations or for 

 dispersion. If, therefore, these facts are to be accounted for, 

 we must look to the direct action of matter on the aether. 



These are some of the results which I proposed to lay before 

 your readers in commencing these papers. They clear away 

 a great deal of mist from the finite-interval theory, and point 

 out the only direction in which we can look for success. Mr. 

 O'Brien has proceeded in that direction, and has announced 

 that in that quarter " the hypothesis of finite intervals cannot 

 be correct ;" if he succeed in establishing that position, and I 

 doubt not he will, the finite-interval theory may be laid aside, 

 and mathematicians will then be at liberty to pursue a more 

 promising hypothesis. In the first of my papers I gave my 

 reasons for thinking that those persons have fallen into error 

 who suppose that the theory in question has accounted for 



* For &i k'2 £3 are absolutely constant for a given value of * ; and by 

 transposing the coordinate axes back again from the axes of dynamical 

 symmetry to their original positions, we shall of course obtain the equa- 

 tions exhibited in that communication : and by the nature of this process, 

 the constants (i. e. A, B, C, D, E, F) will involve only k x £ 2 k s and the an- 

 gles of transposition : they are therefore independent of the position of 

 the waves' front. 



