658 Proceedings of the Royal Society of Edinburgh. [Sess. 
e. Is restricted to indicate the eclipse-angle of the simplest type of vane (shown in 
fig. 1) and no other. 
^°‘j-The values which these symbols have for the “medial” rays of the beam, 
e. Is equal to e 0 - e. 
A. The “Position-Ratio” of a ray, i.e , the horizontal distance of the ray from 0, 
divided by its vertical distance. 
A'. The value of A which is such that the rays having that particular position-ratio 
differ in their transmission coefficient by p per cent, from \ t 0 , the value of 
the transmission coefficient of the medial rays. 
A m . The smallest value that A' assumes through the whole range of azimuth angles 
through which the motor will be swung. 
n. The number of vanes possessed by a paddle-wheel (when, however, the latter is 
of a type having two sets of vanes, one behind the other, the vanes of only 
one set are to be counted). 
0. The point at which the vanes are attached to the motor axle, e.g. see fig. 1. 
p. The greatest percentage difference considered to be permissible between the 
values of the transmission coefficients of the medial and the extreme lateral 
rays respectively. 
t. The “Transmission Coefficient” of any ray, i.e. the fraction of the light of that 
ray transmitted by the paddle-wheel. 
t 0 . The transmission coefficient of the medial rays. 
w.fSee equation 14, page 670. 
u m . See the sentence which follows equation 16, page 670. 
Definitions. 
Eclipse- Angle — See E, above. 
Medial Rays — Those rays which pass through an imaginary vertical line 
through 0. 
“ Position-Ratio ” of a Ray — See A, above. 
“ Transmission Coefficient ” of a Ray — See t above. 
N.B. — In all cases it is supposed that the ends of the vanes remote from the axle 
of the motor lie on the surface of an imaginary circular cylinder, the axis of which 
coincides with the axle : and furthermore, the radius of this imaginary cylinder is 
taken as the unit of length. To put the matter more simply, but less exactly, the 
radius of the paddle-wheel is always taken to be unity. 
§ 2. Different Types of Paddle-Wheel. 
It is evident that an endless variety of paddle-wheels might be suggested, 
differing in the number, shape, and arrangement of their vanes, and perhaps 
also in other ways. In what follows, however, only a few of the simplest 
forms will be considered. 
In the type of wheel depicted in fig. 1, it is clear that whether the motor 
be turned round its pivot to right, or to left, the same reduction of light 
intensity will ensue ; and this repetition is undesirable since it shortens 
the total range of the values of the light intensity, because the amount of 
