376 Prof. E. Wartmann 07i an easy method of measuring 



Let us select in a motionless cloud, or in one which does not 

 move with too great velocity, any point N, fig. 1, distinguishable 



by its colour or peculiar form. Let us place ourselves on an 

 elevated point P, on the summit of a hill or a tower, or even 

 at the window of the upper story of a house. Let us have 

 under us a reflecting plane MM', such as a tranquil surface 

 of water or mercury, or a large horizontal glass. The angle 

 of incidence of a luminous ray which strikes a mirror being 

 equal to the angle of reflexion, it will suffice to determine the 

 angle d formed by the ray which reaches ihe eye directly from 

 the point N, with the ray PI which reaches it by reflexion in 

 I, and to estimate the length PI, in order to solve the problem. 

 In fact, calling e the angle formed by the reflected ray PI 

 with the vertical PS, which passes through the centre of the 

 instrument with which the angle is taken, it is evident that the 

 an'de I contained by the incident and reflected rays =^2e. The 

 two angles d and / being known, it only remains to measure PI. 

 As it might be difiicult to determine p 



precisely the point I of the reflecting /\ 



surface, we may turn the telescope / \ 



round thevertical, keeping the angle e / \ 



constant, and seek the length PL / \ 



or PE of the line joining the point 

 P with the object L or E situated 

 on its margin (fig. 2). If the ob- 

 server is on the top of a vertical wall, 

 or on a tower or house, he will only 

 have to measure its height above 

 the reflecting plane PS = A to deduce 



PI = 



PS 



/? 

 cose' 



