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62

DR. LARDNER'S LECTURES ON MECHANICS.

different forces, and which will be equivalent to the given forces.

The next case is when there are two forces acting in the same straight line, but in opposite directions. Were they equal, they would keep the body on which they acted in equilibrium; but if one have a greater velocity than the other, their difference will be the effect produced, and which will be exerted in the direction of that which has the greater velocity. Thus, if A moves with a velocity of 10, and B only with that of 8, then the body will be projected with a velocity of (10-8=)2, and in the direction of AB.

The next proposition is when there are several forces acting upon a body, but all in the same straight line, though not in the same direction, to find the effect. The sum of all forces acting in one direction must be subtracted from that of the opposite forces, the difference will be the effect produced.

What is said of motion may also be applied to pressure, excepting that the latter does not produce motion.

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This figure is called the parallelogram of forces. This rule is not confined to pressure, but will also apply to motion, for the body P would move along the diagonal PC in the same space of time when moved by the two forces 'A and D together, as it would move along either line PA or PD, when impelled by either of the forces singly. A proposition exactly converse to the composition is the resolution of forces, viz. if one force be given to find what two forces are mechanically equivalent to that force. It is very easy to a person acquainted with the former, to find an answer to the present proposition. It is only to describe a parallelogram on the force taken as a diagonal, and the two sides will be the required forces.

The composition differs from the resolution of forces, inasmuch as the former is a determined and the latter an undetermined problem; for in the former case; the single force is the only one into which the two given forces can be compounded, whereas there are several pairs into which a single force may be compounded.

These two problems are very essential, as the whole doctrine of mechanical powers consists in nothing but the composition and resolution of forces; for any weight to be suspended by a crane or other machine is resolved into two weights, whereof one is thrown upon the fulcrum of the machine, while the other is balanced by the power.

Fig. 3.

P

If the forces act neither in the same direction nor in the same straight line, the foregoing rules will not hold good. Suppose there are two forces, A and D, acting on a body P in the different directions AP and DP, it is required to know what single force will produce the same effect on the body P. Let the line AP bear the same proportion to the force A as DP does to D; thus let it contain as many inches as the force has pounds, &c., then draw the lines AC, DC, parallel to DP, AP, and the diagonal CP of the parallelogram ACDP will be in the same proportion to, and in the same direction as the force required.

C

D

3

There are several familiar instances by which these problems may be illustrated. Suppose a ship A (fig. 3.) were in a current running in the direction AC, and that the wind were blow

DR. LARDNER'S LECTURES ON MECHANICS.

ing in the direction AB, and would impel the ship with the same velocity as the current would were they acting singly, it would neither move along AC nor AB, but along the diagonal AD. Again, suppose a person wished to row a boat across a river (which has a current) so as to arrive at a point exactly opposite to that from which he sets out.

Fig. 4.

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ground at the point required, the person making the leap would reach the ground at a place considerably advanced.

Most persons may have seen the equestrian feat of leaping through a hoop or over a bar, &c., and alighting on the back of the horse again; this is effected by means of this property of inertia.

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Let the two parallel lines AB and CD (fig. 4.) represent the sides of a river, the current of which runs in the direction of the arrows, and that E is the point from which he sets out, and F that he wishes to reach. Now, it is evident that were he to row exactly across he would be carried a considerable way down the stream by the force of the current. Therefore he must row to a point higher up the river, and it is required to find that point. Now, let EG be the distance the boat would float down, were it carried along by the current alone, in the time that the man could row his boat across the same river were there no current. Then, from F draw FH in the direction FA equal to GE, and draw the lines HE and FG, which will be parallel. Consequently, the figure HEGF is a parallelogram, and as the boat would move when impelled by one force (the current) along the side EG in the same time it would be moved by the other (the oárs) along the other side EH, it will when impelled by them both together move, in the direction of the diagonal EF, and would arrive at the point F required.

