1910-11.1 
On Photometric Paddle-Wheels. 
671 
where u m denotes the minimum value of u, obtained by taking a — a m in 
finding t 0 and e 0 the constituents of u. 
The value of \ m for all the cases likely to occur in practice may be 
found by an inspection of Charts III. and IV. The theory of Chart III. 
will be understood on reference to the key fig. 10. If AF be measured 
off equal in length to n, AE equal in length to p* and OG equal in length 
to and GH be drawn parallel to FE, then by similar triangles 
OH = OG.AE/AF = t 0 p/n. If HK be drawn parallel to ON and AB, and 
the angle NOM be drawn equal to e 0 /2,J then OL = LK cot e 0 /2 = OH 
cot e 0 /2 — t 0 p/n . cot ej2 : i.e. the length of OL is equal to the value of u m 
Key to Chart III. 
uJ-^CC 4 “ 
n 2 
in (16). To use Chart III. one places the edge of a parallel ruler at the 
given values of n and of p on their respective scales, and then moves 
the edge parallel to itself until it intersects the t 0 scale at the proper 
value of t 0 (as found from Chart II., putting a — a m ). One follows the 
horizontal line from the point at which the edge now cuts the p scale until 
it meets the radial line, which passes through the given value of e 0 (found 
from Chart I., putting a = a m ) on the e 0 scale : the vertical line through 
this meeting > place cuts the u scale at the required value of u m . If pre- 
ferred, a set square and straight-edge may of course be employed instead 
of a parallel ruler : in either case, despite the necessarily somewhat long 
description, the use of the chart will be found both quick and easy. 
u m having been thus ascertained, A m follows from an inspection of 
* When dealing with small values of p greater accuracy will be obtained if AE is 
made equal to twice p, it being remembered that in that case the value of OL which will 
be obtained is twice the value of n. 
t Found from Chart II., putting a — am. 
| Found from Chart I., putting a = a m . 
