On Photometric Paddle-Wheels. 
673 
1910-11.] 
Chart IV., as will be understood from the key fig. 11. Various values 
of u m are marked off along AC, each being placed at a distance from A 
\ n — \2 “ 1 I * Suppose, for instance, that the given 
( (1 — , 0614u m ) z j 
equal to 
value of u m is found at D, then AD = j f ^ } ’ But f rom 
the geometry of the figure, it follows, that AF = AE cos a = AD cos a, 
therefore, AF == / { 
1 1 cos a m = \ m ( see 16). Only the 
1(1 — - 0314 u m ) 2 
part (shown dotted) of fig. 11 that is needed in practice is drawn in 
c 
Fig. 11. 
Chart IV. In accordance with the above explanation, in using the chart 
one enters the value of u m at the bottom, runs up the corresponding circular 
arc until one meets the radial line corresponding to the required value 
of a m , and then runs along the nearest of the parallel lines, and this line 
will intersect the \ m scale at the required value. Now the beam of light 
is to be so restricted that none of its rays has a position-ratio greater than 
A m . To see what this means we may imagine two straight lines to be 
drawn upwards through the point O in fig. 1, in a plane perpendicular to 
the beam of light, one to the right of the vertical through O, the other to 
the left, and each making with the vertical an angle tan _1 A m ; then the 
necessary condition for equality of intensity among the various rays of 
the beam is that without exception they shall all pass between these 
two lines. 
VOL. XXXI. 
43 
