The experiments of Boyle not only prepared the way for these improvements, but also suggested a method by which the operator might always judge of the degree of exhaustion which he had obtained. We have already seen how, by introducing a common barometer beneath the re ceiver, he was enabled to verify the theory of Torricelli; it only remained, therefore, that the law which connected the density of the air inclosed in the receiver, and the al titude of the barometer, should be discovered, in order to render the indications of the one a criterion of the other. Mr. Boyle, whose genius was more successful in detect ing the chemical than the mechanical properties of air, appears to have overlooked this subject ; at least from his writings there is no evidence that he ever attempted it.
The honour of this discovery has been usually given to Mariotte, whose method of inquiry was as follows :Hav ing taken a bent tube, (Fig. 15, Plate CCCCLXIV.) her metically sealed at the extremity of the shorter branch, but open at the extremity of the longer, which was about six feet in length, he attached to it a wooden frame and sup port ABC. The frame was formed into a scale of inches, which, as the bore of the cylinder was of uniform diame ter, indicated equal volumes.
Having poured mercury into the longer branch, it rose to a certain height in the other, which was observed. The air contained in the shorter branch was now compressed by the weight of the external air, as shown by the baro meter at the time, and also by the excess of the mercury in the longer branch above that in the shorter. Let V be the column which the air occupied, h being the height of the barometer in inches, and cl` the difference of level at which the mercury stood in the two branches, also in in ches; then is h the force by which the air was com pressed. After these observations were made, an addition al portion of mercury was introduced ; and the volume occupied by the air was again observed, as also the differ ence of level at which the mercury stood. Suppose the former were V', and the latter a", then the law which Ma riotte found to obtain was that h : V : : h el': V', or that the compressive force varied inversely as the spaces which the included air occupied. But as the space oc cupied by the air also varies inversely as its density, the compressing force is always proportional to the density of the air which it compresses.
From the manner in which the experiment was made, it will he seen hereafter, that although the observations might favour this general law, they could not exactly con firm it, at least beyond a certain range; for the elasticity of air has been found to be greatly affected by the presence of vapour, a circumstance which was then unknown, and consequently not guarded against. The law of Mariotte
was employed to determine the degree of rarefaction which was produced in the air-pump, by connecting with the orifice 0 a tube OE, communicating with the vessel S, which was cemented to a cylindrical tube F, made of glass. (See Hawksbee's pump.) The lower extremity of this tube was immersed in the vssscl M contaning mercury. Before the pump is worked, as the density of the air con tained in the tube F is the same as that of the external air, the mercury remains at the same level within and without the tube. On placing the receiver over the orifice, and ex hausting a portion of the included air, its density and its elasticity become less : accordingly, the pressure of the ex ternal air causes a portion of the mercury to ascend into the tube. Suppose that, after the pump has been worked for a short time, the mercury stands at a height of p inches above its level in the cistern; then, if the barometer stands at the height of h inches, the included air is compressed by a force of inches.
And, if unity be assumed to express the density of the external air, as h h : h ft : : 1 : it /z will express the degree of rarefaction which has been obtained.
This discovery of Mariotte was extended by the learn ed Cotes, who proved, in his Harmon. Mens. that the den sity of the atmosphere, at uniform distances from the earth's surface, diminishes in geometrical progression.
Let LAB, (Plate CCCCLXV. Fig. 1,) represent a co lumn of air, whose base, AB, rests upon the earth's sur face, and let it be divided into strata of uniform thickness, by the lines CD, El.:, G11, which are to be taken so that the density of the air in each stratum may be equable. Let the densities of the several strata be rep] esented by P P, &c. &c. and the weight of the air by which they are pressed by \V, W' \V".
Then, from the experiment of Marlette, it is known that W : W' : 61`,61" and W' : W" : P : Ste.
But the weights of equal columns of matter are in pro portion to their densities.
Hence " : weight of stratum CB : weight of stratum FD.
or, el' : P : W W' : W' W", wherefore W : W' : \V W' : W' W" and \V' : \V" : : W' \V" W" By alternation and composition,