"In breaking the rope one thing is to be observed, which will much facilitate the performance; and that is, to place the iron eye L, through which the rope goes, in such a situation, that a plane going through its ring shall be parallel, or nearly parallel to the two parts of the rope; because then the rope will in a manner be jammed in it, and not slipping through it, the whole force of the man's action will be exerted on that part of the rope which is in the eye, which will make it break more easily than if more parts of the rope were acted upon. So that the eye, though made round and smooth, may be said in some measure to cut the rope. And it is after this manner that one may break a whip-cord, nay, a small jackline, with one's hand, without hurting it; only by bringing one part of the rope to cut the other; that is, placing it so round one's left hand, that, by a sudden jerk, the whole force exerted shall act upon one point of the rope. See fig. 83, where the cord to be broken at the point L in the left hand, is marked according to its course, by the letters RTSLM NOPQ, folding once about the right hand, then going under the thumb into the middle of the left hand; where crossing under another part, it is brought back under the thumb again to M, then round the back of the hand to N, so through the loop at L to O, and three times round the little finger at P and Q; which last is only that the loop NO may not give way. Before the hands are jerked from one another, the left hand must be shut, but the thumb must be held loose, lest pressing against the fore finger it should hinder the part T L of the rope from carrying the force fully to the point L; but the little finger and that next to it must be held hard, to keep the loop NO firm in its place. "There are several cases, wherein it would be of singular use to apply the force of one or more men, by means of the girdle or hook and chain, in the manner above-mentioned; as for example, when the resistance is very great, but the bodies that resist are to be removed but a little way: if we lift very heavy goods a small height, to remove any thing from under them; if we would draw a bolt or staple, and find we cannot do it even with an iron crow, the hand pulling it upwards at the end; then the hook of the girdle being applied at the end of the crow, the force exerted by stretching the legs would be tenfold of what the hands were able to do, without more help at the same place. "There may also be many occasions on board a ship. I will the root of the trochanter minor, and inner surface of the os femoris, and inserted into the inner edge of the patella, and likewise, through its nedium, into the anterior tuberosity of the tibia with the former muscles. instance but one. Let FG, fig. 84, be the tackle for raising or lowering the main-top-mast, part of which is represented by m 1, m2; the block G is fixed below, and as the block F comes down, it pulls along with it the top rope FBC, m 1 running over the block B, fixed at A, and round the block C in the heel of the top-mast, so as to draw up the lower end m 1 of the said main-top-mast, which, when hoisted up to its due height, is made fast by the iron pin or fid I, which is thrust through it, and then its own weight and the hole D of the cap will keep it in its place. We will suppose that the force required thus to raise the mast must be that of six men pulling upon deck at the fall of the tackle, that is, at the running rope FGK at K on the other side of the main-mast Ll. Now in order to let down this mast on the sudden, as in case of hard weather, it is necessary the tackle and power must be made use of, though it be but to lift it a very little way, that a man may be able to get out the fid I, before the said mast can be let down and slip to N on the side of the main-mast. I say, that if the hands are so employed otherwise, that instead of six men there be only one man at the rope K; if he has a strong girdle to which he fastens it, or makes a bow in the rope itself, to fix it round the lower part of his back, &c., he may exert much more force in the direction G K than the six men in the common way of pulling; and if he draws to him, sitting on the ground, and pushing his feet against the first firm obstacle that he finds, as against OP, only two inches of the rope G K, he will raise up the main-top-mast the third part of an inch, which will be sufficient for the iron fid I to be drawn out." Desaguliers' Philosophy, vol. i. WATER-MILLS. WATER-MILL is the name by which all mills are designated that receive their motion from the impulse of the water. As each of these mills will come under their respective heads, we shall, in the present article, confine ourselves to a minute description of the different kinds of water-wheels, by whose axis the force with which they have been impressed may be transmitted to move any species of machinery, however simple or complex. But, notwithstanding the extensive signification of the term water-mill when applied to the different branches of manufacture carried on therein, we have another, and still more simple division, arising from the peculiar construction of the water-wheel, termed the undershot-mill, the overshot mill, and the breast-mill. There is also another called the mill with horizontal wheels; but as this is very disadvantageous in point of practical utility, we shall forbear to describe it. The undershot-wheel is used only in streams, and is acted upon by the water striking the float-boards at the lower circumference of the wheel. In the overshot-wheel the water is poured over the top of the wheel, and is received in buckets formed all round the wheel for that purpose. And in the breast-wheel the water falls down upon the wheel at right angles to the float-boards, or buckets placed round the circumference of the wheel to receive it. UNDERSHOT-WHEELS. MR. JOHN SMEATON has made numerous experiments upon the different kinds of water-wheels, the results of which were laid before the Royal Society. The time that has elapsed since the period when they were first given to the world, has been sufficient to prove