Read Ebook: Scientific American Supplement No. 441 June 14 1884. by Various

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In this deduction of the formula, as in that of Prof. Rankine, all the motions are supposed to have the same direction, corresponding to that of the hands of the clock; and in its application to any given train, the signs of the terms must be changed in case of any contrary motion, as explained in the preceding article.

And both the deduction and the application, in reference to these incomplete trains in which the last wheel is carried by the train-arm, clearly involve and depend upon the resolving of a motion of revolution into the components of a circular translation and a rotation, in the manner previously discussed.

which means, being interpreted, that F makes two rotations about its axis during one revolution of T, and in the same direction. Again, let A and F be equal in the 3-wheel train, Fig. 16, the former being fixed as before. In this case we have:

that is to say, the wheel F, which now evidently has a motion of circular translation, does not rotate at all about its axis during the revolution of the train-arm.

All this is perfectly consistent, clearly, with the hypothesis that the motion of circular translation is a simple one, and the motion of revolution about a fixed axis is a compound one.

When the definition of an epicyclic train is restricted as it is by Prof. Rankine, the consideration of the hypothesis in question is entirely eliminated, and whether it be accepted or rejected, the whole matter is reduced to merely adding the motion of the train-arm to the rotation of each sun-wheel.

This will be seen by an examination of Fig. 17; in which A and B are two equal spur-wheels, E and F two equal bevel wheels, B and E being secured to the same shaft, and A being fixed to the frame H. As the arm T goes round, B will also turn in its bearings in the same direction: let this direction be that of the clock, when the apparatus is viewed from above, then the motion of F will also have the same direction, when viewed from the central vertical axis, as shown at F': and let these directions be considered as positive. It is perfectly clear that F will turn in its bearings, in the direction indicated, at a rate precisely equal to that of the train-arm. Let P be a pointer carried by F, and R a dial fixed to T; and let the pointer be vertical when OO is the plane containing the axes of A, B, and E. Then, when F has gone through any angle a measured from OO, the pointer will have turned from its original vertical position through an equal angle, as shown also at F'.

Now, there is no conceivable sense in which the motion of T can be said to be added to the rotation of F about its axis, and the expression "absolute revolution," as applied to the motion of the last wheel in this train, is absolutely meaningless.

Nevertheless, Prof. Goodeve states that "We may of course apply the general formula in the case of bevel wheels just as in that of spur wheels." Let us try the experiment; when the train-arm is stationary, and A released and turned to the right, F turns to the left at the same rate, whence:

and the equation becomes

A favorite illustration of the peculiarities of epicyclic mechanism, introduced both by Prof. Willis and Prof. Goodeve, is found in the contrivance known as Ferguson's Mechanical Paradox, shown in Fig. 18. This consists of a fixed sun-wheel A, engaging with a planet-wheel B of the same diameter. Upon the shaft of B are secured the three thin wheels E, G, I, each having 20 teeth, and in gear with the three others F, H, K, which turn freely upon a stud fixed in the train-arm, and have respectively 19, 20, and 21 teeth. In applying the general formula, we have the following results:

The paradoxical appearance, then, consists in this, that although the drivers of the three last wheels each have the same number of teeth, yet the central one, H, having a motion of circular translation, remains always parallel to itself, and relatively to it the upper one seems to turn in the same direction as the train-arm, and the lower in the contrary direction. And the appearance is accepted, too, as a reality; being explained, agreeably to the analysis just given, by saying that H has no absolute rotation about its axis, while the other wheels have; that of F being positive and that of K negative.

The Mechanical Paradox, it is clear, may be regarded as composed of three separate trains, each of which is precisely like that of Fig. 16: and that, again, differs from the one of Fig. 15 only in the addition of a third wheel. Now, we submit that the train shown in Fig. 17 is mechanically equivalent to that of Fig. 15; the velocity ratio and the directional relation being the same in both. And if in Fig. 17 we remove the index P, and fix upon its shaft three wheels like E, G, and I of Fig. 18, we shall have a combination mechanically equivalent to Ferguson's Paradox, the three last wheels rotating in vertical planes about horizontal axes. The relative motions of those three wheels will be the same, obviously, as in Fig. 18; and according to the formula their absolute motions are the same, and we are invited to perceive that the central one does not rotate at all about its axis.

which corresponds with the actual state of things; all three wheels rotate in the same direction, the central one at the same rate as the train arm, one a little more rapidly and the third a little more slowly.

