116 HYDROMECHANICS rato (1643). Pascal's work, written ten years later and published after his death, Sur Vequi- libre des liqueurs, in which he treats the sub- ject in a more systematic manner than any previous writer, contains complete and elegant demonstrations of most of the principles of hy- drostatics, but does not treat of the motions of liquids. The next great student of hydro- mechanics was Sir Isaac Newton, who investi- gated the subject of friction and viscosity in diminishing the velocity of flowing water, and also of the velocity of jets; but upon the latter point he fell into an error by supposing that the velocity with which water issues from an orifice is equal to that which a body would at- tain by falling through half the vertical dis- tance between the surface of the liquid and the orifice. His subsequent discovery of the tena contraeta modified his conclusions, but his theory of efflux is open to objections. He, however, investigated the subject of waves, one of the most difficult in the science of hy- drodynamics, in a manner worthy of his ge- nius. In 1738 Daniel Bernoulli published Hy- drodynamica, sen de. Viribus et Motibus Flu- idorum Commentaria, in which he founds his theory of the velocity of the motion of fluids through orifices upon the supposition that the surface of a fluid which is discharging itself by an orifice preserves a level, and that if the liquid is divided into an infinite number of horizontal strata, all the points in these strata will descend with velocities inversely propor- tioned to their breadth, or to the horizontal section of the reservoir. To determine the motion of each stratum, he employed the prin- ciple of "conservation of living forces;" and from the elegance of his solutions his work is pronounced by the abbe Bossut one of the finest productions of mathemati cal genius. But the uncertainty of the principle which he em- ployed rendered the results of his work of less value than their mathematical excellence. The science afterward received the attention of D'Alembert and of Euler, who enriched it by the application of special mathematical meth- ods of great acuteness and originality. The abbe Bossut also experimentally investigated the discharge of liquids by orifices, and added much to the stock of knowledge on the sub- ject. To the experiments of Venturi, Eytel- wein, and others, the science is indebted for many facts in regard to the flow of water from conically diverging tubes. The flow of water over barrages has been from time to time investigated experimentally by the che- valier Dubuat, D'Aubuisson, Castel, and M. Prony, and also by Smeaton, Brindley, Robin- son, Evans, Blackwell, and others. Before considering the separate branches of the sub- ject, we will notice two important physical properties of liquids, as upon them the action of hydrostatic and hydraulic forces depends. The first important property of a liquid is the perfect mobility of its particles over each other, and one which results from their slight cohe- sion. That there is a certain degree of cohe- sion is shown by the fact that liquids will form drops. There is no active repulsion between the particles until they have been heated to a certain degree; or the repulsion, if there is any, on the hypothesis that both forces are always in action, is less than the cohesion. A certain degree of cold, varying with the liquid, will cause an increase of the cohesive force, so that the liquid will become viscous and then solid; and it is found that the flu- idity of a liquid is promoted by heat, and that water when cold will not flow through pipes as rapidly as when warm. The second important physical property of liquids is their great resistance to compression, so that for a long time it was doubted whether water was compressible. The experiment of Bacon, who hammered a leaden vessel filled with water till it was forced through the pores of the metal, was cited as a proof of the incompressi- bility of water; but a remark of Bacon's to the effect that he estimated the diminished space into which the water was driven, indi- cates that he drew a different conclusion. The experiment of the Florentine academicians in forcing water in a similar manner through the pores of a silver vessel was for some time re- garded as indisputably establishing the incom- pressibility of water; but the apparatus de- vised by Oersted proves in a conclusive man- ner that water and all other liquids are slight- ly compressible. Canton had previously shown that liquids were com- pressible, but the degree could not be ascertained with any accuracy in consequence of the dif- ficulty of determining the amount of expansion which had been pro- duced in the containing vessel. This was obvi- ated by Oersted in pla- cing it within another, so that it would re- ceive equal pressure up- on equal surfaces with- out and within, and thus preserve a uniform ca- pacity. His apparatus is shown in fig. 1. The liquid to be subjected to pressure is placed in the inner glass vessel a, from the top of which a capillary tube turns downward, its open extremity dipping beneath the surface of a layer of mercury contained in the bottom of the outer vessel. Another tube, 6, graduated and used as a manometer, also open at the lower end and dipping in the mer- cury, is placed along with the vessel a in a strong glass cylinder, which is provided at the FIG. 1. Oersted's Appa- ratus.
