Elements of natural philosophy (Volume 2-3) . CD, the latter will move under the actionof the increased repulsion between it and the stra-tum A B. Suppose the stratum A B to take the positionA! B, at the instant the stratum C D begins to distance A A\ will, from the views already given ofthe constitution of a fluid, be indefinitely small. Denote the distance A C by x ; A C by xJ; and theelastic force exerted by the air in its state of rest on a unitof surface by E; then supposing the cross section of thetube uniform, and its area equal to <z, according to Mar-iottes law a xi : a x
Elements of natural philosophy (Volume 2-3) . CD, the latter will move under the actionof the increased repulsion between it and the stra-tum A B. Suppose the stratum A B to take the positionA! B, at the instant the stratum C D begins to distance A A\ will, from the views already given ofthe constitution of a fluid, be indefinitely small. Denote the distance A C by x ; A C by xJ; and theelastic force exerted by the air in its state of rest on a unitof surface by E; then supposing the cross section of thetube uniform, and its area equal to <z, according to Mar-iottes law a xi : a x : : aE: aE{ Mariotteyiaw. in which Et denotes the elastic force exerted by the airon a unit of surface between A!Br and 0 D\ whence zyi Elastic force of TP 77* «^ -lL* . - ? J-j . — • the compressed a. air. The stratum C I) is urged forward by the elastic force 28 NATURAL PHILOSOPHY. Moving forceacting on astratum; En and is opposed by the elastic forceE ; its motion will therefore be due to a X x— X (E-E)^aE ~-aE=aE---r1\^ * J x x,. US which is the moving force. And denoting the mass ofthe stratum C D t by m, the acceleration due to this force,or the velocity generated in a unit of time, will be Velocity due tothis force; a E x x 7/1 X. and the velocity % generated in an elementary portionof time £, equal to that during which the stratum A Bmoves to th will be the same whetherwe regard it concentrated into the plane CD, or ex-panded in both directions half way to the adjacent strata;in which caae, its volume would be a. a?, and it would havean actual density equal to the
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