452 Mr James, The Theoretical Value of Sutherland's 

 The numerical values of RSjcji {a) are as follows : 



n 

 RSI(t> (a) 



4 

 0-213 



5 

 0196 



6 

 0-183 



7 

 0-172 



0-163 



9 

 0-156 



Prof. Chapman's value is 0-333 in all cases. The calculation is 

 very simple for n odd, from w = 9 (inclusive). The other values 

 are more troublesome. The value f or w = 8 was interpolated merely. 



§ 7. We proceed now to the same calculation for the law of force. 



f{r) = A, a<r<aa, 



/ (r) = 0, r > aor. 



^{or) = Aa{a-1). 



dr Aj) f'^'^^ fpY^dr 



2_^2)i~ V^ ' ^^^ 



Thus 

 Hence 



'A= T72 



Ap 



_ Ag 



- F2 



logo: 



1 2r f 2r 



•/ o- 

 acr) 



ff^dr 

 \r J r ' 



This leads to 

 where 



00 



noga+S/fSr+i 

 1 2r 



1 



^Q."{V) = lQAa^7^K|V, 

 (r+1) 



r 2r (2r + 3) (2r + 5) (2r + 7) |^ «2.| + Jos ^""^ '^• 



By comparison with § 6 we can at once write down the number 

 corresponding to A„', namely 



h: = 2ih^l{a-l). 

 In this way we draw up the table 



RSI^fi (a-) 



1-25 



0-166 



1-50 



0-206 



1-75 

 0-227 



2-00 

 0-241 



2-50 

 0-259 



3 4 



0-270 0-283 



MS/cj) (o-) 



5 



0-291 



6 7 



0-297 0-301 



9 



0-304 0-307 



10 

 0-309 



§ 8. For a given value of (a), Sutherland's constant S decreases, 

 so that finally for a thin shell of intense force it vanishes. The result 

 is thus, to this order at any rate, the same as for elastic spheres 

 exerting no force. 



Thus suppose / (r) = for r > a+ t, while O {a) = [" f{r) dr 

 remains finite. This gives without approximation 



