Chapter 2

This condition takes out of every day practical drawing use the integraph invented by Professors James and Sir William Thomson, in which the sum curve is drawn on a revolving cylinder. It is essential that the sum curve should be drawn on the board not far from the primitive, and that this sum curve can be summed once or twice again without difficulty. The time involved in drawing the four sum curves, for example, required in passing from the load curve to the deflection curve of a simple beam, if these curves were drawn on different pieces of paper and had to be shifted on and off cylinders, would probably be as long as the ordinary graphical processes. Coradi's integraph works on an ordinary drawing board, but since there are nearly 10 inches between the guide point and tracer, the sum curve is thrown 10 inches behind the primitive in each integration. Thus a double summation requires say 26 inches of board, and it is impossible to integrate thrice without reproducing the primitive. The fact that the primitive and sum curve are not plotted off on the same base is also troublesome for comparison, and involves scaling of a new base for each summation. I have endeavored to obviate this by always drawing the second sum curve on a thin piece of paper pinned to the board, which can then be moved back to the position of the first primitive. But this shifting, of course, involves additional labor, and is also a source of error.

I should like to see the trace and guide chariots on the same line of rails, one below the other, were this possible without producing the bad effect of a skew, pull or push.

4. The practical integraph must not have a greater maximum error than 2 per cent. The mathematical calculations, which are correct to five or six places of decimals, are only a source of danger to the practical calculator of stresses and strains. They tend to disguise the important fact that he cannot possibly know the properties of the material within 2 per cent. error, and therefore there is not only a waste of time, but a false feeling of accuracy engendered by human and mechanical calculation which is over-refined for technical purposes.

For comparative purposes I have measured the areas of circles of 1 inch, 2 inches, and 3 inches radius, the guide being taken round the circumference by means of a "control lineal," first with an ordinary Amsler's planimeter and then with the integraph. I have obtained the following results:

+------------+-----------+----------------------------------- | | | By integraph. Radius | | By |--------+--------+--------+-------- of | Calculated |Planimeter.| | Upper | | Upper circle. | areas. | |Middle. | end. |Middle. | end. | | |p=2 in. |p=2 in. |p=4 in. |p=4 in. ---------+------------+-----------+--------+--------+--------+-------- in. | | | | | | 1 | 3.14159 | 3.140 | 3.140 | 3.138 | 3.120 | 3.120 | | | | | | 2 | 12.56636 | 12.55 | 12.36* | 12.546 | 12.568 | 12.552 | | | | | | 3 | 28.27431 | 28.24 | ...... | ...... | 28.280 | 28.288 ---------+------------+-----------+--------+--------+--------+--------

* Cross bar had to be moved during tracing.

From this it follows that the error of the planimeter is less than 0.1 per cent. and that of the integraph about 0.5 per cent. Obviously we could make this error much less if we excluded small areas measured with large polar distances, or such polar distances that the cross bar must be shifted. Excluding such cases, we see that the accuracy of the integraph scarcely falls behind that of the planimeter and is quite efficient for practical purposes. It must be borne in mind that the above measurements were made with the "control lineal," an arrangement which carries the guide round a circle of the exact test area. In most cases the curve has to be followed by hand, and the error will be greater--greater probably for the integraph than for the planimeter, as the former is distinctly hard to guide well.

I think, then, we should be safe in saying that the error of the integraph is not likely to be greater and is probably less than 2 per cent., so that in this respect the instrument may be considered a practical one.

5. A further condition for a good integraph is that it should have a wide range of polar distances, and that it should be easily set at those distances.

One of the conditions I gave to the maker of the instrument was that it should be able to take all polar distances from one to ten half-inches. This condition he can scarcely be said to have fulfilled. With polar distances of 1/2 inch and 1 inch, the machine works unsatisfactorily, which indeed might have been foreseen from the construction of its sliding bars. It works best from 2.5 inches to 5 inches, and this is the range to which I think we ought to confine the present type of instrument. As the last conditions I may note that:

6. A practical integraph ought to be easy to read.

7. Draw a good clear curve.

The scale on the present instrument is very inconvenient, as it is often almost out of sight; the curve it draws, on the other hand, I consider very satisfactory, when the pencil is loaded, say, with a planimeter weight. On the whole, I think you will agree with me that this integraph goes a good way, if not the whole way, toward fulfilling the conditions of a practical instrument.

I next turn to its construction and the claim it has to be considered in any way new. Let me briefly remind our members of the process by which an element Q R of the sum curve (Fig. 1) corresponding to the point P on the primitive is drawn; P M being the mid-ordinate of L N, a horizontal element, P B is drawn perpendicular to any vertical line A B; and O A being a constant distance termed the base or "polar distance," Q R is drawn between the ordinates of L and W, parallel to O B. If P' be the point where P M meets Q R, we note the following relationship of P' to P.

