43G Proceedings of the Royal IrUh Academy. 



intermediate positions its amount is doubtful. There ^rill be some 

 due to the component of v perpendicaihir to V, and some to that part 

 of the convex ^hieh is not reached by R or R' . 



The combined effect of these and the eentiifugal resistance may be 

 put = Slv-. 



Fourthly. The last resistance is friction, -which may be of three 

 kinds. It is independent of the relative velocity of the rubbing sur- 

 faces, but is as their pressure. 



(1). In the ordinary use of the Anemometer, its axis is vertical and 

 the friction due to its weight is constant ; this is easily measured by 

 attaching weights to a thread passing over a pulley (whose friction is 

 known), and coiled on its axle or a cylinder fixed on it of known 

 radius = p, till it just moves on tapping. This weight multiplied by 

 ?. is/. (2). The pressure of the wind on the cups is another cause of 



friction by pressing the axle against the upper bearing. As in perma- 

 nent rotation the impelling = the retarding forces, and they balance at 

 the axle, the pressui-e there = their sum, or twice the impelling force. 

 This, as is evident from equation (I.) = {a - a') x ( F^ + v^). Let/" be 

 the friction due to a unit pressure _L to the axis, then this fi'iction 

 = 2/a ( V^ + v^). The effect of this is simply to substitute for a in (II.) 

 a (1 - 2/J. It therefore need not be taken into account, as it will be 

 included in any determination of that co-efficient. The pressure will 

 be something gTeater than the above from resultants in the dii-ection 

 of the arms, but since these also are as V^ they do not alter the result. 

 (3). "Wlien an Anemometer is carried by a whirling machine, its move- 

 able parts are urged outwards by centrifugal force, which produces 

 pressure on its bearings and therefore fiiction. Let/^, be the fi'iction 

 due to a unit pressure parallel to the arm A of the whirling machine ; 

 R the centrifugal pressiu'e due to the unit V 



W O 



= — X -Jo, 

 9 A~ 



TiP" being the weight of the moving parts, and (? the distance of their 

 CG from the centre of the whirler ; then /^^ R V~ is the centiifugal 

 friction ; this is equivalent to multiplying a by (1 - /^^ P) and need 

 not be computed. But the a ofund by a whirling machine must be 

 divided by this factor to make it apply to real wind measurement. 

 Combining these four forces, and putting for R and R' their values, 

 we obtain for the moving force in the position 0, 



-Q = ( a4,-a'Ar' -2nl a4, + a'^] sin e -v^yl + a'^- aA-f. (I.) 



If we have a series of values of ^^and a' through the aixs on which 



