s = 



the Robinson Cup- Anemometer. 8i 



where 



a 2 (v — v 1 )(v + v 2 ) = ao + a^ + biV + a 2 v 2 + 2b 2 vV — c 2 Y 2 . (36) 



It is obvious that v x represents the value of v in the steady 

 state answering to the wind- velocity V. 

 Supposing that initially 



t = 0, v =v 0J 

 we easily find 



v = Vi+Oo— vAe-^i+^-i- i l + V °~ Vl (l — e- a 2( v i+ v ^) \ (37) 



I t\ + v 2 s J v 



The space s traversed in time i by the cups' centres is 

 given by 



^£vdt = Bl « + I log{ l+g^i (1-^0,+^) J . (38) 



From (37) we see that, theoretically, an infinite time is 

 required to assume the final velocity v 1 answering to the 

 steady state. 



When t becomes very large, s approaches asymptotically 

 the value 



..In V +V 2 



v ± t H — log , . 



Thus the true run of the cups cannot differ from what is given 

 by the equilibrium theory by more than 



i kg ^- 2 . 



a 2 ° t\ + v 2 



§ 14. As an interesting development of the results of the last 

 paragraph, suppose that v = v when t = t , and that thereafter 

 there are alternate intervals T l and T 2 during which V has the 

 different constant values V and V" respectively. 



Let v[ and v l 2 be the values of the v 1 and v 2 of last paragraph 

 which answer to Y', and v", v' 2 ' the values which answer to V". 

 In the present paragraph we shall employ v\ to denote the value 

 of v at the end of the first interval T 1? v 2 to denote its value at 

 the end of the succeeding interval T 2 , and so on. The corre- 

 sponding values of s (the space traversed by the cups' centres) 

 are denoted by s 1? s 2 , &c. 



For brevity we shall write 



e -*' I (39) 



e - aa ( k v 1 "+v 2 "yr a = x n. J 



Noticing that the 2?i-lf h and 2/? th intervals are of lengths 

 Phil. Mag. S. 5. Vol. 40. No. 242. July 1895. G- 