It is, then, absolutely necessary to make this modification in the general formula, in order to apply it in determining the rotations of any wheel of an epicyclic train whose axis is not parallel to that of the sun-wheels. And in this modified form it applies equally well to the original arrangement of Ferguson's paradox, if we abandon the artificial distinction between "absolute" and "relative" rotations of the planet-wheels, and regard a spur-wheel, like any other, as rotating on its axis when it turns in its bearings; the action of the device shown in Fig. 18 being thus explained by saying that the wheel H turns once backward during each forward revolution of the train-arm, while F turns a little more and K a little less than once, in the same direction. In this way the classification and analysis of these combinations are made more simple and consistent, and the incongruities above pointed out are avoided; since, without regard to the kind of gearing employed or the relative positions of the axes, we have the two equations:

As another example of the difference in the application of these formulae, let us take Watt's sun and planet wheels, Fig. 19. This device, as is well known, was employed by the illustrious inventor as a substitute for the crank, which some one had succeeded in patenting. It consists merely of two wheels A and F connected by the link T; A being keyed on the shaft of the engine and F being rigidly secured to the connecting-rod. Suppose the rod to be of infinite length, so as to remain always parallel to itself, and the two wheels to be of equal size.

Then, according to Prof. Willis' analysis, we shall have--

The other view of the question is, that F turns once backward in its bearings during each forward revolution of T; whence in Eq. 2 we have--

as before.

For example, take the combination shown in Fig. 20. This consists of a train-arm T revolving about the vertical axis OO of the fixed wheel A, which is equal in diameter to F, which receives its motion by the intervention of one idle wheel carried by a stud S fixed in the arm. The second train-arm T' is fixed to the shaft of F and turns with it; A' is secured to the arm T, and F' is actuated by A' also through a single idler carried by T'.

We have here a compound train, consisting of two simple planetary trains, A--F and A'--F'; and its action is to be determined by considering them separately. First suppose T' to be removed and find the motion of F; next suppose F to be removed and T fixed, and find the rotation of F'; and finally combine these results, noting that the motion of T' is the same as that of F, and the motion of A' the same as that of T.

Then, according to the analysis of Prof. Willis, we shall have :

This is, unquestionably, correct; and indeed it is quite obvious that the effect upon F' is the same, whether we say that during a revolution of T the wheel A' turns once forward and T' not at all, or adopt the other view and assert that T' turns once backward and A' not at all. But the latter view has the advantage of giving concordant results when the trains are considered separately, and that without regard to the relative positions of the axes or the kind of gearing employed. Analyzing the action upon this hypothesis, we have:

In train A--F:

In train A'--F':

Now it happens that the only examples given by Prof. Willis of incomplete trains in which the axis of a planet-wheel whose motion is to be determined is not parallel to the central axis of the system, are similar to the one just discussed; the wheel in question being carried by a secondary train-arm which derives its motion from a wheel of the primary train.

The application of his general equation in these cases gives results which agree with observed facts; and it would seem that this circumstance, in connection doubtless with the complexity of these compound trains, led him to the too hasty conclusion that the formula would hold true in all cases; although we are still left to wonder at his overlooking the fact that in these very cases the "absolute" and the "relative" rotations of the last wheel are identical.

In Fig. 21 is shown a combination consisting also of two distinct trains, in which, however, there is but one train-arm T turning freely upon the horizontal shaft OO, to which shaft the wheels A', F, are secured; the train-arm has two studs, upon which turn the idlers B B', and also carries the bearings of the last wheel F'; the first wheel A is annular, and fixed to the frame of the machine. Let it be required to determine the results of one revolution of the crank H, the numbers of teeth being assigned as follows:

We shall then have, for the train ABF ,

And for the train A'B'F' ,

This result, no doubt, might be near enough to the truth to serve all practical purposes in the application of this mechanism to its original object, which was that of paring apples, impaled upon the fork K; but it can hardly be regarded as entirely satisfactory in a general way; nor can the analysis which renders such a result possible.

THE PANTANEMONE.

The need of irrigating prairies, inundating vines, drying marshes, and accumulating electricity cheaply has, for some time past, led to a search for some means of utilizing the forces of nature better than has ever hitherto been done. Wind, which figures in the first rank as a force, has thus far, with all the mills known to us, rendered services that are much inferior to those that we have a right to expect from it with improved apparatus; for the work produced, whatever the velocity of the wind, has never been greater than that that could be effected by wind of seven meters per second. But, thanks to the experiments of recent years, we are now obtaining an effective performance double that which we did with apparatus on the old system.

