• 7 



(a = .y), hence k. = oo; and in the opposite limiting case n = s {a : .v= oo). 



'/,rr 



hence k^O, approaches k | .sin ip X \p d xp =:^ ki^ \p cos tp + 







+ I cos \p (l\p]=z k ( — \\y cos- \p 4" "^"^'^ ^)' which yields the value k 



between and Va-'^- 



Hence the integral in question lies between Vs^ ' and k = s: Va^ — s^ = 

 z:zzs:a^=zti (as in the latter case s is infinitely small with respect 

 to a), so that we can represent it by 



in which f will lie between 1 (when n = 1) and S : Jt^ = 0,811 

 (when n = 0). Accordingly the factor 8 is little variable. It appears 

 from the expansion into series (see Appendix A), that e becomes 

 = 0,845 for n = 0,6 (i. e. s = 0,Qa)- 

 We now have : 



(A). 



1 



2a 



i^' 



Bg" t9^\ — ^nX\n' 



so that taking the factor to yi {2a* -. s [a"^ — 6-^)) into account, the fol- 

 lowing equation is found : 



(a,), = to X 



w(l— n') 



li nis near \ [a ^ s), this approaches to X 



i;i'(l - en)- BgUg 

 1 



l/l-«'' 



• (11) 



■71' 



[i.V(l-n)-(l-n')l: 



= tü X d^" — 1) = 0,234 to. The limits of integration p and ,r, are 



s' a'—s" 



determined by .r," = 1 (l + y) = - 



a" a' 



temperatures ((p = 0), resp. (0) at lower temperatures {<f = <ƒ„) , and 



(l-f-f/) = — — = 1 —n' = ±0 at high 



/> - 



.r/ = (1), resp. (0) ; so that (9 lies between (0°) and ± 90' 



a — s 



at high temperatures, and (90'^) and (90°) at lower temperatures. 

 And if n is near (a great with respect to s), then (aji approaches to 



a>X— X [{i:t'~2n)—{i^'—jrn)] — m X (:t— 2) := 1,14 to . Then we 



71 



have as limits of integration ± 1 for j-^ (^/^ = 0), resp. (0) at rp =r rp^, 

 and (1), resp. (0) for /> ; so that /9 lies between (0°) and ± 0° at high 

 temperatures, and (90°) and (90°) at low temperatures. 



When (a.Jj is added to aj, we find for the part of the constant 

 of attraction a that is independent of the temperature (coming from 



