the Robinson Cup- Anemometer. 75 



2. There are no mathematical objections to its use for all 

 possible positive values of v and V. 



3. It accords with the fact that if, during a calm, the 

 instrument be set in motion the velocity is gradually reduced 

 to rest. 



4. In a uniform high wind it gives to a close degree of 

 approximation a quadratic equation, 



a 2 (v/Y) 2 + 2b 2 (v/Y)-c 2 =0, 



to determine the value of v/Y in the steady state, being 

 thus apparently in accordance with Dr. Robinson's experi- 

 mental conclusions in the ' Philosophical Transactions' for 1878. 



It may seem a waste of time to expend further thought on 

 a formula whose basis is so uncertain. This is a view of the 

 case I should certainly adopt if there were reasonable grounds 

 for expecting in the near future an approximately exact 

 mathematical treatment of the problem. The chance of this 

 seems, however, rather remote, and I have thus decided that 

 it is worth while to examine the conclusions to which (14) 

 leads. 



The desirability of some attempt to utilize the best existing 

 data will, I think, be recognized by any one who has com- 

 pared the regular march of the trace given by an ordinary 

 Robinson cup-anemometer with the large and incessant fluc- 

 tuations in the trace from such an instrument as " Dines' 

 tube-anemometer ""*. 



§ 9. Before entering on the mathematical treatment of (14) 

 we must justify the signs given the various terms, it being 

 supposed that the coefficients a , %, . . . themselves are all 

 positive. 



The motion in a calm is given by 



dv 

 di 



= —a — a 1 v — a 2 v 2 (16) 



If a 2 were a negative quantity, it would be possible, by giving 



dv 

 v a sufficiently big initial value, to make -*- initially positive. 



LLC 



The velocity of the cups would then go on continually acce- 

 lerating, though all the forces acting would be of a frictional 

 or viscous character and would necessarily oppose the motion. 

 The hypothesis that a 2 is negative may thus be rejected. If 

 next we suppose the cups, initially at rest, suddenly allowed 

 to move under the influence of the wind, the motion at the 



* Quart. Journ, R. Met. Soc. vol. xviii. pp. 1(38 et req. 



