Address of the Secretaries of the British Association. 441 



j — 



fr- r t,—a bcvi 



& c* (f 2 + w a + C 2 ) + at*ee-abctf' 

 Putting those values of x if z 1 in (a), and making 



V = frc 1 (f+« 2 + ? 2 ) + 2 ac'eg-a 2 f-c\ 

 we shall find for the resulting equation 



b A c* a { 2 b cy £ — c-^f— «e 2 }V = 0, which is satisfied by 

 putting V = 0, or b- c 2 [P + u°~ + J») + 2 a c 3 * f = a* >f + c a , 

 the tangential equation of an ellipsoid of revolution whose 

 focus coincides with the origin. It is easily shown that the 

 tangential equation of the given surface referred to the same 

 origin and axes is &~(£~ + tr) -+- c 3, £ 2 + 2 a e£ = 1. 



Hence if the given surface is a surface of revolution >j = 0, 

 and the locus found becomes identical with the given sur- 

 face, as is otherwise known. 



When the given surface is an oblate spheroid e = 0, a = b, 

 and the locus becomes c°- (£ 2 + u 1 + £ 2 ) = 1, the tangential 

 equation of a sphere described on the axis of revolution of 

 the oblate spheroid as diameter. 



Similarly may it be shown, that if through any fixed point 

 in space, a right line and a plane are always drawn at right 

 angles to each other; the former meeting a fixed plane in 

 a point r, and the second intersecting another fixed plane in 

 a right line m m' ; the plane ?nm'r envelopes a surface of re- 

 volution of the second order, one of whose foci is at the fixed 

 point. 



In a future Number, after treating of the general and 

 numerous kindred properties of the two surfaces of the se- 

 cond order, whose generatrices are right lines, the author 

 proposes resuming this subject, and developing briefly a 

 general method, by the theory of reciprocal polar s, of de- 

 monstrating these and other similar theorems, many of which 

 want of space has compelled him to omit in the present com- 

 munication. 



LXIV. Address of the General Secretaries qfthe British Associa- 

 tion, Roderick Impey Murchison, F.R.S., F.G.S.,and 

 Major Edward Sabine, V.P.R.S.: read at the Meeting 

 at Glasgow, September 1840. 



TN entering upon the duty assigned to us, we heartily con- 

 ■*• gratulate our associates on this our second assembly in 

 Scotland. As on our first visit we were sustained by the in- 

 tellectual force of the metropolis of this kingdom, so now, by 

 visiting the chief mart of Scottish commerce, and an ancient 



