on Mr. Meikle's Paper « On the Lunar Observations." 403 



to be had in every corner, as Mr. R. has done with great ability 

 in your Number for October, although it did not in the least suit 

 his purpose. For the original intention of that demonstration 

 was merely to show that the instrument only gives half the ob- 

 served angle ; and on no account to prove, what is not true, — 

 that the halving is owing to the duuhle reflexion. To talk of the 

 " actual construction of the instrument " is nothing to the pur- 

 pose ; for that construction includes several other glasses which 

 are just as much concerned in halving the angle as the horizon 

 glass is. Indeed we might on the same grounds ascribe that ef- 

 fect to the frame's being constructed of wood or brass. But the 

 grand thing to be kept in mind is, that the '* instrument as ac- 

 tually constructed and used," involves nothing on which the halv- 

 ing of the angle depends but the single reflexion of the index- 

 mirror. 



Let M I be the position of the index at zero, or when the al- 

 titude of an object © is =0; and let © M a ray from the ob- 

 ject impinge against the mirror M, ^/ 

 and be reflected to R, making, by 

 the principles of optics, the angle 

 of incidence ©MP=PMR the 

 angle of reflexion. p' 



Suppose now that the object has 



attained a certain altitude ©M©', © 



and that we turn the index I till the ", 



ray ©'M is reflected to R, making ...■••■' 

 as before ©' M P' = P' M R. j^.--::'.'.'. 



It is then evident that the angle 

 PMP'=P'MR-PMR = |©'MR 

 -i©MR = i©'M©. But PMI 

 = 90°=P'Mr3 from each take 

 P M I', and I' M I = P' M P= i ©' M © = | observed angle. 



The same thing may be shown in several ways ; but since the 

 halving of the observed angle is thus completely effected by the 

 first, the single reflexion, it is clear that the only use of the se- 

 cond mirror fixed at R, is to reflect the ray M R in a direction 

 parallel to ©M ; so that an observer at A might see the object 

 in contact with the horizon. 



Each mirror, therefore, serves as distinct a purpose from that 

 of the other, as it is possible for any two mirrors to do in one in- 

 strument ; and to confound the use of the one with that of the 

 other, is to explain a simple principle into a mystery, where no 

 real mystery exists. 



Upon the whole, Mr. Riddle is certainly very bright on the 



quadrant. *' It is true," says he, " that if a ray of light be re- 



C c 2 fleeted 



