18 
Proceedings of Royal Society of Edinburgh. [sess. 
Doing so, we find the series 
= 17*320512 820512 820512 820512 82...) 
*000004 744824 047577 546049 39 ... i 
= 17*320508 075688 772935 274463 4 ... . 
This gives us 
J3 =1*732050 807568 877293 527446 34..., 
which is correct to the last-written figure, that is to say, to the 
tiventy-sixth place. 
Note on Cayley’s Demonstration of Pascal’s Theorem 
By Thomas Muir, M.A., LL.D. 
(Received Aug. 17. Read December 16, 1889.) 
The demonstration referred to is given in the Cambridge Mathe- 
matical Journal , vol. iv. pp. 18-20. It opens with the enuncia- 
tion of a lemma to the effect that the intersection of the planes 
a Y x + b±y + c x z = 0, a 2 x + b 2 y -}- c$ — 0 , 
the intersection of 
a 3 x 4- b z y + c 3 z = 0, a 4 x + b$ + c 4 z = 0 , 
and the intersection of 
a b x + byy + c h z = 0, a Q x + b 6 y + c Q z = 0 
will he in the same plane if 
a 2 a s 
Now, first of all, this condition may be obtained in a different 
form as follows. If a point in the first intersection, we 
have evidently 
£12 : V12 : ^12 : : I V2I : M ' \ a A \ i 
