ples; of simple pulleys, merely to alter the direction of motion (97), we have a few instances. The structure of the pulley-like organ is always extremely simple, usually being merely a groove in the bone covered with cartilage, sometimes a bony hook, and in another case a tendinous ring. The tendon of the obturator internus, in passing out of the pelvis, glides in a groove in the ischium, so as to alter its direction, affords an example of the first and simplest pulley in the human body; the hook-like process through which the tendon of the circumflexus palati glides, so as to alter its direction to a right angle, illustrates the second form of pulley; and of the third, or tendinous ring, we have an example in the ring in the depression in the frontal bone, through which the tendon of the obliquus superior muscle of the eye glides, becoming thereby bent to an acute angle.

113. Of the inclined plane or its modifications, we have no instance in the skeleton; the sacrum is certainly not an example of the wedge, notwithstanding its figure. The only approach to a wedge in animal structure which I am acquainted with, is that bony apparatus discovered, by Sir Philip Egerton, in the neck of the ichthyosaurus, an extinct antediluvian reptile; three wedge-like bones have been described by him as connected with the cervical vertebræ, fitting into spaces between them; these wedges are supposed to have been withdrawn when the animal flexed the head upon the trunk, and to be introduced between the vertebræ when the head was raised; so as to prevent that vast muscular effort which would otherwise be required, to keep the enormous and disproportionate heads, of these animals extended.

NOTE.

On the subjects treated of, in the preceding five chapters, the student may consult, with advantage, Sir David Brewster's edition of Ferguson's Mechanics, and Dr. Olinthus Gregory's Mechanics, as well as the monographs in Sir David Brewster's Encyclopædia, Dr. Lardner's Cabinet Cyclopædia, and the Cyclopædia Metropolitana. Among continental authors, the works of Poisson, Pouillet, Biot, Hauy, Quetelet, &c. should be carefully studied.

In the Essays on Mechanics, by the late Dr. Wood, of Cambridge, and Professor Whewell, the reader will find the laws of statics and dynamics mathematically treated. The propositions in the Principia of Newton, bearing on these subjects, will of course be studied with attention by all who desire an intimate acquaintance with them, whilst those who content themselves with a more general knowledge of these subjects, would do well to consult Euler's Letters to the Princess of Anhalt-Dessau. To facilitate the study of these works, the following references to the portions bearing on the contents of the preceding chapters may be useful to the student:

Chap. 1.-Newton, bk. i, def. 1, 3; bk. iii, rule 3; Euler, vol. 1, letters 1, 69, 74, and vol. 2, let. 7, 12.

Chap. 2.-Newton, bk. i, def. 5, 6, 7; bk. iii, prop. 1, 7, 9; Euler, vol. 1, let. 45, 58, 62, 68.

Chap. 3.-Newton, bk. i, cor. 1, 2, def. 8; bk. iii, prop. 19; Euler, vol. 1 let. 3, 71.

Chap. 4.-Newton, bk. i, cor. 6, prop. 50-55, sect. 7; bk. ii, prop. 40, sect. 1-3, 6; bk. 3, prop. 19, 20, 24; Euler, vol. 1, let. 45-68. Chap. 5.-Newton, bk. 1, cor. 6, scholium.

CHAPTER VI.

GENERAL PROPERTIES OF FLUIDS AT REST. (HYDROSTATICS.)

Properties of Fluids, 114. Elasticity of, 115. Compressibility of Water,

116. Equality of Pressure, 117, 118-Level surface of, 119. Level of the Sea, 120. Downward Pressure, 121. Upward Pressure, 124. Lateral Pressure, 126,7. Centre of Pressure, 128. Communicating Vessels, 129, 130. Equilibrium of Solids in Fluids, 131. Principle of Archimedes, 132. Specific Gravity of Solids, 133-136—of Liquids, 137—of Gases, 139. Aerometer, 138. Table of Specific Gravity.

