THEOREMS IN TRIGONOMETRY AND ON PARTITIONS. 
[From the Messenger of Mathematics, vol. v. (1876), p. 164, and p. 188.] 
A+B+C+F+G+H= 0, 
sin A + F sin B + F sin C + F, cos F, sin F 
sin A 4- G sin B + G sin C + G, cos G, sin G 
sin A + if sin B + H sin C + H, cos H, sin H 
Let u n = number of partitions of n, no part less than 2, the order attended to; e.g. 
if n= 7, the partitions are 7, 52, 25, 43, 34, 322, 232, 223, u 7 = 8; the series is 
Mo = 1, 
u 3 = 1, 
«4= % 
u 5 = 3, 
m 6 = 5, 
u 7 = 8, 
Ms =13, 
u 9 =21, 
where each term is the sum of the next preceding two terms.