214 
MR. W. H. BARLOW ON DIFFERENT MODES 
minated with a standard Argand lamp, the diameter of th ejlame of which is one inch, 
and its altitude If inch. Here the depth of reflector is 9 inches and the area of its 
339'28 
end 4 (12 2 — 6 2 ) 7854 = 339’28 inches. And by the first rule = 193'8 is the 
amount of power obtained. 
By the second rule we have the angle subtended by the reflector equal 240° ; mean 
focal distance — \/ 12x3 = 6 inches. The angle subtended by the flame of an 
Argand lamp, which is in the form of a cylinder, will be greater in the vertical direc- 
tion than in the horizontal ; in order therefore that we may be able to measure the 
surface of the segment by its versed sine, we will assume that the light is in the form 
of a sphere whose apparent surface and intensity is equal to that of the lamp, and 
therefore equal to it in illuminating power. 
Now the angle subtended by a sphere whose apparent surface is 175 at a distance 
of 6 inches is 14° 18' 
vers* 120° 
therefore by the second rule Tp c - 7 - o n i = 192-9 amount of illu- 
v ci b* i y 
minating power obtained. 
Let us now suppose Drummond’s lime ball to be placed in the focus to find its 
illuminating effect. Here the section of the ball, the diameter being -fths of an 
inch, is -110445, and on the first principle 
339-28 
•11044 5 = amount of power. 
and by the second 
vers. 120° 
vers. 1° 47 ' 27 " 
= 3071 amount of power*. 
And as it is known that the illuminating power of the lime ball when -f-ths of an inch 
in diameter is equal to 166 Argand lamps, it follows that a reflector of the above 
dimensions will give a light equal to 3079 X 16-6 = 51112 Argand lamps, or 264 
such reflectors illuminated with Argand lamps ; which agrees with Drummond’s 
observations^. 
These rules are equally applicable to lenses, the same effect being produced in 
them by refraction as in the reflectors by reflection, except the difference between the 
light absorbed and transmitted. 
It is, however, almost impossible here to determine the mean focal distance very 
exactly, the lens being built in pieces ; and its form being square increases the diffi- 
culty; still if we take the mean between the distance of the focal point from the 
* It may not be seen immediately why these rules do not give precisely the same numerical results, but it 
will be found that if the angle of divergence be very great, the position of the reflector will at the extreme 
edge have a considerable obliquity to the line of direction in which it acts and its apparent surface, and con- 
sequently its illuminating powers will be reduced. The difference, however, is very small when the mean 
divergence is under 20°. 
f Phil. Trans. 1830, p. 390. 