Every one knows the effect produced by leaping from a carriage during its progress, There are two forces to be here compounded, viz. that produced by the velocity of the carriage, and that by the muscular effort exerted on the occasion'; consequently, instead of alighting on the

B

Let AB (fig. 5.) be the line on which the horse is supposed to run, and CF the board or obstacle to be leapt over by the rider. In order to alight on the horse again, he must not leap forward, but only upwards, and must so measure his effort that he may ascend from A to D and back again in the time that the horse would take to run from A to B; consequently, he would arrive at D in the same time that the horse would reach C; thus his muscular effort may be represented by the line AD, while his velocity (retained by his inertia) may be shewn by AC, and these two forces when combined would move him in the direction AG, and he would reach G at the same time that the horse would be at C. By saying he would move along the diagonal AG, his upward motion is considered as uniform, but it is not So, for it is quickest at first, and gradually becomes slower till he reaches as high as D, when he would descend; therefore the force AD being at first stronger than that of AC, he will ascend along the curved line AHG. But he is now at G while the horse is at C. Now he has not lost his velocity yet, but keeps it acting in the line GE, while his gravity acts in the direction GC, consequently, he will descend along the diagonal GB of the parallelogram GEBC, or rather for the same reason as given before, along the curve GIB, and will arrive again on the horse's back at B. (To be continued.)

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OXALIC ACID NOT ALWAYS POISONOUS.

OXALIC ACID NOT ALWAYS PDISONOUS.

It is not generally known, we believe, that oxalic acid is only poisonous when taken in a considerable quantity. It may be, and is, taken in smaller quantities, not only without deleterious effects, but the contrary. In France it is used very commonly in the proportion of from ten to twenty drops, or more, of the saturated solution, to half. a pint of water, and, in such quantities, is refreshing and slightly diuretic. It is often used, also, instead of the citric and tartaric acids for making punch, and we believe in such cases it is equally innocent and pleasant. It ought to be known, that it requires at least half an ounce or more to produce serious or fatal effects. Nobody need be poisoned by mistaking it for Epsom salts, if, before taking the dose, a single drop of the solution be tasted, the oxalic acid being extremely sour-the Epsom salts not at all. Or if a drop of the solution is put upon black leather, or cloth, or into a little ink, it will, if it is oxalic acid, change the black colour to reddish brown; if it is Epsom salts the black colour will remain unchanged. reason of this is, that black colours be ing more or less formed by an oxide of iron, the oxalic acid seizes upon the iron and forms an oxalate which is reddish brown. It is on the same principle that it cleans boot-tops, with the iron on which it unites and effaces the black stains arising from its oxidation in the leather by the agency of the gallic acid, or of the tannin used in the process of preparing it.

THE LIFE' IN AN OYSTER.

The

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The liquor of the oyster contains incredible multitudes of small embryo, covered with little shells, perfectly transparent, swimming nimbly about. One hundred and twenty of these in row would extend one inch. Besides these young oysters, the liquor contains a great variety of animalculæ, five hundred times less in size, which emit a phosphoric light. The list of inhabitants, however, does not conclude here, for besides these last mentioned, there are three distinct species of worms, called the oyster-worm half an inch long, found in oysters which shine in the dark like glow-worms. The seastar, cockles, and muscles are the great enemies of the oyster. The first gets within the shell when they gape and

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George Straker, of South Shields, for an improvement in ships' windlasses. 25 July. Specification to be enrolled in two months.

Louis Quetin, of Great Winchester-street, London, for a new vehicle for the carriage of passengers and goods. 25th of July. 6 months. F. H. N. Drake, Esq., of Colyton-house, Devon, for improvements in tiles for houses, 25th of July. 6 months.

John Nicholls, of Pershall, Stafford, for certain improvements in the lever and the application of its power. 25th July. 2 months.

Joshua Bates, of Bishopsgate-street Within, London, for a new process of whitening sugars. 1st of August. 6 months.

The same, for an improved method of constructing steam boilers. 1st of August. 6 months.

John Hutchinson of Liverpool, for improvements in machinery for spinning cotton, &c. 30th of July. 6 months.

Nathaniel Jocelyn, of New Haven, North America, for improvements in the manufacture of blank forms for bankers' checks, &c., to prevent forgery. 3rd of August. 4 months.

Thomas Bailey, of Leicester, for improvements in lace-making machinery, 5th of August. 6 mouths.

Thomas Brown, of Birmingham, for an improved coach. 5th of August. 6 months.

INTERIM NOTICES.

In conformity with the plan announced in the Postscript to the Preface to our last Volume, we shall next week publish a Double Number, which will enable us to give insertion sooner. than we could otherwise do, to a number of important communications; among others, to the Portable Trigonometry of P. M. W. which we aunounced two weeks ago as being worth apples of gold to practical men.

