G. E. Curtis — Theory of the Wind Vane. 51 



Substituting these values of t in the preceding equation for 6, 

 the amplitudes of vibration become successively 



— 2k — 4k 



7t 



a, al h, , ae "'/ 



Similarly, the amplitudes of vibration of a straight vane are, 

 successively, 



— k —2k 

 —r- ■ k —j- • n 

 a, ae /l > ae n , 



To determine the relative magnitude of the oscillation in 



2k k 



these two cases, let us substitute for — and - their original val- 



h t h 



ues, 



2k Kr 



h , Vi-aK—KV 



k_ E> 



h~ aAK-KV 



If it be desired to take account of the diminution of pressure 

 on the sheltered side of the straight vane, the value of K is 

 not the same for both vanes, but will become so by multiplying 

 K in the equations of the straight vane by the factor 1 + n. 



Jc Ivy* 



Making this correction, =■ = For all possi- 



i/— - . K-KV 2 



y 1+71 



2 k k 

 ble values of n, — -> -, and, consequently, at any time t, the 



amplitude of oscillation of the spread vane will be less than 

 that of the straight vane, and so the former will sooner come to 

 rest. 



This difference in amplitude of oscillation is least when RV 

 is negligible in comparison with l'QK, in which case the differ- 

 ence between the amplitudes of oscillation is determined by 



the ratio i/ '• Vl'9 as exponential factors in the expres- 



. l+ n 

 sion for the amplitude. This difference is increased by the 

 term KV, r and K being constants depending on the length 

 and surface of the vane. 



The formulae, therefore, show 1st, that the oscillations of both 

 vanes are smaller as the vanes are longer and larger ; 2d, that the 

 spread vane is always more stable than the straight vane ; and 3d, 

 thai this advantage in stability is greater for long vanes than for 

 short vanes, and is independent of the wind velocity. 



