163 



trial refraction j but it is probable, that this supposition did 

 not much differ from one -tenth of the arc. The distance of 

 the volcano is nine miles, and a variation of refraction of 

 22 " would change the total height of the mountain but one 

 toise. 



As bases adapted to the measurement of mountains are not 

 generally to be found on a coast, and at the level of the 

 Ocean, travellers are forced to recur, either to barometrical 

 measurements, or to the depression of the horizon. In Mr. 

 de Borda's operation, these reductions have been pretty con- 

 siderable, d being elevated 169 toises, and c 55 toises above 

 the surface of the sea. But when the subject of discussion is 

 the comparing barometrical and geometrical measurements, 

 which differ but a small number of toises, we must examine, 

 what is the limit of the mistakes that may be committed, and 

 whether the measure be too great or too little. The varia- 

 tions of the terrestrial refraction elevate or depress the horizon 

 of the sea two or three minutes, to an observer placed on the 

 coast three or four toises high. At this distance the trajec- 

 tories may be more or less concave or convex, according to 

 the temperature of the land and of the sea, and the unequal 

 decrement of density in the successive strata of the air. In 

 proportion as the observer increases his height above the 

 coast, the mistakes owing to the irregular variation of the 

 refractions diminish considerably j and it is easy to show, 

 that at the time of Mr. de Borda's operation they did not 

 exceed three or four toises*. As the sea at this period was 

 colder than the air, the stations c and d may have been found 



* The numerous observations of depression made by Mr. 

 M6chain at Montjouy, near Barcelona, differ from each other 

 but 7| toises, the total height of the mountain being 105 

 toises. Delambre, Base du Systeme metrique, t. ii, p. 759 

 and 765. 