their fallacy, if any had existed; and the high estimation in which they still continue to be held by mathematicians and mechanics, is certain evidence of their value and importance. Mr. Smeaton prefaces a minute description of the machines and models used by him for his experiments, with an observation, that what he has to communicate on the subject was originally deduced from experiments, which he looks upon as the best means of obtaining the outlines in mechanical inquiry. "But in such cases," says he, "it is very necessary to distinguish the circumstances in which a model differs from a machine in large; otherwise a model is more apt to lead us from the truth than towards it: and, indeed, though the utmost circumspection be used in this way, the best structure of machines cannot be fully ascertained but by making trials with them, when made of their proper size. It was for this reason, though the models and experiments referred to were made in the years 1752 and 1753, that I have deferred offering them to the Society until I had an opportunity of putting the deductions made therefrom in real practice, in a variety of cases, and for various purposes, so as to be able to assure the Society that I have found them to answer." Mr. Smeaton then remarks, that the word power, as used in practical mechanics, signifies the exertion of strength, gravitation, impulse, or pressure, so as to produce motion: and by means of strength, gravitation, impulse, or pressure, compounded with motion, to be capable of producing an effect F and that no effect is properly mechanical, but what requires such a kind of power to produce it. Having described the models and machines used for making his experiments, he observes that with regard to power, it is most properly measured by the raising of a weight, the relative height to which it can be raised in a given time being the actual extent; or, in other words, if the weight raised be multiplied by the height to which it can be raised in a given time, the product is the measure of the power raising it; and, consequently, all those powers are equal, whose products, made by such multiplication, are the saine : for if a power can raise twice the weight to the same height, or the same weight to twice the height, in the same time that another power can, the first power is double the second; but if the power can only raise half the weight to double the height, or double the weight to half the height, in the same time that another can, those two powers are equal. This, however, must be understood to be only in cases of slow and equable motion, where there is no acceleration or retardation. In comparing the effects produced by water-wheels with the powers producing them, or, in other words, to know what part of the original power is necessarily lost in the application, we must previously know how much of the power is spent in overcoming the friction of the machinery and the resistance of the air; also, what is the real velocity of the water at the instant that it strikes the wheel, and the real quantity of water expended in a given time. From the velocity of the water at the instant that it strikes the wheel, the height of head productive of such velocity can be deduced, from acknowledged and experimented principles of hydrostatics: so that. by multiplying the quantity or weight of water really expended in a given time, by the height of a head so obtained, which must be considered as the height from which that weight of water had descended in such given time, we shall have a product equal to the original power of the water, and clear of all uncertainty that would arise from the friction of the water, in passing small apertures, and from all doubts arising from the different measure of spouting waters, assigned by different writers. On the other hand, if the sum of the weights raised by the action of this water, and of the weight required to overcome the friction and resistance of the machine, be multiplied by the height to which the weight can be raised in the time given, the product will be equal to the effect of that power; and the proportion of the two products will be in proportion of the power to the effect: so that by loading the wheel with different weights successively, we shall be able to determine at what particular load, and velocity of the wheel, the effect is a muximum. The experiments made by Mr. Smeaton may thus be reduced. The circumference of the wheel, 75 inches, multiplied by 86 turns, gives 6450 inches for the velocity of the water in a minute; of which will be the velocity in a second, equal to 107.5 inches, or 8.96 feet, which is due to a head of 15 inches; and this we call the virtual or effective head. The area of the head being 105.8 inches, this multiplied by the weight of water of the cubic inch, equal to the decimal 579 of the ounce avoirdupois, gives 61.26 ounces for the weight of as much water as is contained in the head, upon one inch in depth, ' of which is 3.83 pounds; this multiplied by the depth 21 inches, gives 80.43 pounds for the value of 12 strokes; and by proportion, 39 (the number made in a minute) will give 264.7 pounds, the weight of water expended in a minute. Now as 264.7 pounds of water may be considered as having descended through a space of 15 inches in a minute, the product of these two numbers 3970 will express the power of the water to produce mechanical effects; which were as follows: The velocity of the wheel at the maximum, as appears above, was 30 turns a minute; which multiplied by nine inches, the circumference of the cylinder, makes 270 inches; but as the scale was hung by a pulley and double line, the weight was only raised half of this, viz. 135 inches. lb. 0%. The weight in the scale at the maximum .. 8 ... .... -- 10 Now as 9.375 pounds is raised 135 inches, these two numbers being multiplied together, the product is 1266, which expresses the effect produced at a maximum; so that the proportion of the power to the effect is as 3970: 1266, or as 10: 3.18. But though this is the greatest single effect producible from the power mentioned, by the impulse of the water upon |