On the Porism of the In-and-circumscribed Th-iangle. 19 



currents, I may now sum up the cliief points ascertained. The 

 currents under consideration are not due to thermo-electric pro- 

 perties of the liquids, nor are they influenced in any material 

 degree by the simple thermo-electric properties of the metals. 

 They arise from a differential action of heat at the surface of 

 liquid contact of the two plates, and not from any action in the 

 body of the liquid, the latter functioning merely as a conductor 

 of the current. Hot platinum is almost invariably positive to 

 cold platinum in alkaline liquids, and as often negative in acid 

 liquids ; and as far as I have examined other metals, they are 

 the same, provided chemical action is completely or sufficiently 

 excluded. The currents obtained with platinum plates are not 

 due (except with a very few liquids, such as aqua-regia) to che- 

 mical action, but to some cause which I have not yet completely 

 determined ; whilst with base metals, both this cause and che- 

 mical affinity are in most cases operating ; the one tending to 

 produce a current in one direction, and the other in an oppo- 

 site one. 



86. As the currents obtained with platinum are extremely 

 minute, it is necessary to use a very sensitive galvanometer ; and 

 it would be an advantage to have an examiner with larger plates 

 than the one described, say of 4 inches diameter. 



Birmingbam. 



II. Supplementary Remarks on the Porism of the In-and-circum- 

 scribed Triangle. By A. Cayley, Esq.*- 

 IN my former papers (see Phil. Mag. August and November 

 1853) I established (as part of a more general one) the fol- 

 lowing theorem, viz. the condition that there may be inscribed 

 in the conic U = an infinity of triangles circumscribed about 

 the conic V = 0, is, that if we develope in ascending powers of k 

 the square root of the discriminant of k\] + V, the coefficient of 

 k"^ in this development must vanish. Thus writing 



disct. (ytV -<- U) = (K, ©, 0', K' JX-, 1)^, 

 the condition in question is found to be 

 302_4KCh)' = O. 

 The following investigations, although relating only to par- 

 ticular cases of the theorem, arc, I think, not without interest. 

 If the equation of the conic containing the angles is 

 U = 2ayz + 2bzx-\- 2cxy = 0, 

 and the equation of the conic touched by the sides is 

 V = »2 + ,/ + ~2 _ 2yz - 2^x - 2xy = 0, 



* f'ommunicatcd by tbc Atitlior. 

 C 2 



