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Ordinary Meeting, April 5th, 1881. 
E. W. Binney, F.R.S., F.G.S., President, in the Chair. 
“On Du Bourguet’s ‘Calcul’ and on Ternaries,” by Sir 
James Cockle, F.R.S, Corresponding Member of the 
Society. 
1. In “Notes and Queries” for June 12, 1880 (6th S., No. 
24, vol. I., pp. 469, 470), I have given a further bibliography 
of Du Bourguet’s ‘Calcul’, a work on which I have already 
commented (ante, vol. xix., pp. 9, 10; 181, 182). 
2. Doubting Du Bourguet’s calculations, so far as they 
relate to his example (6), I communicated with Mr. Robert 
Rawson who, in a letter to me dated May 3rd, 1880, replied 
that he found, after going over the work twice, that the 
criterion of integrability for (6) becomes 
and that Du Bourguet’s result is obtained by leaving out 
3. Mr. Rawson’s result will be verified if in Art 9 (infra) 
we put m—\-=.r and n—\. 
4 . This seeming error of Du Bourguet may perhaps be 
corrected by treating the x which multiplies the cube root 
in the coefficient of dy (ante, vol. xix., p. 9) as a misprint for 
some constant, r Tf wo cm*. 
wherein u = z — y — x, and his conclusion follows. Du Bour- 
guet’s theorem may be paraphrased thus, viz., “ a factor of 
U (the criterion of integrability being U— 0) may yield a 
solution if equated to a constant.” 
the first term from the above equation. 
Proceedings — Lit. & Phil, Soc. — Vol. XX.— No. 9.— Session 1880=81, 
