2/8 Nature and Oplical EJJicieney of the Minors [April 



The lamps, which are 12 in number, Fire ?Jso arranged in three tiers, 

 corresponding to those in which the rairrors are placed, but the nuiisber 

 in each ro\y is not the same, that of the top row being 3; in the second 

 4, and in the third 5. 



Fiom the accompanying section (Fig. li)itis evident, that no assist- 

 ance whatever is derived by any lamp, from any of tlie mirrors except 

 those in the same tier with itself, an inspection of the figure shovving at 

 oncC; that the image reflected from a mirror situated in the row heneath 

 the lamp, would be merely visible at the very foot of the Light-house> 

 even if it did not fall within the limits of the building itself ; and I 

 have before said enough to explain, that no benefit whatever would be 

 derived by any aid from a mirror in the tier alove it, all the rays of 

 v.diicli v^'ould strike the roof of the lantern, or be lost in the air. It 

 is unnecessary therefore to pay any attention to the operation of the 

 reflectors, with reference to any of the lamps except those belonging to 

 the same tier, and I shall therefore proceed to enquire into the aid af- 

 forded by those in each row to every lamp belonging to it, in turn ; and 

 admitting the very favourable assumption before alluded to, th.at tlie 

 images when visible at any point on the horizon, will also be visible at 

 every point in a direct line between it and the Light-house, shall now 

 measure the extent of the circumference in a lateral direction through 

 which this effect will take place. 



In order to calculate this, it is merely necessary to consider, that the 

 reflected image of any one of the lamps, will, as before explaineJ, be 

 visible in each mirror merely within the limits embraced by the pyra- 

 mid of rays reflected from its surface, and also, that any attention to the 

 vertical divergence, or angle formed between the tipper and lower sides 

 of this pyramid, is rendered entirely unnecessary, by assuming that it 

 produces the greatest possible elfect it is capable of, in rendering the 

 image visible to the very foot of the Light-house. It will therefore 

 only remain to ascertain the lateral extent of these rays from each mir- 

 ror, to obtain the number of the degrees of the horizon illuminated by 

 the reflected light of the lamp from wliich they proceed, and within 

 which its image will be visible ; and by repeating this with each lamp 

 and each mirror, ascertain the effect produced by the wdiole combined. 

 Now, it has been before observed, that the divergence of the rays before 

 and after reflection remains th.e same, and that the sides of a cone or 

 pyramid of reflected light, have exactly the, same mutual inclination, and 

 comprehend the same angle after quitting the plane, which they sub- 

 tended before reaching it. For intWance, that if a be the lamp_'(FiG. 12) 

 andrti, ac the limits of a pyramid of ra3^s striking the surface of the 



