1883.] Prof. Cayley, A new form of equation, etc. 321 



writings of no mathematician could shew a higher average. Great 

 and irreparable as was the loss caused by his death, it was yet 

 some consolation to feel that what he had left formed a worthy 

 memorial of his powers and of the brilliance of his genius, and 

 that his permanent place in the very highest rank of mathe- 

 maticians was assured to him. 



Professor Cayley endorsed every word Mr Glaisher had said : 

 it was impossible to speak in too high terms of the value of 

 Professor Smith's work. His wonderful knowledge of the processes 

 of the higher parts of the Theory of Numbers shewed itself in 

 everything he did. His work was of the very highest quality and 

 excellence, and he could not too strongly express his sense of the 

 great loss caused by his death. 



The following communications were made to the Society : 



(1) A new form, of equation of the lQ-nodal quartic surface. 

 By Prof. Cayley*. 



It was shewn that if x, y, z, f, rj, £ be homogeneous linear 

 functions of four co-ordinates, subject to the identical relations 



x + y + z + £ + i7 + ?=0, 

 ax + by + cz +/| + gy + h%= 0, 



where af= bg = ch = 1, then *J~x% + Nyr\ + Vg^= is the equation 

 of a quartic surface having the sixteen singular tangent planes 

 (each touching it along a conic). 



x±=0, y = 0, z = 0, £=0,77 = 0, f = 0, 

 x + y + z = 0, ax + by + cz = 0, 



%+y + z=Q, f£+by + cz = 0, 



x + 7] + z = 0, ax -f gn + cz = 0, 



x + y+£=Q, ax + by + h£=0, 



y 



+ r-2— + =-=-,« 0, v-^+7-V^+r-V=0. 



1 - be 1 - ca 1 - ab ' 1 - gh 1 - hf \-fg 



(2) On the mean radius of coils of insulated wire. By Lord 

 Eayleigh. 



In electrical work it is often necessary to use coils of such 

 proportions that their constants cannot well be obtained from the 

 data of construction, but must be determined by electrical com- 

 parison with other coils whose proportions are more favourable. A 

 method for comparing the galvanometer-constants of two coils, 

 i.e. of finding the ratio of magnetic forces at their centres when 



* This paper is published in full in the Journal filr die reine und atifiewandte 

 Matheviatik, Bd. 94. " On the bitangents of a plane quartic." 



