341 



ferred to, in which matter generally considered inanimate 

 assumes additional properties and becomes alive. Many argu- 

 ments were then brought forward to show that organic life is 

 the result of exalting inorganic life by combination of elemen- 

 tary properties. 



The following extract of a letter from Sir William Rowan 

 Hamilton to the Rev. Charles Graves was read to the Aca- 

 demy : 



" If I had been more at leisure when last writing, I should 

 have remarked that besides the construction 

 of the ellipsoid by the two sliding spheres, 

 which, in fact, led me last summer to an 

 equation nearly the same as that lately sub- 

 mitted to the Academy, a simple interpreta- i 

 tion may be given to the equation, 



9^ _m „2. 



TV 



np 



U(r,-0)" 

 which may also be thus written, 



pTl]-Bp 



TVJ 



92 - «2 



,-0 T(r,-0)" 



0) 



(2) 



" At an umbilic u, draw a tangent tuv to the focal hy- 

 perbola, meeting the asymptotes in t and v ; then I can 

 shew geometrically, as also in other ways, — what, indeed, is 

 likely enough to be known, — that the sides of the triangle 

 TA.V are, as respects their lengths. 



a + c; AT = a-c; tv = 2b. 



(3) 



Now my rj and 9 are precisely the halves of the sides av and 

 AT of this triangle ; or they are the two co-ordinates of the 

 umbilic u, referred to the two asymptotes, when directions 

 as well as lengths are attended to. This explains several of 

 my formulae, and accounts for the remarkable circumstance 