1. If P moves along a horizontal line, O B remains unchanged, and, therefore, Q R or P' must move in the straight line Q R parallel to O B.

2. If P moves along a vertical line, P' does not change, but Q R turns round it, remaining parallel to O B.

Without taking the trouble, as I ought to have done, to inquire what previous investigations had achieved in this matter, I thought, three years ago, I could get an apparatus to save me the trouble of drawing sum curves, made somewhat after the following fashion.

P (Fig. 2) is the guide or point to be taken round the primitive. It is attached to a block, D, which works along the bar, B C, which in its turn moves on the four wheels, e e f f, upon the frame R S U T fixed upon the drawing board. O A is fixed perpendicular to R U, and is such that O may be fixed at various points to determine the polar distance. O B D is a light bar passing freely through B and forming one side of a parallel ruler of two or more points, g g, h h, i i. Along i i is a slot and in this works a loaded block containing a wheel P', whose plane is always parallel to i i. This block also passes through a slot in D E, an arm at right angles to B C. A little consideration will show that P', if worked at all, would trace out the sum curve of P.

It was only when I showed the rough idea of this to Professor Kennedy, with the view of ascertaining what would be the amount of back-lash and friction, that I learned that Mr. Boys had already invented a very similar integrator. In his model the double parallel ruler is replaced by two endless strings and pulleys, and the bar, B C, by a T square.

Although this integrator was afterward made in a less crude form, I do not think it has ever been a practical instrument for the draughtsman. Shortly afterward I came across a work by Abdank-Abakanowicz, entitled "Les Integraphes," being a study of a "new kind of mechanical integrator."

The new kind of integrator was really only an independent version of Boys' instrument, but in many respects a great improvement. The real merit will ultimately belong to the scientific instrument maker who constructs an instrument reasonably cheap and capable of efficient practical service. Abdank-Abakanowicz's integrator however certainly went further in the practical direction than any previously constructed. The drawing board machines, it is true, of rather a complex nature, were actually exhibited to the Paris Academy, but no more have been made. The instrument before me was made by Coradi, of Zurich, on conditions laid down by me, namely, that the cost should not exceed £14, and that polar distances should range between one and ten half-inches. The first machine made by Coradi on these lines was, by a misunderstanding, sold in Germany, but the one I exhibit is the first, I believe, that has reached England, and to this extent I may, perhaps, be permitted to call it new. I look upon it rather as a suggestion upon which a still more practical instrument can be made in this country than as a perfect model. I believe there would be a wide sale for such an instrument were it once generally known to exist, and, what is more to work efficiently. It remains for me to point out in what the Abdank-Abakanowicz, or, rather, Coradi, integraph differs from Boys' instrument.

Two points deserve special attention. In the first place, the fixed frame is abolished, and the horizontal motion of P (Fig. 3), the guide point, is produced by putting the whole frame on friction rollers; in the second place, as a necessary result of the first change, the guide point carries about with it its own polar system, which renders the changes in length of "rays" much more manageable. f f, f' f' is a frame moving on four roughed wheels, e e e e, so that it can only move in the direction, f', which we may term horizontal. f f and f' f' are rails guiding the chariots, A and B, from f to f and from f' to f'. Of these chariots, A contains the guide point, P, to trace out the primitive with, and B the pencil, P', to draw the sum curve, i.e., the tracer. The chariot, B, like Boys' tracer, is heavily loaded. g g is a horizontal bar rigidly attached to the crossbars, q q and q' q', of the frame. On g g is a movable pivot, to which h, which determines the pole, k0 h being the polar distance. k0 is the position of a second point, k, on the chariot, A, when the guide point, P, is on the initial line, g g. l l is a bar with a long slot in it, in which work the pivots, h and k; this bar represents the "ray." A projecting arm k k' has been introduced to enable me to shorten the polar distance down to 2 in. and under by removing the pivot, k to k'. m m is a bar attached to the block, n, which runs on l l, so that m m is always perpendicular to l l. On the chariot, B, is another bar, m' m', capable of turning round the pivot, d, and always maintained parallel to m m by the rods, m m', m m'. Attached to m' m' is a wheel, w, whose axis is parallel to m' m'. This wheel, therefore, always moves perpendicular to m' m', and therefore to m m; hence it moves parallel to the ray, h k. A pencil, P', attached traces out the sum curve. If we wish to use the machine as an integrator, we have merely to measure the vertical distance traversed by P', or the distance B has run along f' f'. This is done by means of a scale on f f'. If k be brought down to k0, w runs parallel to g g, or P' traces out a horizontal straight line, which is thus the base line. If k be fixed as near as possible to k0, which is done by means of a screw in f f at k0, the chariot, B, can be run down f' f' as nearly opposite to k0 as can be guessed at; a horizontal line may then be drawn as base line, and the guide point, P, brought into this line by a clamping screw with which it is provided. The instrument is then ready for action. There is a brake on one of the roughed wheels to check or stop the motion of the integraph when required.

