88 • Mr. C. Chree on the Theory of 



The result is 



T/r 2 = v /(v" + j)/(v + ||). . .(62) 



The interval during which the wind has the lower value 

 should thus for the maximum effect be the greater. 



When a x vanishes, or approximately in general when V 

 and V" are both large compared to a 1 /2b 2 , (62) reduces to 



Ti/T 2 = VVTV^ (63) 



§ 17. In §§ 14 & 16, Tj/Ts and V'/V" may both vary 

 within wide limits, so that the conditions under which it has 

 been proved that during a variable wind the cup-anemometer 

 exaggerates the mean velocity are pretty comprehensive. It 

 might still, however, be supposed that the result followed in 

 some way from the restriction of there being only two 

 velocities V and V", and evidence to the contrary is thus 

 desirable. 



The methods we have employed can be extended to apply 

 to any number of different wind-velocities forming a regular 

 sequence, but the work increases in length and the results in 

 complexity as the number of intervals increases. I have thus 

 worked out only one further case, where there are three inter- 

 vals T,, T 2 , T 3 , during which the wind's velocity has the 

 respective values V, V", V". As in § 16, we shall suppose 

 a 2 zero. 



v ,n denotes the velocity of the cups in the steady state 

 answering to V w , and 



Also for shortness, 



(a l + 2b 2 Y')- l = C l , (a l + 2b 2 V»y 1 = C», (a l + 2b 2 V»')- 1 = C" f . 



The rest of the notation is as in § 16. 



For the space 8 travelled by the cups' centres in the time 

 rcCTi+Ta + T^Ifind 



$ = n(v% + v"T 2 + v'"T 5 ) 



+ i-l/y^ l^^) {C"(W) +c"y , (W")+ (W"(i-jr| 



«y y y 



+(s"-s"Q{C" / (i--/ // ) +cy"(i-#o+c / yV( 1 -y 



+ (£"' _ $') (C (1 - y f ) + C'V (1 -y") + W'y'y" (1 -y'"\ 



^l — (yry"y'") n C _ _, v' — X)" ' + ?/ " ' (%' " — v") + if ' y" {v" ~ v') 



+ l l-^yy- r° r+ " i- y yy" 



xiCXi-^+CYCi-yO + c-y/^i-^)}}. . (6 



