592 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
43d Meeting. May 16, 1888. 
The Chairman presided. 
Present, thirteen members and guests. 
The minutes of the 42d meeting were read and approved. 
Mr. Artemus Martin presented a paper on An Error in Bar¬ 
low’s Theory of Numbers. The following is an abstract: 
[Abstract.] 
It is stated on page 299 of Barlow’s “ Theory of Numbers ” that “ the 
equation 
x 2 — 5658 y 2 = l 
has the least values of x and y as follows, viz: 
x =166100725257977318398207998462201324702014613503, 
y = 698253616416770487157775940222021002391003072.” 
But I have found the least values of x and y satisfying this equation to 
be— 
x = 1284836351, 
y= 17081120. 
As J3arlow’s value of x contains three more figures than his value of y, 
it is plain that the coefficient of y 2 should contain five figures, and that he 
(or some one else) left out one of them. Our problem is to determine and 
locate the missing digit. 
From x 2 — Ny 2 = 1 we easily obtain 
very nearly when x and y are large numbers; 
. *. - = •/ N very nearlv. 
y 
In the example under consideration I find 
~ = 237.8802219 +, = / 5658Y 
Hence it appears that the last figure, 7, of the coefficient of y 2 was left out, 
probably by the compositor, possibly by the writer of the “ copy.” 
I have computed the least values of x and y in the equation 
x 2 —56587 y 2 = 1, 
and find them to be correctly given by Barlow. 
