392 m. ^Y. HOPKIXS OX THE COXSTKUCTIOX OF A XEV CALOEDIETEE 
and 
The proper limits of 6 are + cos“* («= radius of the diametral surface), but they 
would render the next integration unmanageable. Take the integral from 6=—- to 
0= I- Then 
since q' vanishes with §. 
With the increase of § (zi being very small) this expression rapidly approximates to 
i. e. if Zi be sufficiently small we shall have approximately 
or since the a is an element of our narrow diametral annulus, we have 
0 = - 1. area of the annulus, 
2 ’ 
q being the quantity of heat which radiates upon the annulus. If the breadth of the 
annulus be denoted by (3, its area will =2‘Taj3, and 
q=:7r^laj3. 
Again, let Q be the quantity of heat which radiates in a unit of time from the whole 
radiating surface. Conceive two right cones with common vertex at SS and common 
axes perpendicular to the radiating surface, their vertical angles being 0 and 
The quantity of heat radiating between these two conical surfaces will 
= ^S . I cos 0 . 27r sin 0 . 
and therefore the whole quantity radiating from will 
. ^S, 
Q = 7rl . 
= 
or 
