the Robinson Cup- Anemometer . 71 



I being the moment of inertia round the axis of rotation, the 

 equation of motion is 



^jKt) d(±)= P WWlf{f)dd. . . (5) 



Supposing 4 cups and arms, there would really exist 4 terms 

 on the right, each deducible from the previous by writing 



| + 0for0. 



Eventually a steady state will be reached in which ( ^ I 



will be a pure periodic function of 0, and so the left-hand side 

 of (5) must vanish when integrated from = to d — ^ir. 

 Consequently, we must have also 



fuy(t)<z0=o (6) 



Jo 



(d) It is clear that in an anemometer in which I is con- 

 siderable v/V is very nearly constant during a revolution ; 

 thus to a first approximation constancy may be assumed. On 

 this assumption (4) gives 



IT/ V 2 \~i 



^=^(l-^_sin*f) dr , . . . . ( 7 ) 

 and so, as V is supposed constant, we can replace (6) by 



^(^)\ i -T^ n2 ^r /wd ^ =o ' ■ • (8) 



where U/V may be regarded as a function of -yjr from the 

 geometrical relation 



(e) It is assumed that 



/(^)=/(-^)=A + A 1 cos^ + A 2 cos2i|r+ ..., . (10) 



where A , A 1? &c, are constants. 



(/) Suppose that if v/V be treated in (8) as constant, the 

 proper value to assign it is 2 a. Then substituting 2 a for v/V 9 

 and employing the series for f{-f), expand the quantities 

 under the integral sign in (8) in powers of a and integrate. 

 There results to determine a the equation 



A -3aA 1 + 4a 2 (A + A 2 )-J r a 3 (3A 1 + 5A 3 )+ ...=0. . (11) 



As a is supposed to be as small as 1/6, presumably a few 



