7. The diagonal of the rectangle formed by the (sum of the sines of the angles of the arms with AB) into (AB--sum of cosines of same) will be the length of link, E.

[Ill.u.s.tration]

G. R. NASH, Civil Engineer.

North Adams, Ma.s.s.

[We have received other solutions of this problem, but as this covers the ground in a very simple manner, we think it will be sufficient.

Those forwarding the solutions not published will accept our thanks and a.s.surances that it is not because they lack merit that they are declined.--EDS.

RECIPROCATING PARTS OF STEAM ENGINES.

MESSRS. EDITORS:--In one of the late numbers of your journal, you publish a paper, read by Mr. Porter before some learned society in New York, on something about the possibility or practicability of running a steam engine at a high rate of speed, and claiming to give a scientific explanation of the why and wherefore. Now, scientifically, I know nothing about a steam engine; practically, I know how to stop and start one. Therefore, you will understand that what I say is not as coming from one who claims to be wise above what is written, but as simply being a statement of the case, as it appears to one who wants to learn, and takes this way to draw out the truth. A scientific theory, invested with all its sines, coefficients, and other paraphernalia, is a very pretty thing to look at, no doubt, for those who understand it, and, when properly applied, is invaluable; but when, as in this case, a practical question is to be decided, by the aid of a scientific demonstration, it will not do to throw aside the main elements of the problem, or any, in fact, of the minor points, no matter how trivial they may appear.

Mr. Porter's labors were strictly of a scientific nature. He starts out with the proposition that what he is about to explain is very simple, and very likely it is; but, for one, I can't see it, and I want more light. He says that it takes a certain number of pounds to overcome the inertia of the reciprocating parts of a certain weight, to give it a certain speed. What is inertia? He says, "we will not take into account the friction of parts." Now, my understanding of this point is, that friction is practically one of the main elements in the problem. How can we hope to obtain a correct solution when he rubs out one of the terms of the equation? What is friction doing all the time, while he is theoretically having his reciprocating parts storing up power and then giving it out again, just at the right time, and in the right quant.i.ty?

What an immense amount of iron has been wasted by being cast into fly wheels, when a fraction of the amount, if only put into cross heads, would render fly wheels unnecessary!

Mr. Porter stops short in his discussion. He should have added a table giving the proportionate length of stroke, weight of parts, and number of revolutions required to produce the effect of an engine running at a high speed, without the least fraction of inequality in the strain on the crank, and then the sun would have fairly risen in the "dawn of a new era for the steam engine." But, as it is so very simple, we can all figure it out for ourselves.

In the diagram Mr. Porter gives, to ill.u.s.trate the travel of the piston, he wets his finger and draws it over another term in the equation (a method of elimination not taught by Hutton, Davies, and other mathematicians). It is a quick way, but is it correct? He says, "the distance traveled by the piston is the versed sine of an angle formed by a line from the center of the crank pin, in any part of its stroke to the center of the circle described by the crank pin, leaving out of the calculation the angular vibration of the connecting rod."

What he means by the "angular vibration," I do not know. He is wrong in the statement. If he will think of it he will see it. If he meant to say that the piston's travel was measured by the versed sine of the angle formed by the connecting rod and the line of horizontal centers, he is wrong again, yet nearer the truth than before, just as the proportion between the length of the connecting rod and the half diameter of the circle described by the crank pin. This can quickly be seen by supposing the connecting rod to be detached, and allowed to fall down on the center line, at any part of the stroke. If he understood this (as no doubt he did), he should not ignore the facts.

What I am aiming at is this. When a man attempts to demonstrate a thing mathematically, he must take into his calculation everything essentially connected with the problem, just exactly as it is, and not as he would have it; otherwise, he cannot, by any possibility, attain a correct result. When he claims, as now, the practicability of running engines at a high speed, I think he is claiming too much.

Build an engine of proper materials, make it strong, and fit everything as it should be, balance crank and fly wheel to a nicety, keep everything snugly in its place, and the terrors of a quick stroke vanish.

S. W. H.

TEST FOR WHITE LEAD.

MESSRS. EDITORS:--I have read, with much interest, Dr. Chandler's colorimetric test of the purity of white lead, as published in the SCIENTIFIC AMERICAN sometime ago. I enclose another test, which, though not new, is of value to all using white lead on account of its simplicity and effectiveness. It has been in use here for nearly two years, and has been found reliable. Having never seen it in print, I have tried to put it in as simple words as possible.

FELIX MCARDLE, a.n.a.lytical Chemist.

St. Louis, Mo.

