Fundamental Ideas of Matter and Force in Theoretical Physics. 459 



cuprous chloride. The gas formed has no smell, it burns with 

 a luminous flame, and is not absorbed either by fuming sul- 

 phuric acid or by bromine. It is therefore not ethylene. It is 

 probably hydride of ethyle, C 4 H 6 , formed thus : 

 C 4 H 2 + 4H= C 4 H 6 . 



Acetylene. Hydride of ethyle. 



LXVII. On the Fundamental Ideas of Matter and Force in Theore- 

 tical Physics. By Professor Challis, M.A., F.R.S.,F.R.A.S* 



IN an article contained in the Number of the Philosophical 

 Magazine for May, I have completed the discussion and 

 exemplification of the mathematical reasoning proper for de- 

 termining the motion and pressure of an elastic fluid, so far 

 at least as that reasoning may be required for the mainte- 

 nance of the general physical theory respecting matter and 

 force, the principles of which I have on several occasions ex- 

 pounded in this Journal. I propose now, with the aid of the 

 mathematical results obtained in that and previous communica- 

 tions, to reassert those principles, and to answer certain objec- 

 tions to them which I have chanced to meet with in the writings 

 of my contemporaries. But before commencing this discussion, 

 I am desirous of adverting as briefly as possible to two points in 

 the mathematical reasoning which have recently appeared to me 

 to admit of further elucidation. 



The first point is the numerical determination of the velocity 

 of propagation in an elastic fluid. Assuming that the analytical 



expression for it has been correctly found to be al\-\ — ^-j , 



I propose to consider in what way the numerical value of the 

 factor by which a is multiplied may be obtained. In the course 

 of supplementary considerations relating to the Undulatory Theory 

 of Light contained in the Philosophical Magazine for May 1865, 

 I have shown that my first determination of the value of that 

 factor is erroneous, and have arrived at a different result by a 

 process the legitimacy of which I have not hitherto seen reason 

 to question. In this new method, instead of the equation to 

 which the mathematical reasoning conducts, viz. 



dr* + rdr + * e J~ {} ' 

 the integral of which can only be expressed in a series, another 

 equation, dJ df f 



d? + rdr +4,/ ~ r 2 ' 

 * Communicated by the Author. 



