( 239 ) 



(a'2-a'i) j ia:-h)-{a\-bi) } + 2 A,r |(l-.^) («'i -^-i) + .^«'2-^-2) j " 

 — 2 Ai j (1 - -r) n\ 4- ,r rt'o j — 2 .r (1 — .7-) Ar,' (A„' - 2 Ai). 



.r(l — a) 

 So this quantity taken times represents the first eorree- 



tion of A,> , wliereas .« (1 — r) (Arc — A;,) represents the limitino- 

 value of this quantitj' — so tliat for •'• near zero tlie value of 

 Aw is equal to 



(a'2-a'i) j (rt'a-is) - («'i-^i) j + 2 A„' (a I -bi)-2 Ai (i\) > 

 41-.') (Ar/-A/,)+ ^ ) 



and for t near 1 equal to 



(«'2-a'i) i (aW'2) - («i-Z»!) j + 2 A„' (a'a - ^ - 2 Ai «'3 



;r(l_.r) (Aa'-Ai)+ — 



I «2 



So there is a distinct asymmetry, as soon as a'2 — ^'3 is sensibly 

 greater than a'l — Z»i, but the different cases that may occur are so 

 numerous, that it is better for the present not to enter into a fiirtlier 

 discussion, as the experimental data are wanting. 



Yet it should be observed that the asymmetry is not so great as 

 to account for tlie circumstance that Mr. Kuenen's values for (A/,)' ') 

 at A' = ^/4, •(• = V2 and r = 1/4. differ so little, while with scarcely 

 an exception the highest value is given at a; = ^/^. 



As, however, the accurate value of A» requires too intricate cal- 

 culations to draw general conclusions from them, we shall have 

 recourse to the graphical representation, in order to give at least 

 an idea of the course of this quantity. 



Let us consider for this the formula : 



A« = (1 — .«) {v'l — vi) + X {v'2 — t'n) — {v'x — v), 



from which appears, that A« may be considered as resulting from 

 three separate quantities, viz. v'l — vi, v'^ — v^ and v' — v. Each of 

 these quantities, which have been discussed before, may be repre- 

 sented by curves as have been drawn in the following figure. 



') Proc. Nov. 2üth 1S98, p. 18i. 



