70 Mr. C. Chree on the Theory of 



rotation, varies from point to point of the surface, not merely in 

 intensity but also, especially in short-armed cups, in direction. 

 Unlike a plane plank, whose two faces are symmetrical, the 

 cup experiences very different resultant pressures according 

 as its concavity or its convexity faces the wind. According 

 to Dines * the resultant pressures in the two cases, apparently 

 for wind along the axis, are in the ratio 132 : 45 for a 9 -inch 

 cup and 126 : 55 for a 5-inch cup. Without a difference of 

 this kind the cups of course would not go round. 



Theoretical Investigation by Thiesen. 



§ 6. Of the theoretical investigations into the behaviour of 

 the Robinson cup-anemometer, discussed by Prof. Cleveland 

 Abbe, much the most complete appears to be that of Thiesen 

 (I. c. pp. 294-300). This is of importance for our present 

 object, so I give a brief outline of the method of treatment, 

 deduced from a personal study of the original paper f. Instead 

 of Thiesen's notation, I, p, V, v, U, 6, yjr are employed as in 

 § 4. The angle 0, when the cup is in motion, measures, it 

 will be noticed, the angular position of the arm of a cup, as 

 well as the inclination of the wind's direction to the axis. 

 Thiesen assumes that what he calls the a normal " component 

 of the wind's velocity is alone effective ; by this he means the 

 component along the axis of the cup. His argument pro- 

 ceeds as follows : — 



(a) Suppose that when the wind's direction makes an 

 angle 6 with the axis of a cup at rest, the resultant normal 

 pressure is pV 2 R 2 /(0), where R is the radius of the cup,/(0) 

 an unknown function of 6. 



(b) Then when the cup is in motion the resultant normal 

 pressure is /oU 2 R 2 /(>/r), and the resultant driving couple 

 /oU 2 R 2 //(^). 



(c) The angular velocity of the arm is 



d£_ v_ V/tA 



dt ~ j~ I \v) ; 

 also 



dt 2 == 2d0\dt) 



2 \l J d0\V)' 

 supposing the wind's velocity to have a constant value. Thus, 



* Royal Society's ' Proceedings,' vol. 1. 1891, p. 51. 

 t Repm'toriumfiir Meteorologic, Bd. v. Heft 2 (1877). 



