430 
[948 
948. 
REPORT OF A COMMITTEE APPOINTED FOR THE PURPOSE 
OF CARRYING ON THE TABLES CONNECTED WITH THE 
PELLIAN EQUATION FROM THE POINT WHERE THE WORK 
WAS LEFT BY DEGEN IN 1817. 
[From the British Association Report, (1893), pp. 73—120.] 
We have, on the Pellian Equation, Degen’s tables, the title of which is “Canon 
Pellianus sive Tabula simplicissimam aequationis celebratissimae y 2 = ax 2 + 1 solutionem 
pro singulis numeri dati valoribus ab 1 usque ad 1000 in numeris rationalibus 
iisdemque integris exhibens.” Autore Carolo Ferdinando Degen. Hafniae, apud Ger- 
hardum Bonnierum, mdcccxyii., 8vo. Introductio, pp. v—xxiv. Tabula I. Solutionem 
aequationis y 2 — ax 2 —1=0 exhibens, pp. 3—106. Tabula II. Solutionem aequationis 
y 2 — ax 2 +1 = 0, quotiescunque valor ipsius a talem admiserit, exhibens, pp. 109—112. 
The mode of calculation is explained in the Introduction, and illustrated by the 
examples of the numbers 209, 173. 
As to the first of these, the entry in Table I. is 
209 
14, 2, 5, 3, (2) 
1, 13, 5, 8, 11 
3220 
46551 
where the first line gives the expression of V209 as a continued fraction, viz. we have 
V209 = 14+^ l 
1 
1 
1 
1 
1 
— \ &c., 
2 + 5 + 
3 + 
2 + 
3 + 
5 + 
2 + 
28 + 2 + ’