the Robinson Cup- Anemometer. 85 



When (V ~ V")/V is small, then so likewise are 

 (v[ ~ v[') \v\ and [v[ ~ v'^/v^ ; 

 and (52) may be replaced by 



,_ <T 1+ <T 2 Tl T 2 (<-<)(^-<) 



- T, + T 2 + (T ] +T 2 ){W+^)T f+ (< + <)T 2 }- (M} 



It is clear by (53) that v in this case differs from the mean 

 velocity given by the equilibrium theory only by a term of 

 the order (V'-V")7(V'+V"). Thus, if the fluctuations in 

 the wind's velocity be small, we arrive at the same conclusion 

 as in the different species of fluctuation treated in § 11, viz. 

 that the error in the anemometer-record, treated as if the wind 

 were steady, is very small. 



Case a 2 = 0, V constant. 



§ 15. As explained in § 9, experimental results obtained by 

 Dr. Robinson have been deemed not inconsistent with the 

 hypothesis that a 2 vanishes. 



It is thus desirable to see the results we are led to when a 2 

 is supposed zero in the cases dealt with in §§13 and 14. 



If V be constant throughout the time considered, then the 

 solution (27) takes the form 



v= v+(v — £)<?-^i+ 26 2VK .... (55) 

 where 



v = (c 2 V 2 -b 1 Y-a )/(a 1 + 2b 2 V). . . (56) 



We see from (55) how the influence of the initial velocity 

 v gradually dies out, and how v approaches the value v, 

 which is clearly the velocity of the cups in the steady state 

 answering to the given wind-velocity V. 



The size of c 2 , the coefficient in the principal term in the 

 driving-force, influences largely the value of v, but has no 

 direct influence on the rate at which the cups pick up their 

 final velocity. 



§ 16. We shall now examine what modifications the hypo- 

 thesis a 2 = introduces in the results when there are regular 

 alternations of the wind's velocity, as in § 14. 



Let v be the initial value of v, and let v', v" be the velocities 

 of the cups in steady states answering to the wind- velocities 

 V and V" respectively. Use v-i, v 2 ,... v 2n , $i . . . s 2n , as in 

 § 14, and for shortness let 



^_{(a 1 +26 2 V')T 1 } _ yf 



''■}■ 



(•") 



