c. V. L. Charlier 



+ OD 



(25) a(C) JlfcW =/^P ^(P) ^(^ + P)^^- 



— 00 



With respect to the distances between the components of double stars we 

 finally put 



(26) Y = ii^t' log ^1 ^ = ii^t. log A, r = eP, 



and obtain 



+ 05 



(27) c(y) = / r/p A(p) <î), (Y + p) 



and 



(27*) c(y) ilf^(r) A(p) <D,(Y + p) e?. 



• 00 



+ 00 



where A(p) has the same expression as before (24*). If the density of the double 

 stars is assumed to be different from the density of the stars in common (which 

 is however not necessary to assume), the function A(y/) in (27) and (27*) differs 

 from (24*). 



In (21) and (22) there occurs another density function than in (24) etc. This 

 difference may however be made to vanish. Introducing for m another quantity w 

 through the relation 



(28) n = — hm 

 and putting 



(28*) cE>,(a.) = ^_| 



the equation (11*) may be written 



+ 00 



(29) a{m)=fdpàip)%{n + p) 



— 00 



and then we have 



+ 0C 



(29*) a{m) M^r) = / dp A(p) (i>^(n + p) e?. 



— cc 



All equations are now of the same mathematical form. 



The integral of Fourier. Before going on to the mathematical solution of these 

 equations I shall give a simple demonstration of a celebrated theorem of Fourier 

 which is of great use in the consideration of the problems in stellar statistics. 

 The line of thought used in the derivation of the theorem is identical to that 

 followed in my deduction of the general formula in the theory of errors. (Meddel. 

 N:o 25, 26 and otbers). , 