The instrument works best when the chariots, A and B, are about opposite to each other; when they are at opposite extremities of f f and f' f' respectively, the pull at P tends to produce a skewing couple. If the chariot, B, could be put upon f f and work, if needful, by a double parallelogram from m m, we should have, excepting the skew pull, some great practical advantages. We might throw the whole of the weight of the machine on the one pair of friction wheels, and replace the other pair by a single wheel, the portion q' f' f' q' of the machine virtually disappearing. Three wheels, of course, would be a real improvement. Further, we should have the sum curve and primitive drawn to the same base line, and the simplification in the number of parts ought largely to reduce the cost of the instrument.

To be able to perform "inverse summation" (which in the language of differential calculus is to find y as a function of x, when we are given y=f(dy/dx), and not dy/dx=f(x) as usual), we only want a means of making the plane of the wheel, w, parallel instead of perpendicular to m' m', and it is easy to design a modification in the construction which will allow of this change.

I hope the above description of the integraph may have made its construction and method of working sufficiently clear. Those of you who have a taste for mechanical work, and the necessary tools, might, I think, with some patience, construct a workable integraph. I expect the pivots would be the hardest part of the work. I hope, some day, myself to have another instrument made with a more readily changeable polar distance, with trace and guide points working in the same vertical, and a wheel permitting of inverse summation. If this project is ever carried out, I hope I may be permitted to communicate further particulars to our society.

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After some forty years of immersion in the waters of the pool of Echoschacht, not far from Hermannstadt, several human bodies have been brought to the surface in a state of perfect preservation.

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SOME HINTS ON SPIKING TRACK.

The usual dimensions of track spikes are 51/2 X 9.16 inches square, their weight about half a pound each. Their common defects are brittleness and imperfect points. In spiking track, the most important points to be attended to are the proper spacing of the ties and driving the spikes in such a manner that the ties shall be held in place at right angles to the track and the rails in true gauge; to insure the latter, the track gauge should always be used when spiking the gauge side, the rail being held to proper position by a lining bar. The gauge should be kept about 6 or 8 in. ahead of the tie being spiked and should not be lifted until the spikes are driven home; gauges should be tested regularly and every morning when they are to be used all day, so as to insure a true gauge all the time. The two inner spikes should be set on one side of the tie and the two outer spikes on the other, as indicated in the accompanying sketch. This prevents the tie from slewing around, and thus deranging the gauge of the track, as well as interfering with the proper spacing of the ties. The joints and centers should be spiked first, which will bring the rails to their proper position on the ties, which in turn will assist intermediate spiking. Each tie should be carefully gauged as spiked and, as before indicated, the ties with the broadest faces being selected for the joints.

In gauging ties it is very convenient to have measured off on the handles of the mauls in the hands of the forward spikers the distance from the outside of the rail to the end of the tie. This distance will then be gauged on the tie, when it will be lifted to the rail and securely spiked; the gauge is then used, and the loose rail held in place with the lining bar as previously indicated, loose gauge being given on curves, in accordance with directions of the engineer, the allowance for which is about 1/8 in. on a 2° curve, up to about 3/4 in. on a 12° curve.

This widening of the gauge should begin on the tangent, back of the P.C., the full amount of excess over true gauge being reached by the time the P.C. is reached and continue all the way around the curve, running from the P.T. in the same manner as back of the P.C.

The spikes should always be driven home straight and at right angles with the face of the ties. When the foreman in charge of the track-laying work sees a spiker, when the spike is nearly home, strike the spike head laterally, which is done to make it lie snugly to the rail, he should at once check such imperfect work and put the man who does it at other work. The foreman in charge of gang of spikers should be experienced in this branch of the work, and by weeding out imperfect workers, can soon get together a first-rate gang of spikers. But no trouble will be experienced from carelessly driven spikes, if the tie has the spike holes bored into it, before laying. This is considered good practice, but rather expensive.

For boring the holes quickly and accurately, a proper template should be made, by which the ties are marked for the borers, who should be provided with boring machines, by the use of which a hole, square with the face of the tie is bored. The boring machines should be so arranged as not to cut the hole beyond the required depth, which should be slightly less than the length of the spike. The diameter of the holes should be about 1-16 of an inch less than the thickness of the spike. This not only does away with the spike tearing its way through the timber and thus injuring its fiber to a great extent and causing it to be much more susceptible to rot, but it is said to increase the adhesion of the spike in hard wood ties at least 50 per cent. But in order that the best results may be obtained, the spike should be flattened on either side of the sloping point, which will generally prevent it leaving the hole.

