( 690 ) 

 TABLE II. 



The sums fR, multiplied respectively by cos 8 and sin 6 and 

 divided by 1800, immediately furnish the quantities M x and M y ; 

 the sums fR* must be multiplied successively by cos* 6 } sin* 6 and 

 sin 6 cos 6. 



It is easier to multiply the latter sums by cos 16 and sin 28; if 

 the total mean is aS, we find : 



M x * — fR* cos* 6 =\S + \fR* cos W 

 My* = jR* sin* 6 —\S - \ fR* cos 26 

 2M xy = fR*sin26. 



So the whole operation greatly resembles the calculation of Fourier 

 terms; indeed, also by the way of operation indicated here an 

 analysis of the movement of the air is obtained. 



In the Tables III and IV we find the values of the wind-constants 

 calculated in this way ; besides the five characteristic quantities we 

 find still given as quantities practically serviceable for various ends: 



e = 



[/M*—M'* 

 M ' 



the excentricity of the ellipse of which M and 



M' represent the half principal axes, 



(R ' and a) the resultants of the squares of the velocities giving 

 an image of the mean flux of energy, 



V the mean velocity independent of the direction, 



V 2 the mean square of the velocity independent of the direction, 

 i.e. a measure for the total energy ; this quantity is according to (4) 

 analogous to the square of the mean error, not corrected for the 

 constant part, in the theory of errors, 



N~ the number of used observations. 



