ly Lunar Observations. 247 



yet, as the instrument is constructed, the principle of its opera- 

 tion may be explained, and in fact is generally explained, from 

 the elementary property of vvliich this one is a consequence ; viz. 

 " the angle of reflexion is equal to the angle of incidence." With 

 the assistance of this elementary property of reflexion, the prin- 

 ciple of the instrument is generally demonstrated from the geo- 

 metrical properties of the figures formed by the rays and the 

 planes of the mirrors, at the time at which an observation is con- 

 ceived to be completed. The angle to be measured, and that by 

 which its magnitude is inferred from the instrument, are thus ex- 

 hibited and directly compared. ,(;. 



Let B represent the index mirror, \ 



and C the horizon glass, and let the \ 



planes of those mirrors be produced to 

 meet in D. Let G !)e a distant object, , .-■■ /P 



GB a ray from it falling on the index *■- ...V- •■ i'J; . 



mirror, and reflected from it to th* ho- -p-"" ^\ 

 rizon glass C ; and reflected there again 

 to the eye at A, the point at which the / 



reflected ray would meet the direct one I / 



GB produced. -p 



To an observer at A, the reflected 

 image of G would appear at E a point in AC ; and the angle 

 GAE would measure tiie angular distance of the object and its 

 reflected image ; or of the object and any thing with which the 

 reflected image appeared to coincide. Now from the elementary 

 optical property already referred to, AJ3 C is bisected by B D ; 

 and A C F formed by A C and B C produced is bisected by 

 CD. Whence CD B"= FC D - C BD= i FCA- 4 AB C =i. 

 ABC + BAC-iABC = iBAC. But B D C, the incH- 

 nation of the mirrors, is equal to the angle measured by the 

 revolutmn of the index ; and that angle is therefore half that 

 which it is required to determine. 



With a view to this method of investigating the principle of 

 the instrument, as it is actually constructed and used, there is 

 therefore nothing vague or insignificant in the description which 

 those authors have given, who have stated in substance that "in 

 conse(juence of the double reflr-xion, the angle measured by the 

 instrument is doul)led to obtain the measure of the recjuired an- 

 gle."— From the first reflexion the angle ABC is insected, and 

 from the second the angle ACF ; and it is in conse(|uence of these 

 two reflexions that the angle BAG is formed in the instrument. 



The caution with which Mr. Meikle represents the writers on 

 navigation to liave followed " the old Ijeatcn track," will not 

 probal)|y be diniinislied by the success of his '* wanderings in 

 warch of improvement." 



Q4 By 



