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823 
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6. On Tungsten. By John Waddell, D.Sc. Communicated 
by Dr Crum Brown. 
7. On Certain Theorems mainly connected with Alternants. 
By A. H. Anglin, M.A., LL.B., E.B.S. (Edin.), &c. 
1. It is well known that if h n denote the sum of the homo- 
geneous products of a, b, c, . . . I of n dimensions, while li' n refers 
similarly to b, c, d, . . . I, then 
h n = h n ah n _ ! . 
The proof, which is very simple, may be stated thus : — 
We have 
h n = a n +a n ~ V? \ + a n " Vi 2 +■...+ a?h' n _ 2 + ah' n _ x + h' n 
= a(a n ~ 1 -\-a n Vi' x + a n 3 A 2 + . . . +u// n . 2 + h! n _ x f -\-h' n 
— ah n _ j + h n , 
that is, 
h' n = h n -ah n _ 1 . 
