MECHANICS. 58 
iron vessel, by means of the shoulder, . The apparatus, qy ( fig. 39), served 
to move along the vernier of the manometer, which was inclosed in a glass 
tube. 
It has been mentioned above that the barometer was applicable to the 
measurement of heights, as the atmosphere in its lower strata exercises a 
greater pressure than in the upper, and that consequently the height of the 
barometer would be greater in one case than in the other. These measure- 
ments would be very simple if the air were not elastic, or at least very 
slightly compressible ; for then, by obtaining a point of departure or unity 
by direct measurement of one height, other altitudes could be readily cal- 
culated. This, however, is impossible, as the less the pressure upon a layer 
of air, the less is its density; or in other words, the greater the ascent, the. 
greater the rarity of the air. Mariotte’s law renders it possible, however, 
to attain to accurate results. Suppose the height of the barometer at a certain- 
elevation to be 760 millimetres, and by ascending 11.5 millimetres, the height 
~). Taking 11.5 
metres as unity—then as the density of the air is proportional to its pres- 
of the mercury to be only 759 millimetres = 760/( 
; 7 
sure, the next layer will be less dense, and, indeed, only 760 28 dense as the 
one below it; the height of the barometer then is there only 760 
759 a 2 cay : - 
On SY 760! — 760 760/ ° 20d so on, so that for n x 11.5 metres, the height 
799\n 
of the barometer is 760 es . Ifnow B be the height of the barometer 
at a, and B’ that at a place, b, higher than a by unity, and the quotient, 
/ 
B — % then, according to the preceding considerations, the height of the 
barometer for a place, 6, higher by m units, will be =Bg”, and m can 
: i ; b ae ar a 
be obtained from this equation. Thus ag” =p and m= wih = Here, how- 
ever, must be taken into account the temperature and the vapors present in 
the atmosphere; the consideration of the corrections necessary on this 
account would carry us too far beyond our limits. 
For determining altitudes where the greatest possible accuracy is uot 
required, the easily transportable Differential Barometer of Kopp (pl. 18, 
Jig. 42), may be employed to advantage. It consists of a straight cylindrical 
glass tube, k, united by means of a narrow tube with a glass vessel, 2, closed 
tight above, through whose upper cap a thinner tube, cd, passes. In the 
tube, 4, is a leather piston, which may be movedupanddown. The instru- 
ment is filled with mercury, so that when the piston, Jf, is raised, in conse. - 
quence of the atmospheric pressure, almost all the mercury passes from 7 
into k, and the air contained in the vessel, i, communicates with the 
external atmosphere. A scale is attached to the tube, cd. Depressing the 
piston, the mercury is again forced into i, and there confines, as it closes. 
227 
