Mr W. Ritchie on Radiant Heat 
17 
to that surface, is equal to the quantity radiated in the same di« 
rection from the sides of the furrows, whatever be their number 
or depth. For, since the quantity radiated from AC, in lines pa- 
rallel to CD, is to the quantity thrown off from AC, in lines 
perpendicular to AC, as the sine of ^ACD is to radius. But the 
sine of is to radius, as AD is to AC. Hence the quantity 
of heat thrown off from AC in lines parallel to CD, is equal to 
the portion which would have been radiated from AD, had the 
plane surface remained ; and, consequently the quantity thrown 
off from both sides of the groove, is equal to what would have 
been radiated from the plane surface AB. 
From this property, it evidently follows, that the increased ef- 
fect upon the focal ball, when a striated surface was used, does 
not depend upon the increase of surface, but upon the quantity 
of heat reflected by the sides of the furrows. 
From the preceding reasoning, we may also conclude, that the 
quantity of heat radiated from the surface of a hemisphere, in 
lines perpendicular to the plane of its great circle, is equal to the 
quantity which would be radiated in the same direction from the 
plane of that great circle. For, let the surface of the hemi- 
sphere be conceived to be made up of an indefinite number of 
plane surfaces, AC, C D, &c. draw C E and D F perpendicular 
to A B, and C G at right angles D F. 