Desirous of making known the efforts that have been made in this direction, we lately described Mr. Dumont's atmospheric turbine. In speaking of this apparatus we stated that aerial motors generally stop or are destroyed in high winds. Recently, Mr. Sanderson has communicated to us the result of some experiments that he has been making for years back by means of an apparatus which he styles a pantanemone.

The engraving that we give of this machine shows merely a cabinet model of it; and it goes without saying that it is simply designed to exhibit the principle upon which its construction is based.

Two plane surfaces in the form of semicircles are mounted at right angles to each other upon a horizontal shaft, and at an angle of 45? with respect to the latter. It results from this that the apparatus will operate whatever be the direction of the wind, except when it blows perpendicularly upon the axle, thus permitting of three-score days more work per year being obtained than can be with other mills. Three distinct apparatus have been successively constructed. The first of these has been running for nine years in the vicinity of Poissy, where it lifts about 40,000 liters of water to a height of 20 meters every 24 hours, in a wind of a velocity of from 7 to 8 meters per second. The second raises about 150,000 liters of water to the Villejuif reservoir, at a height of 10 meters, every 24 hours, in a wind of from 5 to 6 meters. The third supplies the laboratory of the Montsouris observatory.

RELVAS'S NEW LIFE-BOAT.

The Spanish and Portuguese papers have recently made known some interesting experiments that have been made by Mr. Carlos Relvas with a new life-boat which parts the waves with great facility and exhibits remarkable stability. This boat, which is shown in front view in one of the corners of our engraving, is T-shaped, and consists of a very thin keel connected with the side-timbers by iron rods. Cushions of cork and canvas are adapted to the upper part, and, when the boat is on the sea, it has the appearance of an ordinary canoe, although, as may be seen, it differs essentially therefrom in the submerged part. When the sea is heavy, says Mr. Relvas, and the high waves are tumbling over each other, they pass over my boat, and are powerless to capsize it. My boat clears waves that others are obliged to recoil before. It has the advantage of being able to move forward, whatever be the fury of the sea, and is capable, besides, of approaching rocks without any danger of its being broken.

A committee was appointed by the Portuguese government to examine this new life-boat, and comparative experiments were made with it and an ordinary life-boat at Porto on a very rough sea. Mr. Relvas's boat was manned by eight rowers all provided with cork girdles, while the government life-boat was manned by twelve rowers and a pilot, all likewise wearing cork girdles. The chief of the maritime department, an engineer of the Portuguese navy and a Portuguese deputy were present at the trial in a pilot boat. The three boats proceeded to the entrance of the bar, where the sea was roughest, and numerous spectators collected upon the shore and wharfs followed their evolutions from afar.

The experiments began at half past three o'clock in the afternoon. The two life-boats shot forward to seek the most furious waves, and were seen from afar to surmount the billows and then suddenly disappear. It was a spectacle as moving as it was curious. It was observed that Mr. Relvas's boat cleft the waves, while the other floated upon their surface like a nut-shell. After an hour's navigation the two boats returned to their starting point.

EXPERIMENTS WITH DOUBLE-BARRELED GUNS AND RIFLES.

The series of experiments we are about to describe has recently been made by Mr. Horatio Phillips, a practical gun maker of London. The results will no doubt prove of interest to those concerned in the use or manufacture of firearms.

The reason that the two barrels of a shot gun or rifle will, if put together parallel, throw their charges in diverging lines has never yet been satisfactorily accounted for, although many plausible and ingenious theories have been advanced for the purpose. The natural supposition would be that this divergence resulted from the axes of the barrels not being in the same vertical plane as the center line of the stock. That this is not the true explanation of the fact, the following experiment would tend to prove.

Fig. 1 represents a single barrel fitted with sights and firmly attached to a heavy block of beech. This was placed on an ordinary rifle rest, being fastened thereto by a pin at the corner, A, the block and barrel being free to revolve upon the pin as a center. Several shots were fired both with the pin in position and with it removed, the barrel being carefully pointed at the target each time. No practical difference in the accuracy of fire was discernible under either condition. When the pin was holding the corner of the block, the recoil caused the barrel to move from right to left in a circular path; but when the pin was removed, so that the block was not attached to the rest in any way, the recoil took place in a line with the axis of the bore. It will be observed that the conditions which are present when a double barreled gun is fired in the ordinary way from the shoulder were in some respects much exaggerated in the apparatus, for the pin was a distance of 3 in. laterally from the axis of the barrel, whereas the center of resistance of the stock of a gun against the shoulder would ordinarily be about one-sixth of this distance from the axis of the barrel. This experiment would apparently tend to prove that the recoil does not appreciably affect the path of the projectile, as it would seem that the latter must clear the muzzle before any considerable movement of the barrel takes place.

