2S'2 Xatiirc aud Oj'tica/ FjUcicirj/ of /lie Mirrors [Apim, 



bv marking oiX the ani^les h d fc c ciual lo [\w\v coriosiunuling 

 angles of incidenco a h <; aiul a c a. 



The same hiving been done vegaiding the olher two nMli^clors A and 

 C, a similar operation was iHM t'ornied.and a siuiilar sol of angles obtained 

 from the sei oud or middle lanij). aiul alterwar.ls m.ni the lliird, until the 

 whole set belonging to the lust tier of lamps and relh-etors was com- 

 plete. 



As the fiijnre would have been very much confused from the intersec- 

 tion of so many diverging lines from different jioints, owing to the dilU- 

 ciilty of referring then) to their resi)eelive centres, and comparing their 

 relative directions, 1 have in the diagrams representing the spaciis illu- 

 minated by ttie three ditl'erent tiers (I'Iut iU'S IO, 17, and IS), referred 

 the whole to a common centre, an arrangennMU which greatly facilitates 

 their comparison with one another, as it exhibits ihem combined nnder 

 one view, at the same lime that it dois not in the least affect the truth 

 of the representation, as the distances of the real points of divergence 

 from the central point of the light room lo whi< h ihey are referred, is so 

 small when compared with the distance of the < ir umference of the 

 horizon on v. hich the angii'.ar spaces are measured, that the efiect pro- 

 duced by the change in })()sition which such an arrange mcnt requires, is 

 in reality entirely imperceptible. 



In order to render the oporaiion here ailu:1ed to, still more easily nn- 

 derslood, 1 have represented the manner of effecting it in 'he figure last 

 given. The point to which all the cones of rays are referred is there re- 

 presented by cc- b d \'-\<(\ c e, are the resulting lines of direction of the 

 two rays a^», ac proceeding from the lanip«and r(^f^ected from ihe mirror 

 B. The angle which they sublfml v\ ilh one f.noihcr, and the general 

 direction of tlie cone of ravs, is at once obtained by producing tbcm till 

 they meet in K, and the angle whi( h is substituted for it at the point x 

 is found by div.wing xy and ocz [ arallel to k d and h e. In the three figures 

 Kos. 16, 17 and 18, these angles have been laid dt wn scj'arate'y for each 

 row^ of reflectors and lamps, as it has before been shown, that no reflected 

 light is visible, from the lamps of one row and mirrors of another. In 

 order to distinguish the different sectors of rays from one another, they 

 have all been marked, both with the number of the lamp whence the 

 light originates, and the particular reflector from which it is thrown, in 

 the same manner as in the tables before given. For greater convenience 

 in summing up the results also, the number of degrees comprehended by 

 each group of rays is also marked upon the plan, and in Fig. 19, tlie 

 w^hole of the preceding results are brought together at once, by com- 

 bining the three Figures 16, 17 and 18, into one. In considering the 



