( 816 ) 



§ 5. Indefinite limits, two variables. 



The treatment of wind ()l)ser\'ti(ions now oilers no (lifficnlties as, 

 in calenlating the means of diiferent order, the two variables (pro- 

 jections upon two axes arbitrarily chosen) can always be separated 

 and the method remains in all other respects qnite the same. Only, 

 instead of one mean of each order, we can now dispose of ji -\- J 

 means of order p. 



If by I'^, be denoted the same fnnction of // as / ',, is of ./;, the e([n. 

 of the cnrve assnmes, as l\, = K„ = 1, the form : 



n{.v,y) = e-^'-f [/lo + ^'li.o l\ + A^a Vi + .la.o ih + vli.i T, K, + Ao.i F, 

 + yi3.o Tg + ^2.1 U. V, + .4, .2 U, V2 + ylo., V3 -f etc.] . (30) 

 The general expression for the polynomia is : 



and as, evidently -. 



— 00 — 00 



for all valnes of /> ditferent from n and of q different from in, we 

 find for the .1-coeff. : 



— 00 - 00 



where : 



:-l 





From the considerations of § 4 it follows that thi function : 



may as well be gix'en the form : 



(/" ■ '" '/""!"'" 



d.v"di/"' d.r"dif" 



as this satisties the j)remised condition : then the series (30) assumes 

 the form of a sum of ditf. (|uot. like the series of Brl'ns and 



in accordance (o which (31) has to be modified. If it is possible to 

 remove the origin of coordinates to the arithmetical mean by a correction 

 of the |)rojections for their average value, then the terms with the 

 coeff. A\i.) and .lo.i vanish from (30). 



If w'e wish to alter the scale values according to the nature of the 



