On Photometric Paddle-Wheels. 
667 
1910-11.] 
of the chart enter the value of a in the scale so marked ; follow the nearest 
radial line until it meets the vertical line which passes through the given 
value of c, and the horizontal line through this point of meeting will cut 
the e 0 scale at the required value. 
In the above only the effect of one vane has been considered : we now 
go on to find the fraction of the light which is transmitted by the entire 
wheel, taking account of the whole set of vanes. 
Evidently the transmitted fraction t is given by the equation 
( 1-0 = 
nE 
360 ’ 
( 10 ) 
where, as before, E is the eclipse-angle, n being the total number of vanes of 
the wheel. This equation is graphically plotted in Chart II. If we consider 
t to be the dependent variable, E the independent, and n a variable parameter 
which takes only integral values, then the equation is linear, and is repre- 
sented by a series of straight lines, corresponding to the different values of n. 
The value of E is obtained from e 0 (Chart I.) and equations A, A', B, or B' 
as the case may be ; and the method of using the chart is obvious. 
§ 4. The Condition necessary to ensure that all the Rays of the 
Beam of Light shall have sensibly the same Intensity after 
their Transmission by the Paddle-Wheel. 
We shall consider first the case of wheels of types A and B, the 
formulas for which may be written as one, 
E = K+ | e | (11) 
where K is a constant not less than zero. As in the above equation 
the sign of e is indifferent, it will be sufficient to consider only positive 
values of e. 
