Robinson — On the Cup A)ie)no))icter. 435 



concave, or from minus pressure behind the cup ; * but it is the more 

 remarkable, because in this case more than half a hemisphere is 

 exposed to negative action. This seems to imply that the original 

 expression for the rotating power 8V^ x a sin 6, should be of the form 

 a sin 6 + b cos 6. As in this case a and h cannot be separated by any 

 experimental process, it will be best to make a include the functions 

 of 6, which express the rotation, so that the power to turn the cup 

 shall be SaR^ ; and this in general. 



Secondly. Putting the opposite cup in its place, while the concave 

 of the first moves fi-om the wind the convex moves against it, and 

 meets a resistance = Sa'R'- (2.) The co-efficients a and a', are diffe- 

 rent functions of 6. When it is 90, I determined their ratio to be 

 4'011 : on either side of this the ratio is greater, though the absolute 

 values are less. Both positive and negative pressures are increased a 

 little by the so-called fiiction of the passing air. Since this acts by 

 producing eddies, it may be expected to vary as R^ and R'- : indeed, 

 Mr. Proude has shown that in the case of water it is as the square of 

 the relative velocity. Here its influence must be very small. 



Thirdly. There are two resistances as v^, which may be grouped 

 together. The fii'st of them is the amount of power expended in 

 throwing outwards the aii" in the Anemometer's track by centrifugal 

 force, as in a blowing fan ; this will be probably as 



2Slv^ 



I measured its amount in quiescent air, by making two cups similar to 

 those of my instrument, and with the same length of arm, revolve 

 with various velocities, by weights acting on a thread coiled on their 

 axles, whose pull at their centres was measured. "When the concaves 

 moved foremost, I thus obtained a^o ; when the convex «9o + 3 ; and as 

 I had found the ratio of a^o and ff'go = 4*011, I' was found to be 

 a' go X 0, 9535. Whether it will have the same value in moving as in 

 quiescent air is uncertain ; the escape of air against the wind will be 

 impeded, but will be accelerated with it, so that the above mode of 

 computing it may be provisionally assumed. 



The other part of this resistance is one arising from the motion of 

 the convexes against the air independent of the wind, which is still 

 more difficult to estimate. At ^ = or 180, they move at right angles 

 to the wind, and are resisted as if it were null, therefore as 



2Sa'go X v^ ; 



at 90 and 270, this action (as separate from that of F) vanishes ; at 



* It is possible that eddies from the following convex may reach into the con- 

 cave, and increase the force. 



