19 



that as far as conducting power for liuat is concerni.'d, bolii tlie liut 

 and tlie cold metal should possess it in the highest degree. The 

 author is led by the striking analogy of the powerful repulsive action 

 of electricity in passing from a good to a bad conductor, to infer a 

 similar property in hoat, which, without entering into any specu- 

 lations as to the nature of those principles, appear to have a repul- 

 sive character in common indicated by a tendency to diffusion and 

 equilibrium. He conceives, that while some very delicate experi- 

 ments in France have given indications of the actual force exerted 

 by heat equally diffused through two adjoining masses, that the 

 energy in this case is produced by the accumulated repulsive power 

 in the last particles of the good conductor, the current (without 

 meaning any thing hypothetical by the term) being suddenly cut 

 short by the resistance opposed by the inferioi- conductor to its pass- 

 age. The destructive energy of electricity indicative of its repulsive 

 force, is never exerted in a state of equilibrium, but by the accumu- 

 lation of separate repulsive energies which take place in the transi- 

 tion from a good to a bad conductor, or during its passage through 

 the latter. 



2. On the Equations of Loci traced upon the surface of the 

 Sphere, as expressed by spherical co-ordinates. By 

 T. S. Davies, Esq., F.R.S.E. 



This paper is intended as a necessary supplement to the paper 

 bearing the same title already printed in the Society's Transactions, 

 though but an abridgment of a larger one which the author had pre- 

 pared on the subject. Particular circumstances induced him to alter 

 the plan he had originally contemplated, and instead of a complete 

 development in detail of his researches and his views, he has only on 

 the present occasion given so much of his results as were necessary 

 to bring the system of polar spherical co-ordinates to a state analo- 

 gous to that in which plane polar curves has long been stationary, 

 one point of the analogy excepted, viz. where the author has extend- 

 ed the method of treating tangents and normals, and the consequent 

 investigations dependent on these, by giving the polar equations of 

 those lines, instead of merely examining the relation between the 

 radius-vector, and perpendicular upon the tangent. In a note the 

 equations of the tangent and normal, to plane curves, is given from 

 first principles ; and the analogy between plane and spherical curves 

 is shown to be remarkably close. 



