On Photometric Paddle-Wheels. 
659 
1910-11.] 
turning that can be done in either direction is limited, for reasons that will 
appear later on. Duplication of values may, however, be got rid of by in- 
clining all the vanes of the wheel at an angle to the axle, instead of having 
them parallel to it. In fig. 2, AB represents the top edge of such an 
inclined vane, when at its highest position, looked at from above. Now it is 
evident that the effect of this vane will be the same as the joint effect of two 
others which we may imagine to take its place, namely, a vane BC parallel to 
the axle as before, and a triangular vane AC, having its outer edge AC 
perpendicular to the outer edge BC of the other, all the vanes, both the real 
and the imaginary, meeting the axle at a common point of attachment 0. 
L JC-HT LitHT 
'i' V 
C A 
If now the eclipse-angle of a vane be defined as the angle through which the 
motor axle turns while the particular ray of light considered is being 
intercepted by that vane, then clearly the eclipse-angle of the vane AB is 
equal to that of the vane BC, plus that of the vane AC. Or in symbols, 
E = <x + e . . . . . . (1) 
where E is the eclipse-angle of the vane AB, <r that of the vane AC (<x is 
evidently a constant), and e that of BC. As the figure is drawn cr is evi- 
dently positive; but in the cases where AB lies across the axle in the 
opposite direction, A being on what in the present figure is the B side of 
the axle, and vice versa — then <r is negative. 
It will be convenient to continue this notation throughout, using E as the 
symbol for the eclipse-angles of all vanes whatever their shape or inclination, 
and employing the letter e only for the eclipse-angles of the sort of vane 
shown in fig. 1, which has its plane parallel to the axle. We shall further con- 
sider E to be always positive, but e to have the same sign as a the azimuth 
