xlii 



THE PROGRESS OF 



times during its passage along the pipe. It in 

 this case the whole pressure were divided into 

 a hundred equal parts, one of those only gene- 

 rates the velocity, while ninety-nine parts an* 

 expended in merely surmounting the impedi- 

 ments to the flow. 



Smeaton's experiments, by means of small mo- 

 dels, in 175!), on the action of water and wind 

 against the sails of mills, though made upon n 

 very contracted scale, have been made generally 

 to regulate practice. The experiments of colo- 

 nel Beaufoy were made with great care. But 

 tin.- most complete set are said to be those made 

 at l-'uliluu between 1811 and 1815, by Lager- 

 hjelm and Forselles. Their publication, which 

 appeared in 1818, contains also many experi- 

 ments on friction. 



The resistance of fluids to bodies moving 

 through them is partly occasioned by the accu- 

 mulation of fluid before them, and partly by the 

 dilatation and consequent partial vacuum pro- 

 duced behind the moving body. Both of these 

 impediments increase at a great rate, according 

 to the velocity. Robins first showed, that when 

 n body moves through air at a rate exceeding 

 1350 feet per second, a vacuum is formed behind 

 it, and the body in consequence is retarded by a 

 force equal to the whole pressure of the atmos- 

 phere. This pressure completely deranges the 

 parabolic theory of the motion of cannon balls. 

 It explains also why the motion of a missile is 

 very much affected by the shape of the posterior 

 extremity. 



Robins employed an ingenious method of de- 

 termining the impulse of balls, by firing them 

 against a heavy loaded pendulum, whose deflec- 

 tion indicated the momentum thus communicated. 

 By intercepting the flight at different distances, 

 he discovered the diminution of velocity, and 

 consequently the effect produced by the resis- 

 tance of the air. Dr Hutton adopted the balistic 

 pendulum in his extensive set of experiments, 

 made on Woolwich common during the years 

 1790 and 1791. It comprehended the whole 

 range of velocities from 5 feet in a second to 

 2000. The resistance was found to increase in 

 a greater ratio than that of the square of the ve- 

 locity. 



Coulomb showed by his balance of tortion, that 

 when the motion is very slow, the resistance of 

 fluids is proportional to the velocity simply. In 

 rapid motions it would appear to increase as the 

 square of the velocity. Probably when the mo- 

 tion is very rapid, the resistance may increase as 

 the cube of the velocity. But this point has not 

 yet been cleared up by a satisfactory series of 

 experiments. 



The flow of air through a small orifice suffers 

 nearly the same loss as water, or delivers only 



about five-eighths of the measure indicted by 

 theory. But when airs pass through a long pipe, 

 the obstruction seems to be considerably greater 

 than happens to water in the same circumstances. 



When different gases are made to pass through 

 .1 small aperture by a given pressure, the time 

 occupied by the various gases is precisely in- 

 versely as the square root of the specific gravity 

 of the gases. Thus oxygen gas is 16 times heavier 

 than hydrogen gas ; and a given bulk of hydro- 

 gen gas will pass through a given aperture, urged 

 by the same pressure, in the fourth |>art of the 

 time that the same volume of oxygen gas will 

 take to pass. 



One of the finest consequences drawn from the 

 principles of pneumatics is the method of deter 

 mining the height of mountains by means of ba- 

 rometrical observations. Boyle first observed, 

 that the density of the air is always proportional 

 to the pressure. This was also announced by 

 Mariotte, in his work on the atmosphere, pub- 

 lished in 1676 ; and, in consequence, is usually 

 known in France by the name of the law of Ma- 

 riotte. In 1685, Halley gave a geometrical de- 

 monstration, that the density of the atmosphere di- 

 minishes in a continued geometrical proportion, 

 when the heights increase in an arithmetical pro- 

 portion. For the sake of round numbers, he as- 

 sumed thirty inches for the standard mercurial co- 

 lumn ; air at the surface being 800 times less dense 

 than water ; and he made the elevation propor- 

 tional to the difference of the logarithms of these 

 columns. The interval between thirty and 

 twenty-nine inches corresponding to 900 feet. 

 This rule, drawn directly from theoretical con- 

 siderations, was found to apply, with tolerable 

 accuracy, to an observation made a few years 

 afterwards on the top of Snowdon. Newton 

 generalized the principle in his Principia, by 

 taking into the estimate the decrease of gravity 

 in receding from the earth, and arrived at the 

 conclusion, that the densities of the higher strata 

 of the atmosphere, form a geometrical progres- 

 sion corresponding to altitudes disposed in har- 

 monic proportion. But this correction, in most 

 cases of barometrical measurement, is superfluous. 



After this the subject fell asleep for almost 

 half a century. Bouguer took the opportunity 

 of his journey to Peru, to compare theory with 

 observation, upon the grandest scale, by measur- 

 ing the heights of the Cordilleras. His investiga- 

 tion was published in 1753, when he gave the 

 very simple rule which is the ground of our pre- 

 sent practice. That the difference between the 

 logarithms of the barometrical columns, reckoning 

 as integers the first four figures, and deducting a 

 thirtieth part, will express the altitude in toises. 

 To accommodate the result to English measure, 

 it is only required to odd, instead of subtracting, 