With a view to obtain a further confirmation of the result of this experiment, it was repeated in a different form by a number of shots being fired from a "cross-eyed" rifle, in which the sights were fixed in the center of the rib. Very accurate shooting was obtained with this arm.

So far the experiments were of a negative character, and the next step was made with a view to discover the actual cause of the divergence referred to. A single barrel was now taken, to which a template was fitted, in order to record its exact length. The barrel was then subjected to a heavy internal hydrostatic pressure. Under this treatment it expanded circumferentially and at the same time was reduced in length. This, it was considered, gave a clew to the solution of the problem. A pair of barrels was now taken and a template fitted accurately to the side of the right-hand one. As the template fitted the barrel when the latter was not subject to internal pressure, upon such pressure being applied any alterations that might ensue in the length or contour of the barrel could be duly noted. The right-hand barrel was then subjected to internal hydrostatic pressure. The result is shown in an exaggerated form in Fig. 2. It will be seen that both barrels are bent into an arched form. This would be caused by the barrel under pressure becoming extended circumferentially, and thereby reduced in length, because the metal that is required to supply the increased circumference is taken to some extent from the length, although the substance of metal in the walls of the barrel by its expansion contributes also to the increased diameter. A simple illustration of this effect is supplied by subjecting an India-rubber tube to internal pressure. Supposing the material to be sufficiently elastic and the pressure strong enough, the tube would ultimately assume a spherical form. It is a well known fact that heavy barrels with light charges give less divergence than light barrels with heavy charges.

After the above experiments it was hoped that, if a pair of barrels were put together parallel and soldered only for a space of 3 in. at the breech end, and were then coupled by two encircling rings joined together as in Fig. 4, the left-hand ring only being soldered to the barrel, very accurate shooting would be obtained. For, it was argued, that by these means the barrel under fire would be able to contract without affecting or being affected by the other barrel; that on the right-hand, it will be seen by the illustration, was the one to slide in its ring.

A pair of able 0.500 bore express rifle barrels were accordingly fitted in this way. Fig. 3 shows the arrangement with the rings in position. Upon firing these barrels with ordinary express charges it was found that the lines of fire from each barrel respectively crossed each other, the bullet from the right-hand barrel striking the target 10 in. to the left of the bull's eye, while the left barrel placed its projectile a similar distance in the opposite direction; or, as would be technically said, the barrels crossed 20 in. at 100 yards, the latter distance being the range at which the experiment was made. These last results have been accounted for in the following manner: The two barrels were rigidly joined for a space of 3 in., and for that distance they would behave in a manner similar to that illustrated in Fig. 2, and were they not coupled at the muzzles by the connecting rings they would shoot very wide, the charges taking diverging courses. When the connecting rings are fitted on, the barrel not being fired will remain practically straight, and, as it is coupled to the barrel being fired by the rings, the muzzle of the latter will be restrained from pointing outward.

The result will be as shown in an exaggerated manner by the dotted lines on the right barrel in Fig. 3.

BALL TURNING MACHINE.

The distinguishing feature in the ball turning machine shown opposite is that the tool is stationary, while the work revolves in two directions simultaneously. In the case of an ordinary spherical object, such as brass clack ball, the casting is made from a perfect pattern having two small caps or shanks, in which the centers are also marked to avoid centering by hand. It is fixed in the machine between two centers carried on a face plate or chuck, with which they revolve. One of these centers, when the machine is in motion, receives a continuous rotary motion about its axis from a wormwheel, D. This is driven by a worm, C, carried on a shaft at the back of the chuck, and driven itself by a wormwheel, B, which gears with a screw which rides loosely upon the mandrel, and is kept from rotating by a finger on the headstock. This center, in its rotation, carries with it the ball, which is thus slowly moved round an axis parallel to the face plate, at the same time that it revolves about the axis of the mandrel, the result being that the tool cuts upon the ball a scroll, of which each convolution is approximately a circle, and lies in a plane parallel to the line of centers.

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