1823.] the Barometer to the Measurement of Heights, 97 



conceive this new application of tables hitherto signalized by so 

 many services of a totally different kind. The name of Mariotte 

 remains coupled with a happy approximation, which seemed as 

 if it ought to have been made at once by every one, but which 

 he himself did not turn to any advantage. We know, however^ 

 that the heights of the barometer at the two stations being 

 expressed whether in inches or any other measure, the difference 

 of level is represented by the difference of the logarithms of 

 these heights. 



But this representation is only an abstract one ; it indicates a 

 ratio, and not absolute measures, because the system of the 

 tables is not framed in the particular system belonging to the 

 measures of heights. 



In order that the difference of the logarithms may be trans- 

 formed into feet, we must apply to it in a particular manner the 

 value corresponding to these measures,''^ combined with the 

 ratio of the densities of mercury and air. These conditions are 

 more easy to fulfil than it might appear. The whole operation 

 consists in finding once for all the number of feet, fathoms, &c# 

 which, multiphed by the difference of the logarithms, will reduce 

 the abstract expression to one, giving absolute measures regulated 

 by the ratio of the densities. Nothing is more simple provided 

 we know this latter ratio. Let us suppose that at the pressure 

 of 29'92i inches of mercury, and at the temperature of melting 

 ice, the weights of air and mercury were as unity to 10477'9. 

 The heights of the two columns being inversely as their densities, 

 it is clear that we must ascend 1-lOOth of 10477-9, or 104*779, 

 in order that the barometer may sink 1-lOOth of the same 

 denomination as that in which our ascent is expressed, or 

 nearly 8*7 feet, that it may sink 1-lOOth inch. Now the pressure 

 being supposed equal to 29*921 inches, we shall find the number 

 sought by dividing 104*779 by the difference of the tabular loga- 

 rithms of the barometrical heights, 29*921 and 29*91 1. 



The exact ratio of the densities being on the contrary supposed 

 imknown, the operation will not be at all more difficult if we 

 have measured geometrically and with great exactness a differ- 

 ence of elevation : for then, taking the barometer to the two 

 extremities of the measured height, and dividing the difference 

 of the logarithms by the difference of elevation, we shall equally 

 obtain the number we seek ; it will, however, correspond only 

 to the particular temperature and pressure under the influence 

 of which we have been operating. If, from hence, we wished 

 to deduce the absolute ratio of the densities of mercury and air; 

 we may arrive at it very easily by means of a formula, which is 

 extremely simple, given in the '^ Astronomic Physique,'* of 

 M. Biot.f My first memoir contains the application of the 

 methods of proceeding which I have here alluded to. 



* " Le Type de ces Mesures." •]- Tom. i. {). 143, 



l^ew Series, voi,. vj, ^ 



