' 



the Robinson Cup- Anemometer. 65 



complete theory the wind's action on the arms and stays should 

 be taken into account. 



The frictional forces are exerted on the supports, the 

 rotating vertical axis, and any machinery driven by the arms. 

 These forces are of at least two distinct kinds. Supposing no 

 wind to blow, but the cups rotated by hand, there is a frictional 

 force such as exists when a heavy body rotates on a horizontal 

 table. When wind blows, the rotating vertical axis is pressed 

 against the surfaces guiding it, with a force which is practi- 

 cally equal to the resultant of the horizontal forces exerted at 

 the time by the wind on the cups, stays, and arms. The first 

 mentioned frictional force depends on the weight of the 

 instrument, the latter on the force of the wind, and both on 

 the state of the lubricant. 



When, as in some experimental comparisons, the ane- 

 mometer is mounted on a whirling machine, with its axis at a 

 considerable distance from the axis of rotation of the whirler, 

 the " centrifugal force " calls into play a third frictional force. 

 These facts were clearly pointed out by Dr. Robinson * in 

 describing his experiments. 



§ 3. The action of the wind on the cups and arms is 

 presumably of two kinds — tangential viscous action and normal 

 pressure. If the air were a " perfect fluid/' only the latter 

 would exist ; but doubtless in practice there is alwa}^s a 

 certain amount of viscous action. For slow motion it is 

 usual to assume such action proportional to the first power of 

 the relative velocity. But it must, I think, be regarded as 

 somewhat doubtful whether this law is a sufficiently correct 

 representation of the facts for velocities such as 100 feet per 

 second, a value which is sometimes exceeded by the velocity 

 of a Robinson cup relative to the wind in a gale. 



As regards the normal pressure, the assumption used to be 

 made that it varied at each point of a solid's surface as the 

 square of the normal component of the relative motion of the 

 undisturbed fluid, irrespective of the shape or size of the solid, 

 or the relative velocity elsewhere than at the point considered. 

 It is now supposed, however, that when the solid surface has 

 a sharp edge discontinuity is set up in the fluid, the nature 

 of the discontinuity and the resultant of the normal pressures 

 depending on the shape of this edge. 



Until some mathematically complete solution has been 

 obtained for some practical three-dimensional case,^ and 

 numerical allowance can be made for the departure of existing 

 fluids from the "perfect" state, comparison of theory and 



* Phil. Trans, for 1878, pp. 788-793. 

 Phil. Mag. S. 5. Vol. 40. No. 242. July 1895. F 



