THE BAROMETER.] 



MECHANICAL PHILOSOPHY. PNEUMATICS. 



769 



the experiment was actually performed, in 1G47, by the 

 celebrated Pascal : he procured glass tubes closed at one 

 end, of forty feet long, and found, that when filled with 

 water in a deep river, and then raised vertically with the 

 open end downwards, the fluid ceased to fall when water 

 in the tube stood about 32 English feet 2\ inches from 

 the surface of the river. This experiment clearly proved 

 that the pressure of the whole atmosphere on any sur- 

 face was equal to the pressure of a column of water 32J 

 feet high on the same surface. And thus was satis- 

 factorily shown not only that air has weight, but what 

 i amount of weight was sustained by a given area of the 

 surface of the earth pressed upon by the atmospheric 

 column resting upon it : the weight sustained would be 

 equal to that of a column of water, on the same area, 

 about 32} feet high. 



The same conclusion is obtained with a more manage- 

 able length of tube by using mercury instead of water. 

 And in this way the experiment had been tried previously 

 by Torricelli, and it is hence called the Torricellian ex- 

 periment : it led to the invention of the barometer. 

 When a tube about three feet in length, and closed at one 

 end, is filled with mercury, and then inverted in a basin 

 of that fluid, the column of mercury held suspended in 

 the tube is found to be about '29 inches above the surface; 

 and as mercury is about 13^ times the weight of the 

 same volume of water, we arrive at the eauie result 

 namely, that the pressure of the atmosphere on any area, 

 e same as the pressure of a column of water on that 

 area of about the height 



29 X 13J inches = about 32J feet. 



An exact correspondence between the results of such 

 experiments made at wide intervals of time must not be 

 expected, because the weight of the atmosphere fluc- 

 tuates, like the other changes in its condition. The 

 average height of the mercurial column is about 30 

 inches, the ordinary range bein^ between 28 inches and 

 31 inches ; and as 30 cubic inches of mercury weigh 

 about 15 Ibs. , every square inch of the surface of the 

 earth, at the level of the sea, sustains, on the average, 

 15 ibs. of atmospheric pressure. 



WEIGHT OF A VOLUME OF AIR. Besides the 

 foregoing methods of proving that the whole atmosphere 

 exerts a pressure, upon the globe of the earth, equal to 

 that which would be exerted by a sea of mercury 30 

 inches deep, covering its entire surface, a definite portion 

 of the air about us may be taken, and, like any other 

 material substance, be actually weighed in a balance. 



Let a vessel containing a cubic foot, that is, 1000 

 ounces, of water be provided with a stop-cock screwed 

 upon its neck. This vessel may be exhausted of its air 

 by aid of the air-pump, a machine which will be here- 

 after described. Thus emptied, and the stop-cock closed 

 so as to prevent the readmission of air, let the vessel be 

 accurately weighed in a very sensible balance. (See 

 STATICS, page 723). 



When the exact counterpoise is thus ascertained, let 

 the stop-cock be opened and the air admitted into the 

 vessel ; the vessel thus filled, with the stop-cock again 

 closed, to cut off all external pressure, will be seen at 

 once to preponderate, and we shall find it necessary to 

 put about 523 grains of additional weight in the other 

 scale-pan to restore the equilibrium ; thus showing that 

 a cubic foot of air, at the surface of the earth, weighs 

 about 523 grains. 



We cannot, of course, speak accurately as to a few 

 grains more or less, but it will be always found that at 

 least an ounce more weight will be required to counter- 

 poise the vessel when full of air, than was required before 

 the air was admitted. 



It is in this way ascertained, that when the barometer 

 stands at 30 inches, and the temperature of the air is 52 

 of Fahrenheit's thermometer, tlie weight of water is to 

 the weight of an equal volume of the air around us as 

 840 to 1. 



LAW OF MARRIOTTE. Having thus established 

 the truth of the proposition that air has weight, we may 

 now proceed to explain the way in which the law of 



voi. i. 



Mamotte, namely, that the volumes into which air may 

 be compressed are inversely as the pressures applied, is 

 arrived at. 



Let DAG (Fig. 191) be a bent tube of equal bore 

 throughout, or at least equally wide throu A- tig. 191 . 

 out, the shorter vertical leg. Conceive this D - 

 tube to be at first opeu at both ends C and 

 D, and let a little mercury be poured in, 

 so as to fill the bend of the tube ; the level 

 of the mercury at A and B will be at 

 the same height AB in each tube, how- 

 ever dissimilar the two portions of the tube 

 may be (HYDROSTATICS, page 751). Now 

 let the end C be closed, and let such a 

 quantity of mercury be poured in at D as 

 will cause the surface, originally at 0, 

 to rise to B', half-way between B and C. 

 Upon measuring the additional column of 

 mercury thus introduced into the tube 

 that is, having previously marked the 

 level O of B' if we now mark the level 

 E when the surface B has risen to B', we 

 shall find that the length of the mercurial 

 column U E is exactly equal to that of the 

 mercurial column (as shown by the baro- 

 meter) which represents the weight of the 

 atmosphere. The inference is this : when 

 the surface A sustained the pressure of only B. LL U .A 

 the column of air above it, the air in the 

 shorter leg occupied the space B C ; the air in B C was 

 thus compressed into the volume it then had, simply by 

 the weight of the atmosphere applied upwards to the 

 surface B. 



But when the weight of two atmospheric columns 

 pressed on the surface B, that is, the weight of the baro- 

 metric column of mercury in addition to the atmosphere, 

 then the volume of air in B C occupied only half the 

 space namely, B' C ; that is, the original volume was 

 compressed by the double pressure into half its former 

 bulk. Again, if another column of mercury be poured 

 into the tube at D, till the air in the other leg occupies 

 only one-third of its original volume, we shall find that 

 the height of the entire column of mercury, measuring 

 the difference of the levels in two legs, is twice that of 

 the barometric column ; so that the air in B C, when 

 pressed upwards by the weight of three atmospheres the 

 atmosphere itself pressing on the upper surface of the 

 mercury and the double barometric column is com- 

 pressed into one-third of its original volume. Results in 

 harmony with these are always found to follow whatever 

 fractional portion of the whole atmospheric pressure be 

 applied ; and thus the law is experimentally established, 

 that the volumes into which air is compressed by pres- 

 sures are inversely as the intensities of those pressures. 

 And this is only saying that the densities are directly 

 proportional to the pressures. 



As it is the elastic force of the condensed air that thus 

 balances the additional pressures, we further infer that 

 the elastic force is proportional to the density or to the 

 force of compression. 



A form somewhat more mathematical may be given to 

 the foregoing account as follows : 



The mercury, at first poured into the tube at D, stand- 

 ing at the same level A B in both legs, and the end C of 

 the tube being then closed, the space 13 C is occupied by 

 the air in its existing state of atmospheric pressure at 

 the time of the experiment, which pressure is indicated 

 by the column of mercury in the barometric tube at that 

 time. Fresh mercury is now poured in at D ; its surface 

 reaches the level E in one leg, and some lower level B' O 

 in the other, showing that the pressure of the air origi- 

 nally occupying CB, by now being forced to contract itself 

 into C B', exercises an increased pressure ; so that now 

 it not only balances the pressure of the atmosphere, in 

 its original state at D, but also the column of mercury 

 OE. 



Let H be the height of the mercury in the barometer ; 

 then the pressure ou the original volume of air B C is 

 that of a column of mercury of base B and height H, 