The spikers should carefully avoid striking the rail with their mauls, as such carelessness often produces fracture, which sometimes causes the rail to break in two at such points, which is liable to produce derailment and serious accident. Spike mauls should weigh not less than nine nor more than ten pounds, and should be on straight handles, not less than 3 ft. long. After considerable use, the face of the maul will become somewhat rounded, and when this takes place it should be sent to the shop to be redressed. The last blow on the spike should be only sufficiently hard to cause its throat to fit snugly on the rail; a harder blow will often fracture the spike in such a manner as to cause the head in a short time to break off and leave the rail unsupported at that point. Foremen should not allow a spike to be pulled, especially in frosty weather, until it has been first struck a light blow to break the rust and loosen its hold in the wood. The filling of old spike holes with wooden plugs is bad practice, for the reason that they will cause the spike in a short time to slip from its place; to fill the holes with sand is much better, and spikes driven in holes so filled will hold much more firmly. The best form of spike I have seen is the curved safety railroad spike; this spike takes in the tie a position which enables it to resist the thrust of the rail against it much more effectually than the ordinary spike can possibly do. I have seen in good condition, one of these curved spikes which was said to have been driven eight times. The cost of the curved safety spike is more than that of the ordinary spike, but it is better made, holds the track better, and, I believe, is worth more than the difference asked for it.--_J.A. Hall, on Construction and Maintenance of Track, before American Society of Civil Engineers._

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THE EXPERIMENTS AT THE ANNAPOLIS PROVING GROUNDS.

The desperate war that has been waging between the gun and armor plate, ever since the period when protective plates were first applied to naval constructions, is familiar to all. In this conflict the advantage seems to lean toward the side of the gun, the power of penetration of which can be increased to almost indefinite limits, at least theoretically, while we quickly reach the extreme thicknesses of metal that can be practically employed for the protection of ships.

So, in recent times, researches have been making upon the efficacy of armor plating, no longer in its exaggeration of thickness, but in the intrinsic quality of the metal of which it is composed. Metallurgists have applied themselves to the work and have thus brought out various products, among which the plates called "compound," of Messrs. Cammell & Co., have obtained a great notoriety. These plates, formed of a true plating of steel upon a bed of soft iron, have been much in vogue in the English navy, and seemed as if they were to be adopted about everywhere.

The Creusot works alone, of all competitors, were able to fight against the general infatuation. Many comparative experiments had already demonstrated the superiority of the Creusot "all steel" plates over the Cammell plates, but Messrs. Schneider & Go. were not willing to stop here, and finally produced the new nickel steel plate, which is by far superior to their steel plates.

Some comparative trials of these various armor plates have recently been made by a military commission of the United States at the Annapolis proving grounds. Three plates, one a Cammell, the second a steel, and the third a nickel steel (the two last from Creusot), were here submitted to firing, under absolutely identical conditions.

Our engravings show the proving grounds and the details of the arrangements adopted for backing the plates.

Of the three plates, the Cammell was the thickest (11 in.) The steel one was 103/4 in. in thickness, and the nickel steel 101/2 in. The last, therefore, was at a disadvantage with respect to the two others.

The plates were arranged tangentially to an arc of a circle whose center was occupied by the pivot of the gun, and consequently at right angles with the latter. The piece employed was a 6 in. gun, 35 calibers in length. The distance of its muzzle from the plates attacked was 28 ft.

The charge was 44 lb. of brown prismatic powder. The projectile was a 100 lb. Holtzer shell. Under these circumstances, the initial velocity was 2,074 ft. and the energy at the impact was 9,970,396 ft. lb.

A beginning was made by firing four shots at each plate in the bisectrix of the corners. Then the 6 in. gun was replaced by an 8 in. one, throwing a 209 lb. Firth projectile, with an energy at the impact of 20,795,000 ft. lb.

Each of the plates then received in its center a final blow from this projectile.

Our engraving represents the state of the plates after this last shot.

There is no need of being a great expert in questions of artillery to discover on what side the superiority is found, and to see that the Cammell plate, almost entirely in fragments, is absolutely incapable of protection, while its two competitors are still in a state to resist.

In one of our engravings may be seen, too, the state of the shells after each of the three shots.

The commission immediately and unanimously classified the three plates in the following order of superiority: (1) Nickel steel; (2) all steel; (3) compound.

This triumph of French industry merits mention so much the more in that it was obtained in a series of experiments made in a foreign country--that is to say, under indisputable conditions of impartiality.-_L'Illustration._