1878.] 



of coordinates. 



181 



functions of {x, y, z) ; comparing the two forms for each set, we 

 have 



or' w = v-ya^, w-'n = n;' v, 



or, what is the same thing, 



where in each equation the two sides are matrices which must 

 be equal term by term to each other, but the matrices being- 

 symmetrical the equation thus gives (not nine but only) six 

 equations. Writing 



(a, b, c, f, g, h) = (1 - X^, 1 - /^^ 1 - v\ fiv — \, v\— /jl, X/a - v), 



and 



we have 



^~'=;^(a, h, g), 

 h, b, f 



g, i c 



and the first equation written in the form 



F(a, h, g)W=Ka„ 

 I h, b, f 



in fact denotes the six equations 



(a, b, c, f, g, h)( 





(«', /3', 7')' 



(a . P , 7 ) 



(a, ^' , 7')(a", /3", y") = KX„ 



(a, yS. 7)(a', /3' , r^') = Kv,. 

 And similarly writing 



(a„ bj, Cj, f^, g,, hJ = (l-\/, l-^^^ 1-///, /^ii^ -\, i^,\-/ii. \/^ -1^1), 

 and 



