198 Oa ihe Arcs perpondiculdr to the Meridian^ 



feoti in the two directions in which it is desired to establish the 

 signals ; in consequence of which a less elevation is required to 

 be produced by the rockets. 



• To calculate this elevation, or the height to which a signal 

 must be raised at a station A, in order to be visible at a post of 

 observation B, if we take d = the difference of level between 

 the stations ; K = their distance apart ; N = 0.08, the mean 

 refraction ; Z = the observed zenith distance of the horizon, 

 viewed from B, in the direction A ; and z = the zenith dis^ 

 tance at which A would be visible from B, were it not for the 



intervention of the horizon; then is cot. ^ =-i> 0.0000000658 



K, all the measures being expressed in metres ; and z — Z 

 t= a is the vertical angle which the rocket must pass through to 

 bring the signal in view from B ; and from which angle the 

 height in metres is found by K tan, a. The greatest height re- 

 quired on the French arc was about 600 metresj for which 

 rockets of 24 lines diameter were employed. 



If we would take an average of the distances on the parallel, 

 intercepted between the meridian of the stations, so as to be in 

 Bome measure guided in judging of the number of stations that 

 an arc of given extent would require, we find 72200 metres for 

 the average distance on the parallel of 45° ; and 70370 for that 

 on the parallel of Vienna and Paris, of which the German 

 portion averages 73000, and the French portion (in which the 

 countries may be considered as remarkably deficient in natural 

 advantages for such operations) 67850 metres. These num- 

 bers are all between 36.5 and 39.5 geographical miles ; and, of 

 course, are something less than the average direct distance 

 between the signals and the posts at which they were observed; 



We learn from Colonel Bonne that the Heliostat has been 

 introduced with success on the portion of the arc that passes 

 through Baden and Wirtemberg, the disappearance of the 

 reflection of the sun (rendered ' instantaneous by the rapid 

 motion of an intercepting screen) being substituted as signals 

 for the explosion of powder. We perceive also that the em- 

 ployment of M. Fresnel's lamp is recommended both by Colonel 

 Bonne and Colonel Puissant, to answer the same purpose by 

 night as the Heliostat does in the day ; a recommendation enti- 



