1910-11.] On Photometric Paddle-Wheels. 661 
two quantities that must be taken to give E ; hence, as in accordance with 
our convention e changes sign with a , (2) must be written 
E = <r' + | e | (B) 
if it is to apply in all cases. 
If each rear vane B, fig. 4, is not directly behind the corresponding front 
vane A, all the rear vanes as we may suppose having been rotated as a 
whole slightly round the axle with respect to the front set, then a paddle- 
wheel is obtained which has for its formula 
E = cr' + | o- + e | . . . . . (B') 
where cr is the angle through which the hack vanes have been turned 
relative to the front, cr being considered positive if the angle be turned 
through counter-clockwise from zero looking with the light, and vice versa ; 
and where cr' and e have their former meanings. 
The four types of paddle-wheel described above, namely those which 
lead to equations (A), (A'), (B), and (B'), may be designated respectively 
types A, A', B, B'. 
Types A' and B' have the advantage that they avoid, or can be 
arranged so as to avoid, repetition in their values of E; an advantage 
which is not possessed by types A and B. Types A and A" fan the air 
as they rotate ; * this is avoided by the wheels of types B and B r . But 
then again these latter have the disadvantage that their E’s cannot be 
reduced to zero, as in the case of the E’s of the former pair. It will also 
appear from what follows that the different types of wheels may differ 
considerably in the restrictions they impose on the size of the cross 
section of the beam of light. Hence it cannot be said that there is any 
“ best ” type ; it all depends on the particular use to which the wheel is to 
be put; the pattern which is the most suitable for one purpose will 
probably be less suitable for another. The cost of the actual wheel, 
however, is small, and the mounting to be described subsequently has 
* On referring to the photograph of fig. 17 it will be seen that in practice the construction 
of the wheels of types A and A' may be such as to reduce the air resistance considerably. 
