63 



The author, after referring to the paper printed in a former volume 

 of the Society's Memoirs, in which he has shown that the expression 



for the intensity depends on the integral / cos (w 3 —mw) between 



the limits w = 0, w — infinity, where m is proportional to the distance 

 of the point at which the intensity is required, from the geometrical 

 caustic, and in which he has calculated by quadratures the value of 

 the definite integral for different values of m as far as m=+4'0, 

 states that he was induced to have recourse to the method of qua- 

 dratures only because every expansion which he attempted made it 

 necessary to rely (for some of the terms) upon definite integrals 



equivalent to the integral /cos 9 from 9=0 to 9 = infinity, and that 



he was not satisfied with the reasoning upon which some mathema- 

 ticians had given a determinate value to that integral. Professor De 

 Morgan, however, who felt no doubts upon it, had furnished him 

 with a series proceeding by ascending powers of m, and had also 

 explained in detail (in a letter embodied in this paper) his views on 

 the evidence for the value of the series, and on the method of de- 

 termining it. From this series, the values of the definite integral are 

 computed for all the values of m for which the computation had been 

 made by quadratures, and the result is that the two sets of computed 

 numbers are entirely accordant. The computations are also extended 

 to the limit m= + 5-6, which is the greatest value to which it is 

 possible to extend the calculations by the use of 10-figure logarithms. 



May 22, 1848. 



Some Remarks on the Theory of Matter. By R. L. Ellis, Esq., 

 M.A., Fellow of Trinity College, Cambridge. 



The question to which these remarks principally relate is this : 

 Can all phenomena, e. g. those of chemistry, be explained mechani- 

 cally ? The writer, assuming that this question is to be answered 

 negatively, endeavours to determine what principles of causation, 

 beside, mechanical force, may be introduced into physical theories, 

 consistently with the doctrine that the secondary qualities of bodies 

 are to be explained by means of the primary. His conclusion is, 

 that we are at liberty, in constructing an hypothesis as to the mode 

 of action of matter on matter, to introduce a new principle of causa- 

 tion (which he calls (force) 2 ), bearing the same relation to force that 

 force does to velocity ; and further, that following the analogy here 

 suggested, we may introduce an indefinite number of such principles, 

 viz. (force) 3 . . . (force)", &c, all essentially distinct from one another, 

 and from those previously recognised. 



But, on the other hand, he conceives that it is necessary to reject 

 any modification of qualitative action ; and that consequently physical 

 science, though it may cease to be wholly mechanical, will yet always 