114. FLUIDS, or liquids, are characterized by the extreme mobility of their molecules on each other, by which they are prevented having any distinct form like solids, always assuming that of the vessel containing them. Fluids obey all the laws which have been explained in the preceding chapter, with such modifications as depend upon their molecular constitution; they obey most strictly the attraction of gravitation, (25), and are capable of assuming motion, in the same manner as solids, in cases where the ready mobility of their particles on each other does not interfere. A mass of water, or other fluid, in falling from a given height, would produce effects as important as an equal mass of any solid, if no opposing causes existed; and the reason why no one would fear the falling of a pailful of water on his head from an elevation, capable of giving to the pail itself a degree of momentum sufficient to fracture his skull: is that, in falling, the water is opposed by the air, and, from the ready manner in which its particles allow of separation, it becomes divided into a kind of irregular shower, producing no effects likely to be dreaded

COMPRESSIBILITY OF WATER.

79

from their mechanical violence. If the particles of water were tied together by increased attraction of aggregation, as by freezing, then its mechanical effects would be as serious as those of a mass of stone.

115. Fluids have been divided into elastic and non-elastic: a distinction by no means well founded, for it is quite impossible to draw a distinct line of demarcation between those fluids which, as water and alcohol, are but slightly compressible, and therefore but slightly elastic; and those which, like air and all gases, admit of ready compressibility, and consequently are endowed with a considerable share of elasticity. properties of the one class are common to the other, with but slight modifications. We shall therefore first examine the physical characters of fluids generally, reserving for the ensuing chapter a consideration of the properties peculiar to the eminently elastic fluids, or gases.

The

116. Liquids, properly so called, of which water may be taken as the type, are but slightly compressible; this character indeed was for some time doubted, as the celebrated experiment, performed by the Florentine academicians, of inclosing water in an hermetically-sealed ball of gold, and causing the fluid to percolate the pores of the metal by pressure, was for a long time considered conclusive on this point, although all that it really proved was the porosity of the metal. From the experiments of Canton, the compressibility of water under the pressure of our atmosphere, equal to fifteen pounds on each square inch, was estimated at 0·000044; whilst Mr. Perkins has lately estimated the compression under the same pressure at 0.000048; and Professor Oersted, by means of an extremely accurate set of experiments, has fixed on 0.000046 as the degree of compression experienced by a given bulk of water, for each additional pressure of our atmosphere. The compressibility of liquids is also proved by the faint elasticity they really possess, shown by the copious scattering of drops in all directions, when water, or any other liquid, is poured from a height on a smooth surface. A vessel filled with a

liquid gravitates, in common with its contents, towards the earth; the fluid gravitating also independently of it, as, on piercing a hole in the containing vessel, it escapes towards the earth.

B

117. Liquids, on account of their extreme mobility, are capable of communicating pressure exercised on them equally in every direction, forming one of the most interesting characteristics of this class of bodies. To understand this curious property, let AECD be a vessel containing a liquid destitute of weight, and therefore theoretically unacted upon by the attraction of the earth, and let ℗ be a solid piston, also destitute of gravity and exactly covering its surface. Now, as P is without Dweight, it does not press upon the fluid, and the sides of the vessel may be pierced without its escaping; but if we place on P a weight of 100 pounds, it will attempt to descend, and would reach the bottom of the vessel were it not opposed by the water; accordingly, the upper layer of fluid x becomes pressed by the piston, and would fall, if not supported by the subjacent stratum y, which thus in its turn becomes pressed; this acts on the layer z, and this on the subjacent layers transmitting the pressure exerted by the weight with which the piston is loaded to the bottom of the vessel. And as the whole surface of the base BD supports the pressure of 100 pounds, it follows that one half the surface supports but 50, and 01 the surface but one pound, &c. From these considerations we may safely infer that,

A. Pressure is transmitted by fluids from above to below, upon horizontal surfaces, without becoming diminished. B. It is equal in every portion of the fluid.

c. It is proportioned to the area of the surface pressed. 118. The same phenomena will be observed at the sides of the vessel, for if any portion of it be perforated, the liquid rushes out, providing the weight still continues to act upon