( 693 ) 



A closer discussion of the results arrived at in this way may for 

 shortness' sake be left out ; however, the observation is not super- 

 fluous that the two examples represent two types, a reason why 

 they were chosen. At Bergen the ellipse of the variable winds is 

 very constant of shape and the excentricity is very great; at Falmouth 

 the difference between M and M' is always very slight and the 

 differences found there are evidently to be regarded rather as accidental 

 arithmetical results than as facts, the angle £ being subject to great 

 and irregular oscillations ; evidently the ellipse approaches a circle, so 

 that in form (2) we may put h = h'. This leading to a considerable 

 simplification of the formula, these observations at Falmouth are 

 eminently fit for comparison of the results of calculation and obser- 

 vation, whilst also the fact that here real velocities have been 

 observed with well-verified instruments, makes this series very 

 favourable. 



6. The expression (2) shows: the probability that an observation 

 lies between the limits R and R -j- dR, 6 and 6 -f dd ; the same 

 expression without the element RdRdO indicates : the specific proba- 

 bility of' a wind {R,6) i.e. the probability with respect to the 

 unity of surface when one imagines this surface to be small. If we 

 put for simplification : 



h" + h* — 2p, h" — h* — 2q, R 6 2 (p — q cos 2 (« - p)) = \i 

 {p — qcos2(#—p)) = l>, s 1 == iV (j> 2 -f q* — fyq cos 2 (« — /?)) 



p sin a -j- q sin (a — 2 fi) 



s cos {6 — <p) = X tang <p = — — , 



p cos a — q cos (« — 2 £?) 



then (2) takes the form : 



]/p' - q' 



.T 



e-K^ + ïR'-uRdRda (5) 



If here we put : 



R*v — 2RX + ft = c , (6) 



then it follows out of the above formulated definition that the specific 

 probability of all observations lying on the c i re u inference of the 

 excentric ellipse (6) is the same and equal to : 



e c 



-T 



The probability that the velocity of the wind does not surpass the 

 value R c expressed by (6) in function of 6, in other words the number 

 of observations which an; to lie within the area of the ellipse, is 



