587 



h h' \ 



• • (1) 



f{R . d) = P [R sin {6— if) - aY + h" [R cos (^—3) - by ] 



i.e. the standard- value of directed quantities, on the one hand with 

 respect to between the limits 2.t and zero, on the other hand 

 with respect to R between Ihe limits go and zero. 



Both problems were treated in previous communications ') *), but 

 it may appear from the following that now a more principal, and 

 therefore more complete, solution can be obtained than seemed 

 possible a few years hence. 



2. If we wish to develop a function of one variable in an 

 infinite series of poljnomia 



71=0 



the quantities a can be determined so that — as in the Foukier- 

 series — for the assumed limits, « and '^ 



ƒ 



Un Um cU — 



for all values of m different from n. 



The constants An are then gi\'en by the equation : 



An fUn'd.V=:fF{w) Un d.V. 



The values of the constants a are determined by the ?i equations : 



CUn dx — 0, iUn X dx r= . . . \Un .t'"- ^ dx z= , . . (2) 



every integral being taken between the assumed limits. 

 By partial integration we have : 



1) The treatment of wind-observations. Proc. Sci. Kon. Akad. v. Wet. IX, 

 (684—699). 



2) On the Analysis of Frequency curves according to a general method. Proc. 

 Sci. K. Akad. Wet. X, (799-817). 



