the distance and //eigJif of an elevated 2^oi lit. 'ill 

 This value being known, we deduce from it 



h = PI cos e. 

 In like manner since the incident ray 



IN = PI.^^, 

 sin (a + Z) 



thereFore the vertical height NQ = H of the cloud above 

 the mirror is 



H = IN.cosf = /i-^ — T-, — -, 

 sm ((/ + /) 



and its height A = H — // above the observer 

 . , r sinrf "\ 



Tt is sufficient in practice to employ a circle placed vertically 

 and furnished with a tube without lenses. A metallic plate, 

 blackened and pierced at its centre with a small hole, serves 

 instead of an eye-glass. The tube, the interior of which is 

 likewise black, is furnished with cross wires, and a sufficient 

 length is given it to admit only the useful rays, and not those 

 which are reflected by objects surrounding the point which 

 is observed. The reflecting surface may be a pond, a lake, a 

 large sheet of water or mercury, &c. 



Beside its simplicity, the process which I have described, 

 and which evidently applies in the same cases as the other 

 methods which have been proposed, appears to me to offer 

 some advantages over them. It is absolutely independent of 

 the presence of the sun above the horizon. The larger the 

 base to be measured PI, the greater will be the approxima- 

 tion. If the point N is only slowly moved, we may employ 

 Borda's method for the repetition of the angles, and thus limit 

 more nearly their exact value: we may, moreover, observe at 

 short intervals of time, and determine the velocity of transla- 

 tion of the object, — a circumstance which it is often useful to 

 ascertain. We remark, lastly, that there is no longer any 

 possibility for a single observer to confound the point of vision 

 with other surrounding points. Now this confusion frequently 

 occurs in the case of a fleeting cloud, and which requires less 

 time to lose its form than is required, in M. Pouillet's method, 

 for two observers to regain their post and observe after having 

 met to make their arrangements. 



If the wind or any other cause prevents the employment of 

 a liquid as the mirror, a very smooth silvered glass might be 

 substituted, of as large dimensions as possible, and be placed 

 horizontally by means of levels or screws, or thin wedges. 



