OF ILLUMINATING LIGHT HOUSES. 
215 
centre and extreme angle of the lens, in the middle of the thickness of the glass, we 
obtain a tolerably close approximation. 
Also, the lens being square, and eight of them forming the circle or system of 
lenses, 2 ) will be the expression for the light intercepted. 
For example, let it be required to find the increase of illuminating power obtained 
by the French lens with its lamp, as used by Drummond in his experiments, the lens 
being 30 inches square, and the lamp having an intensity equal to 4, and illuminating 
power equal to 10*4 Argand lamps. , 
Here the surface of the flame will be 4'55 inches ; therefore by the first rule 
30 2 
-jTT-r- = 198 increase of power. Again, the mean focal distance being about 39 inches, 
a sphere whose apparent surface is 4'55 inches will subtend 3° 31'; hence by the 
second rule 
1 sin 22° 30 f 
vers. 1° 45' 30" 
= 200 . 
These examples being sufficient for the purpose of illustration, we may now state the 
conclusion which is derived from the above investigation ; namely, that all reflectors 
and lenses of the same diameter have the same illuminating power when illuminated 
with the same lamp, and that decreasing the focal distance, and intercepting more 
rays, does not increase the illuminating power, but simply the divergence, and con- 
sequently the surface or space over which it acts. 
On the Comparison of Lenses and Reflectors in reference to their Perfection as Optical 
Instruments. 
The results obtained by the above rules, as to the actual increase of illumi- 
nating power produced by the use of reflectors and lenses, will of course be consi- 
derably greater than would be found in practice, no account being taken of the 
absorption, obstruction, or undue dispersion of the light ; still, however, by comparing 
their computed powers with those obtained by experiment, we shall be enabled to 
ascertain their merits as optical instruments. 
The French lens with its lamp was found by experiment to be equal to 9‘1 reflect- 
ors 21 inches diameter, illuminated with Argand lamps*. 
Nov/ by computation (the lens being 30 inches square) and the intensity of its 
lamp 4, give 30 2 X 4 = 3600 for its illuminating power. 
And a reflector 21 inches diameter, with a lamp whose intensity is 1, gives 346 il- 
luminating power. 
Therefore the illuminating power of the lens ought to be equal to = 10*4 re- 
flectors. 
* Philosophical Transactions, 1830, p. 383. 
