194 Proceedings of Royal Society of Edinburgh, [april IS, 
Monday, 18 th April 1887. 
Sir WILLIAM THOMSON - , President, in the Chair. 
Professor Rowland’s Photographs of the Solar Spectrum 
were exhibited by the Astronomer-Royal for Scotland. 
The following Communications were read: — 
1. On Ship -Waves. By Sir W. Thomson. 
2. On the Instability in Pluid Motion. By the Same. 
3. Experimental Research in Magnetism. By Mr D. S. 
Sinclair. Communicated by Principal Jamieson. 
4. On the Summation of certain Series of Alternants. 
By A. H. Anglin, M.A., LL.B., &c. 
1. The summations referred to in the title depend on two 
theorems — one already known, the other not hitherto published. 
The first of these is to the effect that the quotient of any simple 
Alternant by the difference-product of the variables is expressible as a 
determinant whose elements are sums of homogeneous products of the 
variables. For example, 
1 a p a q a r 
1 IP b q b r 
1 c p c q c r 
= if (abed) 
1 d p d q d r 
0-1) 0-2) 0-3) 
0-1) 0-2) 0-3) 
0-1) (r- 2) (r-3) 
where, generally, ( n ) denotes the sum of the homogeneous products 
of a, b, c, d of n dimensions. 
The other theorem may he enunciated, in a particular instance, as 
follows : — 
If three rows of four quantities each be taken, as 
a n 
Clc, 
a 3 
h 
a . 
c l c 2 C 3 C 4 J 
