112 Mr. W. Bennett on 
shown in fig. 4. The way in which the ¢ form passes into 
the two-branched form is worthy of attention. 
This method of working can of course be applied to find 
the shadow of an object of any shape, and is applicable to 
other kinds of pencils. If the two sections are drawn to the 
same scale, a thread model of the pencil can be made by 
erecting them in parallel planes and joining corresponding 
points by strings. 
It will be noted that to each point of the wire there 
correspond three points in the shadow, and that all four lie 
in a plane passing through the axis. Thus if the wire 
terminates at the nearest point to the axis, the shadow will 
be as shown in fig. 6. 
Fle. 6. 

The equation of the shadow can be deduced without 
difficulty :— 
The equations of a ray are : 
o=const. 
r= — tan 20 (2 me 
The wire is given by : 
2=ah, 
‘ ad 
"= cos} 
Where the ray meets the screen z=c, and we have 
2 5). 
ah vie a 
p= — tan 20( + —— 3): . 
But since the ray passes through a point in the wire, 
d ; 
ae tn 20(8+ 9 cag) - . (2) 
