Robinson — On the Cup Anemometer. 437 



tliey have positive values, we can get their mean values. For a and a' 



this value = , & and Q" being the limits between which a, is posi- 



tive ; tor the second co-efficient it= — ^ — . 



The integration is easily done by quadratures, and the mean values 

 must be taken, I then gives 



ar^-2l3^xrv-v''xy-f=0, (II.) 



which coincides in form with my original equation, the chief difference 

 being in y. 



Adding a second pair of cups at right angles to the former, the 

 forces are all doubled, except/: that is increased by the increased 

 weight of the cups and their arms ; but the friction due to the weight 

 of the axle and to the registering apparatus is unchanged. This should 

 always be measured as before described. With four cups the motive 

 force is more uniform than with two, and the period of its variations 

 is half that of the other. 



Solving this quadratic, we have 



JIEy.,L,& (in.) 



(\ a' a av a) 



V 



Calling — = w' ; if / were to vanish, 



V 



^y-J-. (IV.) 



This value of m is independent of the size of the instrument, except as 

 relates to the part of y which depends on centrifugal force, unless it be 

 so small that the impulse on one cup interferes with its neighbour ; it is 

 also independent of v. The correction for an instrument which records 

 V as mv is hence easily found; for if m' = m -\- jjl, we have V= mv + fxv ; 

 fxv is therefore the correction. ]S"ow 



m + ix-'^ = w + ^ +^ 

 a \ a/ at;' 



hence 



/3 



/A = I m- 



1+ ,/ /3f!-l (^O 



af'i m -- 



