( 695 ) 



So among a thousand observations there will be 393 lying 

 inside this typical ellipse whilst the specific probability of each of 

 the velocities R m is : 



0.6065 



V?-< 



rr 



In the given diagram such a typical 

 windellipse is represented for Bergen in 

 the month of June by the dotted line • 

 the vector OC represents here the constant 

 part (R , a), the half axes are equal to M 

 and M', and the angle NOM = fi; one 

 millimeter corresponds to 3 / in Beaufort scale- 

 value or to */„ X 1-83 = 0.275 meter a 

 second. 



If necessary this diagram might be am- 

 plified with two circles, one of a radius 



l/if 1 + M'\ 



representing the mean monthly wind velocity corrected for the 

 constant part, the other described with radius 



I/if ' + AT* + (M x y + {M y f, 



which is according to (4) a measure for the mean total velocity, 

 corresponding to the square root of the quantity F s of the tables 

 III and IV. 



An other remarkable ellipse which might be called the probable 

 windellipse is obtained by requiring half of the observations to lie 

 within its dominion ; we have then to determine c in such a way that 



1 - e- c = 7, , c = 0.6932, 



so that the axes of this ellipse are 



[/2c — |/2 X 0.8326 = 1.177 



times longer than those of the typical windellipse ; the number 0.8326 

 is a quantity known in the theory of errors in the plane. 



7. The frequency of the windvelocities, setting aside the direction, 

 cannot be represented in a finite form ; we can arrive at a form 

 serviceable for comparison with the observation by writing (5) thus: 



i/p'-q* 



—uR* 



T 



,-**-*>** BdBM, 



(8) 



