values of the quotient : N,-,, where and N.^ are the numbers of spots belong- 

 inging to the different components of the frequency-surface. 



A'l Ni 



Zone 1.37 Zone 0.90 



_ » K, 2.12 » S., 2.93 



» iVg 0.73 » 0.97 



» N, 0.67 » 0.72 



» Nr, 0.74 » S^, 1.23 



» N,, 0.71 » S,, 1.30. 



On the other hand, several circumstances seem to indicate that the dispersions 

 in longitude are the same in both streams and likewise the dispersions in latitude. 

 Thus, we will assume that our correlation-surfaces may be divided into two normal 

 frequency- surfaces of the form 



(42) 



,271" 



Further we suppose m and n to be the means of F{x., y), and the moment Vy of 

 F{x, y) to be known. 

 In putting 



NF{x, y) = NJ,[x, y) + NJ,[x, y) 



according to Charlier, multiplying with x'-y' and integrating, the following equations 

 may be deduced, if the moments are taken about m and n. 



0 = N,{m^ — m) + iVo(w., - m) , 



0 = i\r>,-n) +N,{n^-i^), 



iVv,, = N^ia.;' + — my-) + + {m, — m)') , 



= N.iy-,' + {n, - nV) + + {n, - n^) , 



iV'Vjj = N^{mi — m) («, — n) + N^J^m.^ — ■ m){n,-, — w), 



N^j^^ = N^{3^.,'{m, — + (m^ — mf) + N,{3'y.,%m, — m) + [m^ — mf) , 



= i^^l(3a2^(^^, — n) + (w^ — nf) + Nl?>^..^[n^ — n) [n^ — nf) , 



i^v,, = -f (rV'K -'0' + k^, — n)') + N,{N,, + 6vjn, — nf + n^ — n)'), 



In the last two equations iV^^, and iS^^j designate the fourth moments of the 

 functions /^(x, \j) and f.jyX, y) . 



Introducing — m., and n^ — n., in stead of — m, — m , — n and 

 «2 — n by means of the relations 



(43) 



