1880.] On the Constants of the Cup Anemometer. 573 



He has tried this, and he thinks successfully. Two instruments of the 

 Kew type, differing only in friction, were established 22 feet asunder 

 on the roof of the house and 16 feet above it : the number of turns 

 made by each, and the time, were recorded by a chronograph, and from 

 these, v and v', the velocity in miles per hour of the centres of the cups 

 was known. 



The friction of one of these (K) was constant ; that of the other (E) 

 was varied by applying to a disk on its axle Prony's brake, which was 

 connected with a spring balance whose tension was recorded during 

 the time of experiment by a pencil moved by clockwork. Thus the 

 mean friction was obtained. It ranged from 353 grains to 4,982. 



The equation of an anemometer's motion is V 2 -f v 3 — 2Vvx — /=0 



a 



where V is the unknown velocity of the wind, a. and x two constants 

 which are to be determined. Each observation gives two equations 

 in which there are four unknown quantities, for it is found that the 

 value of V changes from one instrument to another. This is partly 

 owing to eddies caused by the buildings, but also in great measure to 

 irregularity of the wind itself. It is, however, also found that these 

 wind-differences are as likely to have + as— signs, and therefore it may 

 be expected that their sum will vanish in a large number of observa- 

 tions. The ordinary methods of elimination fail here even to determine 

 with precision a single constant, and he has proceeded by approxi- 

 mation. 



Assuming the value of a. given by the actual measurements in hi» 

 paper =15*315 at 30" and 32° for 9-inch cups, and that there is no 

 resistance as v 2, except that in the equation, and assuming an approxi- 

 mate value for x, we can compute V and V. The difference between 

 these must be due to an error in x and to w the wind error, and taking 

 the sum of a series we have 



S(V'-V) + St0=Aa>xS(e-e'); e being 



If the observations are sufficiently numerous Sw=0, with the 

 assumed x+ Ax thus found, recompute the V till the sum of V— V is 

 insensible, and the final x will give V with a high degree of probability. 

 Twenty-one observations gave a value of x considerably larger than 

 what was obtained with the whirling machine, and of course the 



limiting factor (that when v is so large that i— may be neglected). 



OtV 



It is for the Kew type 9" cups 24" arms =2,831. In this series the 

 differences are so evidently casual as to show that neither x or x change 

 with v. 



With this x, K gives the true value of V at it ; therefore if any 



