Musschenbroek, that the ear of a well exercised musician can only distinguish such sounds as succeed each other about 9 times in a second of time; and consequently two sounds at a less interval than the ninth part of a second of time must coalesce and form one single sound. But sound, as we have _seen, describes 1,142 feet in a second, therefore =127 feet nearly, is the space it passes over in the ninth part of a second; and consequently if AB be less than AC+CB by 127 feet, two distinct sounds will be heard at B.

1142

9

Again, the common rate of clear articulate speaking, is said to be at the rate of three syllables and a half in one second, or seven half syllables in a second; and as sound moves at the rate of 1,142 feet in a second, if the echo arrive at the ear of the speaker after 1, 2, 3, 4, &c. half syllables are pronounced, it is clear that the space described by it will be 1142; 1142×2; 1142 × 2 1142 × 3

7

7

7

aud consequently the distance

of the reflecting object will be half of this fraction.

In an elastic tube, one of whose orifices is very small, and the other very large, the sound of a human voice applied to the smaller orifice, will be augmented. For the lateral expansion of the air is diminished by the sides of the tube, and of course the direct expansion and velocity of the included air must be increased. Every point of the tube against which the air is impelled, has a tremulous motion, and becomes a new centre for propagating the pulses, which, striking against the ear at the same time, must be increased. Again, as the diameter of the tube perpetually increases, and the parts of it vibrate in directions perpendicular to the surface, the vibrations will partly conspire in impelling the particles forward, and thus increase their velocity, on which account the intensity of sound ought to be increased. Such seem to be the principal causes of the augmentation of sound in the speaking trumpet, and that figure for the instrument is to be preferred, in which their combined influence is the greatest.

Besides the works on Hydrostatics, Pneumatics, &c. which

have been already mentioned as elementary, we may notice the third and fourth volumes of the "Scientific Dialogues," which are adapted to students of the lowest form. Also "The Motion of Fluids, natural and artificial, in particular that of the Air and Water, &c. by Martin Clare." This volume includes, like almost all others on the same subject, an illustration of the doctrines of Hydrostatics and Pneumatics: under the former, the nature and motion of fluids, as water, in pipes, pumps, syphons, fire-engines, water-works, &c. are explained in a very easy and familiar manner. In this part of the work, likewise, there are ample descriptions of several hydrostatical instruments, and explanations of the method of finding the specific gravities of all sorts of substances, whether solid or fluid. In the second part of the volume, the pressure and gravity of the air are exhibited by convincing and undeniable experiments. The barometer and the air-pump are particularly described, and we have some useful observations on the effects of the air's pressure, on the art of diving,-and on various pneumatic instruments. Although this work has been published nearly fourscore years, it may be safely recommended as a safe guide to students in these branches of science, in connexion with the works of Vince and Parkinson; who may again be directed to the first of Dr. Hamilton's Essays, referred to at the end of the article Mechanics, which contains a number of simple experiments, that may, for the most part, be easily repeated without much trouble or expense.

Mr. Smeaton's, "Experimental Inquiry concerning the natural Powers of Wind and Water to turn Mills, &c." published in 1794, contains much useful matter depending upon Mechanical and Hydraulic principles; such as (1) the result of twenty-seven sets of experiments upon the power of under-shot wheels, together with maxims and observations deduced from them (2) a variety of experiments upon over-shot wheels, from which (taking for granted that the experiments of so able an engineer, as Mr. Smeaton, are quite accurate) it appears that the effect of over-shot wheels is double that of under-shot :

and (3) an account of windmill-sails, with experiments upon sails of different structures, positions and quantities of surface.

Hitherto, in treating of the topics connected with Natural Philosophy, we have referred to works, and to subjects that are merely elementary, such as will satify the tyro in his first steps; and having proceeded so far, he will scarcely stand in need of more particular directions, his knowledge now will be a sufficient guide to him in his abstruser inquiries, and he will ascend to the more general doctrines included by philosophers under the term Statics. Elementary treatises, generally speaking, are confined to the consideration of the equilibrium of bodies, and the circumstances necessary for producing it.

Every kind of work, which is to be performed by a machine, may be considered, abstractedly, as a retarding force; the impulses of water and wind, which are employed as moving powers, act by means of pressures which they exert on the impelled point of the machine; and the machine itself may be considered as an assemblage of bodies moveable in certain limited circumstances, with determined directions and pro portions of velocity. From these considerations, mechanicians have inferred an abstract condition of a body acted on by known powers. And they have found, says a writer on this subject, that, after all the conditions of equilibrium are satisfied, there remains a surplus of moving force. They can accordingly state the motion which will ensue, the new resistance which this will excite, the additional power which this will absorb; and they have, by a particular mode of reasoning, determined a new kind of equilibrium, not thought of by ancient writers on this subject, between the resistance to the machine performing work, and the moving power, which exactly balance each other, and is indicated, not by the rest, but by the uniform motion of the machine. In the same manner, mathematicians have been enabled to calculate that precise quantity of motion of water, which will balance the superiority of pressure, by which the fluid is forced through a sluice, a pipe, or a canal, with a