( 686 ) 



and the moments of inertia M/ and My and M xy , which furnish 

 the five equations necessary for the calculation of the unknown 

 quantities. 



We arrive at quite the same equations when the distribution of 

 the winds according to direction and velocity is regarded as a system 

 of accidental, directed quantities in a plane. The centre of gravity 

 then represents according to size and direction the constant part of 

 the wind which is supposed to be connected with all observations 

 and of which, therefore, the probability is equal to unity ; the axes of 

 inertia become principal axes of probability and the lengths M and 

 M' are replaced by the reciprocal lengths k and h', so that 



1 1 

 h' = , A' J = (1) 



The sum of the masses is put equal to unity and for the proba- 

 bility that an observation lies between the limits R and R -\- dR 

 of velocity and 6 and 6 -f dd as far as direction is concerned the 

 expression holds 



— e~ f{m RdRd6, (2) 



where : 



f{R,6)^h i [Rcos{6— p)— R cos(a— p)Y + h l *[Rsin(0 — $)— R sin(a— 0)]'.(3) 



In the language of the theory of errors i,/? ,«) would be the 

 so-called constant error, M and M' the greatest and smallest projections 

 of the mean errors. As observations of wind agree still less than 

 other meteorological quantities with the opinion held in the theory 

 of errors, where the constant part is regarded as the end of the 

 operation and the variable quantities as deviations, it is desirable 

 when applying the calculus of probability to quantities of this kind 

 to be entirely free of the terminology used in the theory of errors, 

 but which would be here without meaning and which would give 

 rise to misunderstanding. 



The treatment must also differ somewhat from that of erroneous 

 quantities, it being if not impossible at least impractical to correct 

 all the observations for the constant part. 



3. As examples of treatment two series of observations have been 

 selected from the treated material. 



a. Observations of wind performed at Bergen (Norway) during 

 20 years, 1885—1904, three times daily at 8 A.M, 2 P.M. and 8 P.M. 

 The velocity (or force) of the wind is expressed in the so-called 



