the Robinson Cup- Anemometer, 87 



second term, 



26 2 (V'-v'O(^'0(WHW0 



" (a 1 + 2b 2 Y')(a 1 + 2b 2 Y r ')(l--y'] / *j ' 

 also varies as n. The exponentials y', y", y' y" beino- neces- 

 sarily less than unity, and the signs of V 7 — Y" ancf v f — v n 

 being^ as explained in § 14, necessarily the same, this term is 

 essentially positive. The third and remaining term does not 

 contain n as a factor, and however much n is increased it 

 cannot exceed an asymptotic value 



1 L _ %l + w _ ,/a W If,. 2b 2 (Y'-V") !/ > (!- ,/') 



a 1 + 2J 2 V'f» V+ ( V V ) rw|l 1+ («, + M > F0J-y'ff 



Thus when a large number of double periods Ti + T 2 are 

 considered we may to a close degree of approximation neglect 

 the third term in S. We thus conclude that the total record 

 from the anemometer is practically the same as if the cups 

 had had a uniform velocity £, given by 



v'T 1 + v"% 26,(V'-V")(e'-«")(l-yO(l-v") 



Ti + T 2 + (T x + T f )(o, + 2i 2 V')Oi + 2b 2 Y")(l-y'y")> [ } 



where y\ y" are given by (57). 

 This result has been established for all values of 

 V : V" and T x : T 2 . 



It leads to the same conclusion as § 14, viz., that the record 

 from the anemometer, interpreted in the usual way, always 

 exaggerates the wind's mean velocity when the actual velocity 

 is variable. 



When T x and T 2 are periods so short that (a 1 + 2b 2 Y')T 1 

 and («! + 26 2 V")T 2 are small, we deduce from (60) as a first 

 approximation 



._ J^ + fiT, 2MV'-V")(^")T 1 T 2 



V - T 1 + T 2 + (T 1 + T 2 ){(a 1 + 2b 2 Y>)T 1 + (a 1 + 2b 2 Y'>)T 2 \' (bl) 



This result is easily shown to be in harmony with (52). The 

 identification is simple when it is noticed that when a 2 be- 

 comes zero it is the root v 2 that becomes infinite. We take 



in (52) v 2 'l(a l + 2b 2 Y')-v 2 »l(a 1 + 2b 2 V'') f 



neglect vj/vj, Vi/v 2 n , &c, and finally replace vj by v' and v" 

 by v n . 



Supposiug Y' and V" given, and the conditions such that 

 (61) applies, it is easily found for what value of Tj/Tg the de- 

 parture of v from the equilibrium value (v'T 1 + v ,/ T 2 )/(T 1 + T 2 ) 

 is greatest. We have only to make 



T^fai + 2b 2 Y') + Tr 1 ^! + 2b 2 Y") 



a. minimum, regarding T x + T 2 as a constant, 



