280 Mr A. E. H. Love, On the Motion of a Sod [Oct. 29, 
Hence 
Lee ae QU — a 
b= Siena aA CERRO (era ee Baa. a 
2 ) (v— ae (v — ®g) 6a, Ow, 
h (A? + B’) By eG. an) 
+ 
6 (u-e,—@ 
Ga a) eXp [(7a + Np) (U+) — NaWa — Nae} 
[Fea | RUE ARON ERS Brindle brite. (32), 
where &, is a constant of integration and the terms not expressed 
are to be found from those put down by cyclical interchanges 
ofthe letters a, Saye. A, BCS (a,b, ce fa gn h 
12. The equations for + 7 and n—7 do not admit of 
complete integration in this form. Ifeg. we attempt to prepare 
the term X(A’+2X”) for integration, the part Reece on u is 
© (w—@,) © (u+u—a,) ( se =| 
Pit TRG a oe 21a Bend U)” 
which is equal to 
Go, © (wm —v) fF d (© (w— 2.4 v) } 
© (2a, — 0) | ae cc a Su - 7) ul 
Pe to FF ta, — blo. 
6 (u — 20, + : : Ly or 
|< gy exp( 20 — bv - ar) | 
by the formula for decomposition into simple elements. 
And since ¢€(@,—v)= ne ee 
the second term becomes 
We is 6 (u mats at) eT eee se 
This is proportional to 
6 (w+) et a 
Man exp( fv a)” 
