I9I2.] OF THE GLOBULAR CLUSTERS. 135 



ters, yet it seems worth while to examine the results which will 

 follow from this law. In A. N., 4053, p. 327, it is shown that 



where the expression for fx, with the correction noted in A. N., 4104, 

 p. 386, is 



x^ x^ x"^ x^ igx^^ 2yigx^^ 



^~ 3 ~ 20 240 3888 1425600 4447872000 



20621.1'^^ IQ3^28.t'"' , , 



-J ^^^ . (7,7) 



800616960000 190546836480000 ^^^ 



39667364.^'^ 8078124341,1-^^ ^ ^ ^ 



1042672289218560000 591 1951879869235200000 



Now if we substitute the value of a/o-Q from (36) in the integrals 

 of (35), they are reduced to two series which may be called /x and /, 

 the latter having the same form as (37) but the limit x' instead of .r. 

 Accordingly (35) becomes 



[3 20"^ 240 3888 "^ J 



~G^'^'~ Vx>^ x'" x'' x'" 



x' 



Vx'^ x'" x^ ^ "I 



LT~2o "^240 "3888"^ "J 



,.4 ,.6 



(38) 



_ ''" 1 3 ~ 20 + 240 ~ 3^888 + • • • f 

 ~ \\ x'" x'' x'' 1 ■ 



■'' |3~20 + 24o"~3S88+*""J 



As the coefficients of the series jx and fx are the same, we may cal- 

 culate from the equation (37) or (38) the value of the ratio at 

 suitable intervals throughout the sphere, and ascertain rigorously 

 the law of the variation. The results of my calculations are given 

 in the following table and illustrated by the corresponding curve 

 in Fig. I. 



