On the relative poivei- of Metals to conduct Heat. 383 



■which the number of equivalents of the better conducting metal is 

 greater than the number of equivalents of the worse conductor ; for 

 example, alloys composed of lSn2Cu; ISnSCu; iSn 4Cu, &c. ; 

 in this case each alloy has its own arbitrary conducting power, and 

 the conductibiUty of such an alloy gradually increases and tends 

 towards the conducting power of the better conductor of the two 

 metals composing the alloy. 



Experiments were also made with bars composed of various metals 

 soldered together, in order to compare the results obtained with alloys 

 with those afforded by the same metals when mixed. 



The first part of the paper concludes Avith the conducting power 

 of several commercial brass alloys. 



The second part, which will shortly be published, will contain the 

 conduction of heat by amalgams. 



" On the Surface which is the Envelope of Planes through the 

 Points of an Ellipsoid at right angles to the Radii Vectores from the 

 Centre." By Arthur Cayley, Esq., F.R.S. 



The consideration of the surface in question was suggested to rae 

 some years ago by Professor Stokes ; but it is proper to remark, that 

 the curve which is the envelope of lines through the points of an 

 ellipse at right angles to the radius vectors through the centre occurs 

 incidentally in Tortohui's memoir " Sulle relazione," &c., Tortolini, 

 vol. vi. pp. 433 to 466 (1855), see p. 461, where the equation is 

 found to be 



{ 4 («' + 6' - a-h") - 3 (aV + bhf) ] 3 

 = {%a\2b'-a')sr + ^b\2d--h')y"-A{a^ + ¥){2a--1r){:2b--(r))\ 



an equation which is obtained by equating to zero the discriminant of 

 a quartic function. Tortolini remarks that this equation was first 

 obtained by him in 1846 in the 'Raccolta Scientifica di Roma,' and 

 he notices that the curve is known under the name of Talbot's curve. 



According to my method, the equation of the curve is obtained by 

 equating to zero the discriminant of a cubic function, and the equa- 

 tion of the surface is obtained by equating to zero the discriminant of 

 a quartic function. 



The paper contains a jfl-eparatory discussion of the curve, and the 

 surface is then discussed in a similar manner, viz. by means of the 

 equations 



=z{2-J^(X-4-Y- + Z0}, 



which determine the coordinates x, y, z oi &. point on the surface^ in 

 terms of X, Y, Z, the coordinates of a i)oiiit on the ellipsoid. The 

 surface, which is one of the tenth order, is found to have nodal conies 

 in each of the principal planes, and also a cuspidal curve. The case 

 more particularly considered is that for which «- '^ 21", b'- > 2c-, and 



