90 Theory of the Robinson Cup- Anemometer, 



which depends on (Y ,n —V) (v nt -—v), and there results the 

 obviously positive expression 

 2b 2 C , "Cy(l-y'")(l-y%Y l "-V')(v m -v , )/(l-yy'y /// )^ 



Thus on the hypothesis made as to the relative values of 

 V, V", V", the right-hand side of (65) is essentially positive. 



A similar proof will be found to apply whichever of the 

 three V, V", V" is the greatest and whichever the least. Thus 

 we reach the general result. 



v > (*T X + v"T 2 + »'%)/ (T, + T 2 + T,). 



Summary. 



The principal conclusions to which the formula (14) leads 

 are as follows : — 



1. In steady winds the ratio of the true wind-velocity to 

 that of the cups may, in any given anemometer, be expected 

 to be nearly constant when the wind is high. But there is 

 no reason to expect this constancy when the wind is low, 

 especially in cases where there is considerable friction owing 

 to thickness in the lubricant or any other cause. 



2. In steady winds the runs of two anemometers in which 

 the friction is small may be expected to stand in a nearly 

 constant ratio so long as the wind's velocity is considerable, 

 but in light winds this constancy of ratio cannot be expected. 



3. When the wind is not steady, changes in the velocity of 

 the cups take place much more slowly than the changes in the 

 wind's velocity to which they are due. 



4. If the wind's velocity is nearly uniform, but has one or 

 a series of small harmonic variations, the action of the cups is 

 conspicuously to smooth down these variations when rapid, 

 without introducing appreciable error into the estimate of 

 the mean velocity. 



5. If, however, the wind's velocity has large and frequent 

 oscillations, the anemometer in addition to smoothing down 

 the oscillations exaggerates the mean velocity. This ex- 

 aggeration increases with the extent of the fluctuations ; it 

 is greater in a case where the interval of time between suc- 

 cessive gusts exceeds the duration of the gusts, than in a case 

 where the converse occurs. 



The formula (14) from which these conclusions flow is in 

 part at least empirical. It is advanced provisionally, on the 

 ground that as the prospect of a complete determination of 

 the physical conditions of the problem and its satisfactory 

 mathematical solution appears somewhat remote, it is desirable 

 in the meantime to utilize the best existing data in such a 

 way as to bring into stronger relief the issues which call for 

 experimental investigation, 



