i839] 



in the Madras Light Houss, 



275 



to only half of the whole circumference of the horizon, which is 

 frequently ihe case when the situation of the Light-house is on the 

 edge of a straight line of coast, (as at Madras) and it is required merely 

 to be visible from the sea. Under these circumstances, it is evident, 

 that only a half of the before mentioned hemisphere of serviceahle 

 ravs are available for the purpose required, since all that emanate to- 

 wards the opposite hemisphere fliU in rear of the line of coast, and 

 are consequently entirely useless, as exhibited in figure (No. 3). In 

 other words, in such a situation, out of the whole sphere of rays pro- 

 ceeding fi om the luminous object, one half is lost owing to their being 

 projected in directions above the horizon, and one half of the remaining 

 halfhy falling in rear of the line of coast. 



In other cases, when the situation is such as to require a greater or 

 less portion of ihe circumference of the horizon to be illuminated, as 

 for instance, if the Light-house be placed upon a promontory, or within 

 a channel or harbour, the ratio of the serviceable rays to the whole 

 iiiumiiiating power of the low-er hemisphere will be in proportion 

 lo the extent of that part of the circumference whence they are requir- 

 ed to be seen, to the whole periphery of the circle. When this ratio is one 

 half, or 180° the proportion of the rays from which benefit is derived is as 

 .before slated,, one half of the inferior hemisphere, shown in Fig. 2, 

 or I of the whole of the rays proceeding from the luminous body, ^lo 

 advantage whatever being derived from the remaining three-fourths. 



The great loss of light here shown to occur in situations similar to 

 that of the Madras Light-house, has led amongst other contrivances, to 

 the invention of metallic and glass mirrors for the purpose of reflecting 

 as many as possible of these truant rays, by diverting them from their 

 natural directions into others in which they would be visible. 



These mirrors may be either plane or curved. 



It is my intention in this paper merely to consider the properties of 

 plane mirrors, with a view^ of estimating the assistance they afford when 

 arranged in the manner in which they are at present applied in the 

 Madras Light-house, my object in selecting that work being prin- 

 cipally to put an end to all doubts as to the possibility of great 

 improvement in it, and at the same time, if possible, to lead the 

 way to the rejection and removal of a clumsy contrivance, by demon- 

 strating the extreme inefficiency of the arrangement, and tracing it to its 

 proper causes. 



Previous, however, to entering upon this investigation, it is necessary 

 to prepare the way for it by a brief attention to a few of the fundamental 

 laws of optics upon which it is foundt^d, and which I hope I shall be ex- 



