388 
Proceedings of the Royal Society of Edinburgh. [Sess. 
direction of the wind is reversed. All that remains, therefore, is to 
cause each disc to record its rotation by making it draw a pen along a 
rotating cylinder. 
The geometrical proof of the statement of the preceding paragraph 
is a simple one. We suppose co, the angular velocity of the sphere, 
to be equal to k times Y, the velocity of the wind, where k is 
assumed for the present to be a constant. Let r be the radius of a 
disc measured to its point of contact with the sphere, and d the distance 
of the point of contact below the centre of the sphere. Also suppose 
the axis A' A to make an angle 0 with the west-easterly direction. 
Then if we direct our attention to the point where the sphere touches 
the bevelled edge of the disc, it will be clear that, whatever be the 
motion of that point of the sphere, no part of that motion will 
cause the disc to turn except that which is horizontal and tangential 
to the edge of the disc. The other components of the motion will 
merely give rise to a slide along the slope of the bevel. Now the total 
horizontal component of the motion of either point of contact is 
obviously cod or kYd, and this will be broken up into a component 
kVdcosO tending to make only the east disc turn, and a component 
JcV d sin 0 tending to make only the north disc turn. But Y cos 0 and 
Y sin 0 are the easterly and northerly components of the wind. Hence 
the speeds of rotation of the discs are proportional to them. The speeds 
£ , 1T kVdcosO i /{Yc^sind 
or rotation are actually and . 
J r r 
3. Details of Construction. 
The instrument may be regarded as consisting of two sections : 
the first, that which gives to the sphere the necessary rotation ; the 
second, that whereby the discs actuate the recording pens. In design- 
ing both portions, but especially the former, the object has been to 
be able to calculate the speed of the wind from that of the sphere, 
on the basis of the geometrical connections, after making a small allow- 
ance for “ slip.” This allowance would, of course, be determined by 
experiment. Pains have therefore been taken to diminish friction as 
far as may be. 
Section 1. — A wind- wheel consisting of four carefully made light screw- 
blades projecting outwards from a common horizontal axis is kept with 
its axis facing the wind by being mounted above a wind- vane in much 
the usual manner. Screw-blades of 2 metres pitch, 20 centimetres length 
from centre outwards, and 10 centimetres depth from front to back 
