Elements of analysis as applied to the mechanics of engineering and machinery . ^; hence, the lawof descent may also be graphically illustrated by a parabola AP Q^ Fig. 4, with the parameter p =:^2g. The ab-scissas A31^ of this curve are, ofcourse, the spaces described in the descent,and the corresponding ordinates JXP, corresponding velocities. 2. If a be a certain volume of air underthe pressure of one atmosphere, we have, ac-cording to the Law of Mariotte^ the volume of the same quantity of aair under a pressure of x atmospheres: y = —• a Fig. for X For a? = 1, we have
Elements of analysis as applied to the mechanics of engineering and machinery . ^; hence, the lawof descent may also be graphically illustrated by a parabola AP Q^ Fig. 4, with the parameter p =:^2g. The ab-scissas A31^ of this curve are, ofcourse, the spaces described in the descent,and the corresponding ordinates JXP, corresponding velocities. 2. If a be a certain volume of air underthe pressure of one atmosphere, we have, ac-cording to the Law of Mariotte^ the volume of the same quantity of aair under a pressure of x atmospheres: y = —• a Fig. for X For a? = 1, we have y =z a\ for ^ = 2, ?/1^?2/ = T^; for ^ = 100,2/ 100 for X for ^ = 4,2/: 0; 00, y Art. 3.] ELEMENTS OF A:JsrALTSIS. thus it is clear that the volume becomes less as the tension is greater,and that, if the Laio of 3Iariotte were accurate for all tensions, an infi-nitely small volume y would correspond to an infinitely great tension : ^= i gives 2/= 2 a; ^ = i, ?/= 4 a; hence, the less the tension the greater the volume, and if the tensionbe infinitely small, the volume will be infinitely great. The curve which corresponds to this law is represented in Figc 5,(&c.); J. Jf, are the the tensions or abscissas x^ MP^ corresponding volumes or ordinates y. We perceive that thiscurve gradually approaches the co-ordinate axes A X and A F, with-out ever reaching them. 3. The dependence of the expansive force y of vapor upon thetemperature x ma}^ be expressed, at least within certain limits, bythe formula fa -f- ^A™2/ = I —7— I atmosjoher
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