( 694 ) 



found by integrating (5), first with respect to R between the limits 

 R c and 0, then with respect to S between 2.t and 0. 



For the simple case R = 0, so also (t = and ;. = 0, the 

 first integration gives immediately 



|/y_ 9 » l—e-c 



n 2v 



and as 



2tt 



^f 



rdê 

 — = 1, 



2jt 



u 



the probability to be found becomes simply : 



1— e~ c (7) 



and the number of observations lying inside the circumference of 

 the ellipse (6) : 



iV(l— e~c ). 



This amount remaining the same whether we regard the ellipse 

 (6) from the excentric origin or from the centre, i.e. for R = 0, 

 if with the integration the limits are changed correspondingly, the 

 expression (7) must also be accurate when R is not equal to zero 

 and must thus hold in general. 



Indeed, an other simplification, namely q = (which is applicable 

 to the results for Falmouth) leads to a set of definite integrals, which 

 can be evaluated and which confirm this conclusion. 



Amongst the series of ellipses represented by (6) two are 

 remarkable ; if we assign to c the value 0.5, then on account of 

 (1) the half axes of the ellipse become equal to the greatest and 

 smallest projections ,1/ and M' of the mean velocities, so that the 

 ellipse (6) then represents what we might call the specific or typical 

 loindellipse, thus a kind of windrose, in which the characteristic 

 qualities of the wind-distribution under consideration inmediately 

 become conspicuous. 



The radius vector R m drawn to an arbitrary point in the circum- 

 ference is given in the direction determined by that choice by the 

 equation : 



2 R\ n v — 4 R m X + 2 n — 1 = 0. 

 The probability that a velocity does not surpass this value is : 



1 — e-Vi = 0.39347. 



