96 M, Ra?nond*s I/istructiojis for the Application of [Aug. 



If the air were, like mercury, an incompressible fluid and of 

 uniform density, the solution of the problem would not have 

 presented any difficulty. It would then have sufficed to esta- 

 bhsh once for all the ratio of the densities in order to infer that 

 of the volumes, and to determine the thickness of the stratum of 

 air whose weight was in equilibrio with a given column of mer- 

 cury of the same diameter. 



liut air is elastic ; it dilates or condenses in proportion to the 

 pressure it undergoes ; and in proportion as we rise in the atmo- 

 sphere, we perceive its density diminish along with the weight 

 by which it is compressed. If then we suppose a column of air 

 divided into strata of equal thickness, these strata beginning 

 from below will diminish gradually in weight, and will correspond 

 respectively to portions of the mercurial column gradually 

 smaller : in such a manner that equal differences of elevation will 

 be marked in the barometer by successive depressions of the 

 mercury so much the smaller as we rise higher. 



We perceive then that in a column of air supposed at a uniform 

 temperature, the density of the strata decreases in proportion as 

 the compressing weight diminishes, which is represented by the 

 height of the column of mercury. Setting out from this first 

 datum, and imagining the column of air divided into strata 

 bounded by planes indefinitely near each other, we are led to 

 perceive that the differential variation of the density is propor- 

 tional to the product of this density multiplied into the variation 

 in vertical height. And if we make this height vary by quanti- 

 ties constantly equal, the ratio of the differential of the density 

 to the density itself will be constant, which is the characteristic 

 property of a decreasing geometrical progression whose terms 

 approach indefinitely near to each other.* Hence it follows, 

 that if the heights of the strata increase in arithmetical progres- 

 sion, their density, and consequently their weight, and conse- 

 quently also the heights of the barometer will decrease in 

 geometrical progression. This law is the fundamental principle 

 of the application of the barometer to the measurement of 

 heights. 



Long before philosophers were aware of it, there existed a 

 book which seemed made expressly for facilitating the applica- 

 tion of this principle. The logarithmic tables, the admirable 

 artifice of which had already so much abridged the long calcula- 

 tions of astronomy, offered a double series of corresponding 

 numbers, one of which proceeded in arithmetical, the other in 

 geometrical progression ; numbers, which even the most courage- 

 ous patience would doubtless never have had resolution enough 

 to calculate solely for the sake of the measurement of heights, 

 even if, in other respects, this art, as yet in its infancy, had been 

 capable of suggesting the idea. It required some genius even to 



• Exposiu du Syst. du Monde. Third Edit. torn. j. p. 155, 