The patent, a copy' of which "A Manufac turer" bas sent us for our opinion, is, like the majority of patents, so technically defective. that it would not bear legal investigation.

The conclusion of the paper, On the Universal Vitality of Matter, we are obliged, for want of room, to postpone till next week.

Communications received from J. O.-Henry D-I. H. B.-T.-Cosine-A Navigator-H. R. A.-Divisor-Mr. Renshaw A Constant Reader-Galena,

LONDON: Published for the Proprietor, by M. SALMON, at the Mechanics' Magazine Office, No. 115, Fleet Street; where Commu nications for the Editor (post paid) are requested to be addressed.

M. SALMON, Printer, Fleet Street.

Mechanics' Magazine,

MUSEUM, REGISTER, JOURNAL, AND GAZETTE.

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Sir,-Having apprized you that I had invented a machine for drawing spirals by continuous motion, I now do myself the pleasure to enclose you a rough sketch of the same, and shall be happy to see it inserted in your work, should you think it would be interesting to your readers.

The following is a description of the machine:

Fig. 1. is the plan,

Fig. 2. is the elevation; the same letters are used in both figures.

A. A square frame supported on four short pillars.

B. A bevelled ring with teeth, attached to A.

C. A ring turning upon a ledge on the inner circumference of B, and having a cross-bar D, with a slit throughout its length.

1 E. An upright at one end of D, forming a bearing for the horizontal axis F, on which axis a screw of one thread is cut.

G. A bevelled pinion on F, and working into the ring B.

H. A nut upon F, which is made to advance along F during the revolution of F, by means of a pin 1, taking into the thread of F, its lower end being let into the slit in the cross-bar D; but if the pin 1 is withdrawn, H remains stationary.

I. A bar with a slit in the direction of its length, which is attached to the ring C at right angles to the bar D, when the instrument is required for circular spirals, but removed when the instrument is used for drawing ellipses.

K. A bar in the shape of the letter L, having a slit in each leg, and attached to I by pins, which allow it to slide in the direction of the slit in I.

L. A bar upon K, and capable of being set to any angle by means of the tightning screws OP, which slide in the grooves in K and L.

Q. A bar turning upon a centre, (to which it may be set at any angle by the screw 3) attached to the screw P, but below the frame of the instrument, and carrying the tracer R, which can be set at any part of the bar..

S. A frame sliding along the slit in D, and carrying the bevelled wheel

T, and an upright, through which the axis F passes.

V. A pinion, half the diameter of T, and working into it; it can be fixed at any part of F by sliding the frame S along D, and tightening the

screw 2.

W. A bar attached at right angles to the axis of T, and carrying a movable tracer.

The instrument will describe ellipses, elliptical spirals, and circular spirals, and, by a slight addition, interior and exterior epicycloids.

To describe an ellipse, remove the bars I, K, and L, and sliding the frame S along so as to give T, the required eccentricity, tighten the screw 2, and withdraw the pin 1; then roll the pinion G upon the ring B, and the revolution of the axis F will cause the wheel T to turn twice upon its axis whilst it describes one revolution round the centre of B; by which means the tracer on W will describe an ellipse, the proportions of which will depend upon its position on the bar.

To describe an elliptical spiral.It should have been mentioned before, that the pinion G has a boss in front turning in the upright E, and prevented from sliding by the pin 4 passing through E, and taking into a groove in the boss; there is also a boss on the back of G, having a pin 5, which takes into a longitudinal groove upon the prolonged part of the axis F; therefore, to describe an elliptical spiral, first set the wheel at the least eccentricity of the intended spiral, and bring the nut H up to the frame S, and secure it there by a tightening screw below the bar D, (not shewn.) Set the screw 1 to take into the thread on F, the screw 4 to take into the boss on G, and slack the screw, pin 5, but so as not to withdraw it from the groove; then upon turning the pinion G the wheel will revolve as before, but at the same time the axis F will advance along the bar D, and will consequently carry forward the pinion V, and wheel T, and thus continually vary the eccentricity.

To describe circular spirals, bring the nut H close to the upright F, the screw 1, taking into the thread on F, and the screw beneath being slack;

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