446 SHOET MEMOIRS ON METEOROLOGICAL SUBJECTS. 



that these components may be overcome, there is necessitated an in- 

 crease in the gradient, and therefore, AB increases. Substituting the 

 expression for F, gives the definitive formula for JB as it is presented 

 on p. 100, vol. X, and which therefore must be nearly correct, since the 

 whole effect of the friction upon the ratio between gradient and velocity 

 is, in general, not very large, and therefore a part of it can have only a 

 very slight influence. 



" In the case of spiral movement, AB diminishes in the ratio of unity to 

 cos i', but since the expression for F, as we have deduced it, increases 

 in the ratio of cos^ i to unity, therefore AB will, in consequence of the 

 friction, increase more than it diminishes, and therefore cos i appears 

 in the denominator of equation II. 



" J^ will only be independent of * in case that we can show that the 

 true value of ^ is a function such that, being substituted in equation II, 

 it causes AB to increase precisely in the same ratio in which cos i 

 diminishes. 



"The formulacauuot be rigidly tested by comparison with special cases. 

 For the determination of the gradient we can only use observations at 

 distant places, which do not allow the consideration of the influence of 

 numerous local disturbances of slight extent. However, I quote here 

 certain relations between the gradients and wind velocities from Pro- 

 fessor Loomis, in American Journal of Science, January, 1875. Each of 

 these numbers represents the mean of a considerable number of obser- 

 vations. The velocity of the wind is given in English miles per hour; 

 the gradient in English inches of the barometer per 100 miles of dis- 

 tance: 

 Wind-velocity observed .... 10 15 20 25 30 35 



Gradient observed 086 .096 .105 .105 .124 .152 



Gradient computed 013 .067 .092 .118 .146 .175 



" The mean inclination of the wind-direction to the radius is assumed 

 at 45^, the mean distance from the center of the cyclone at 350 miles, and 

 the mean geographical latitude at 45°. We see that the observed 

 gradients, in a slightly regular manner, increase with the velocity of the 

 wind, because the influence of abnormal disturbances and of other 

 causes are not completely eliminated. We further see that for a velo- 

 city of 22 miles the theory agrees with observation. For lower velocities 

 the theoretical gradient is too small ; for larger velocities it is too large. 

 But in the computation we have assumed that i is constant for all velo- 

 cities. If we assume that for velocities between 10 and 35 miles the 

 value of i is respectively 60° and 35°, then the computed arid observed 

 values agree within the limit of the probable errors of the latter. This, 

 however, gives a mean value of i that is greater than 45^. The theory 

 cannot be rigidly tested until, by means of observations, the connection 

 between the wind-velocity and the angle * is established. If we put 

 cos i = 1, and thus make the gradient AB independent of the angle i, 

 then will all computed values of the gradients be too small." 



