164 The Rev. T. R. Robinson's Description of an improved Anemometer. 



but it is a striking illustration of the imperfect state of this branch of hydro- 

 dynamics.* 



As to the coefficient 6', its limits at least may be obtained by a process 

 which I at first thought might give a and a\ — the same which Edgeworth, 

 Hdtton, Borda, and Vinck, employed in their experiments on resistance. The 

 resisting surface is placed at the extremity of a horizontal arm made to revolve 

 round a vertical axis by a weight attached to a cord wound on the latter, and 

 passing over a pulley. When the rotation becomes uniform, f the resistance 

 must equal the accelerating force, and if this be constant, all the resistances 

 must be equal, and, therefore, can be compared with the velocities. With this 

 hope the apparatus described in the preceding section was placed in a tower 

 of the Observatory, and alternately driven with its concave and convex sur- 

 faces foremost. Twenty revolutions were made before the time was noted ; 

 and then thirty were taken, giving iS= 381 feet. The mean velocities varied 



* From this it follows, that, if the friction do not prevent it, an anemometer of this kind should 

 revolve even when its axis is in the direction of the wind. The small one already described does 

 so, but this may be owing to the oscillation of direction. 



t I fear the physicists just mentioned took the fulfilment of this condition for granted. This 

 does not necessarily happen. Let F= the impelling power, Xthe moment of inertia of the appa- 

 ratus, S the space described, T the time, V the velocity of the centre of the resistance. 



Accelerating force = — -j-, — . 





2y/{Fa) 



S F K V 



Square of mean velocity or-=-= ^ 'r''' 



. , • F K V- 

 mean square of velocity = " 9^ ' 



From these expressions it is manifest, that v cannot be uniform till S is infinite. In my trials 

 it continued to increase even till S was the largest I could command, 1143 feet. Hence also, the 

 mean square of velocity (which ought to be used in computing the resistance) must difier from the 

 square of the mean velocity; the latter, however, has always been used. As. moreover, no esti- 

 mation has been made of the air's centrifugal force in the results which have hitherto been 

 obtained in this way (and in fact it cannot be separated from the resistance), I am compelled to 

 think they require revision, though they are at present received as standard facts. 



