Mr. J. Cockle on a New Species of Differential Equations. 37 



ing powers given by us only serve to show that the amalgams 

 do not conduct electricity in the ratio of the conducting powers 

 of the relative volumes of the components as one might a priori 

 have thought. If such calculations were not made, we should 

 sometimes be unable to get an insight into the laws which regulate 

 those properties ; thus, for instance, it is only from having calcu- 

 lated the conducting powers in this manner of the solid alloys that 

 we have been led to discover the method of calculating the per- 

 centage decrement in the conducting power of an alloy between 

 0° and 100° ; in fact the calculated conducting powers are neces- 

 sary to do this. We have already mentioned that it is more than 

 probable that, when metals are dissolved in one another, the part 

 which they then take in the conducting power of the alloy is the 

 same whether the resulting alloy be a solid or a liquid one. 



In the foregoing we have assumed, with the hypothesis from 

 which we started, that the amalgams are merely a solution of 

 one metal in the other ; but in the case of those of zinc, we have 

 already pointed out that with the richer ones this is not the case ; 

 and as we at present know so little regarding the chemical nature 

 of the amalgams, it seems to us that Dr. Siemens's hypothesis, 

 based only on the determination of six amalgams, viz. three with 

 zinc and three with silver, was rather premature. That chemical 

 combinations exist in the amalgams is more than probable from 

 the experiments of Joule*, Crookewittf, and others; so that it 

 is clearly wrong to try to deduce laws respecting the parts the 

 components take in the properties of the alloys from a few ob- 

 servations, where we have no knowledge as to their chemical 

 nature. 



11 Torrington Street, 

 June 1862. 



VI. On a New Species of Differential Equations. 

 By James Cockle, M.A., F.R.A.S., F.C.P.S. fyc.% 



IN a paper § published in this Journal for May 1861, I an- 

 nounced and demonstrated that from any algebraic equation 

 of the degree n, whereof the coefficients are functions of a variable, 

 there may be derived a linear differential equation, of the order 

 n— 1, soluble by means of the given algebraic equation. Apply- 

 ing this theorem to certain trinomial equations, Mr. Harley has 

 discovered new primary forms of linear differential equations ||, 



* Chem. Gaz. 1850, p. 329. 



t Ann. der Chem. und Pharm. vol. lxviii. p. 289. 



% Communicated by the Author. 



§ "On Transcendental and Algebraic Solution," S. 4. vol. xxi. p. 379. 



|| See the ' Proceedings of the Literary and Philosophical Society of 



