Absorption of a Beam of Heterogeneous Rontgen Rays. 781 

 where 



,\9 



M y — M 



= € 1 , V =€ 2 > ? = 



Eliminating Aj . . . A n from the first (n+ 1) equations, we 

 have 



Vo> 



1, 



yn ft */> f • • • 



y 2 , £ 2 , t, r 2 ... 



0. 



.yn, r, v i , r... 



Expanding the determinant, we get 



^oDo+^iD 1 + // 2 D 2 +... = 0, . . . . (1) 

 where D s is the minor corresponding to y S9 and is equal to 

 1, 1, 1 



ft v, K 



+ 



the row £ s , 77% £ s . . . being left out. 

 We easily see that 



D s = P . S„ 



where P is the product of all the differences of f, 77, f, i. £. 



(?-■>/)(?- ?)(?-«).. . 



and S the sum of the products £, 77, f taken n-s at a time. 

 S = ffyfo S, = &?£+ ft?* 4- . . . 



Since P is a common factor of the D's, we may write 

 equation (1) as 



ySo— yiSi+y a Sj... = 0. 



By eliminating A l5 A 2 , . . . A n from the n equations 

 beginning with y\ instead of ?/ , we get 



yiS — y>Si+y 8 Ss- .. = ; 



and similarly a o , o a 



down to a o , o (\ 