Take a piece of firm, close grained charcoal, and, near one end of it, scoop out a cavity about half an inch in diameter and a quarter of an inch in depth. Place in the cavity a sample, of the lead to be tested, about the size of a small pea, and apply to it continuously the blue or hottest part of the flame of the blow pipe; if the sample be strictly pure, it will in a very short time, say in two minutes, be reduced to metallic lead, leaving no residue; but if it be adulterated to the extent of ten per cent. only, with oxide of zinc, sulphate of baryta, whiting or any other carbonate of lime, (which substances are now the only adulterations used), or if it be composed entirely of these materials, as is sometimes the case with cheap lead, it cannot be reduced, but will remain on the charcoal an infusible ma.s.s.

Dry white lead, (carbonate of lead) is composed of metallic lead, oxygen and carbonic acid, and, when ground with linseed oil, forms the white lead of commerce. When it is subjected to the above treatment, the oil is first burned off, and then at a certain degree of heat, the oxygen and carbonic acid are set free, leaving only the metallic lead from which it was manufactured. If, however, there be present in the sample any of the above mentioned adulterations, they cannot of course be reduced to metallic lead, and cannot be reduced, by any heat of the blow pipe flame, to their own metallic bases; and being intimately incorporated and ground with the carbonate of lead, they prevent it from being reduced.

It is well, after blowing upon the sample, say for half a minute, by which time the oil will be burned off, to loosen the sample from the charcoal, with a knife blade or spatula, in order that the flame may pa.s.s under as well as over and against it. With proper care the lead will run into one b.u.t.ton, instead of scattering over the charcoal, and this is the reason why the cavity above mentioned is necessary. A common star candle or a lard oil lamp furnishes the best flame for use of the blow pipe; a coal oil lamp should not be used.

By the above test, after a little practice, so small an adulteration as one or two per cent. can be detected; it is, however, only a test of the purity or impurity of a lead, and if found adulterated, the degree or percentage of adulteration cannot be well ascertained by it.

Jewellers usually have all the necessary apparatus for making the test, and any one of them can readily make it by observing the above directions, and from them can be obtained a blow pipe at small cost.

If you have no open package of the lead to be tested, a sample can most easily be obtained by boring into the side or top of a keg with a gimlet, and with it taking out the required quant.i.ty; care should be used to free it entirely from the borings or particles of wood, and it should not be larger than the size mentioned; a larger quant.i.ty can be reduced, but of course more time will be required, and the experiment cannot be so neatly performed.

HOW TO BUILD A CHIMNEY.

MESSRS. EDITORS:--I am satisfied that a great many fires originate through poorly constructed chimneys; and, although not a bricklayer by trade, I would offer a few hints how to construct a fire-proof chimney. Let the bed be laid of brick and mortar, iron, or stone; then the workman should take a brick in his left hand, and with the trowel, draw the mortar upon the end of the brick, from the under side, and not from the outside edge, as is usual. Then, by pressing the brick against the next one, the whole s.p.a.ce between the two bricks will be filled with mortar; and so he should point up the inside as perfectly as the outside, as he proceeds.

By drawing the mortar on the edge of the brick, the s.p.a.ce between the ends will not always be entirely filled, and will make (where the inside pointing is not attended to) a leaky and unsafe chimney, which, if not kept clear of soot, will, in burning out, stand a good chance of setting the building on fire. The best thing that I know of, to put the fire out in a burning chimney is salt; but the matter of first importance, after having a chimney properly constructed, is to keep it clean.

AUSTIN B. CULVER.

Westfield, N. Y.

CRYSTALLIZED HONEY.

MESSRS. EDITORS:--Please allow me to say to the querist who, through your columns, asks what to do with crystalline honey, that if he will "doctor" it with almost any artificial honey of the day, it will not become like lard in cold weather, which change is a natural proof that it is pure. For almost any purpose, pure honey is preferable to that which has been adulterated, but purity is a minor consideration with many.

Next we shall hear of some fastidious customer who objects to pure lard, because it looks white when cold. To such we would recommend lard oil as a great improvement, especially for cooking purposes.

A. M. B.

Louisville, Ky.

[For the Scientific American.]

RAMBLES FOR RELICS.

NUMBER II.

At a depth of fifteen feet, we were about to suspend our labors, supposing from the nature and uniformly dark color of the earth, that we had reached the surface of the alluvium, when a sign of the inevitable wood and bark layer was seen in a crevice. An excavation, five or six feet, into the wall, revealed the skeleton of a man laid at length, having an extra coverlid of wooden material. Eighteen large oblong beads, an ax of polished green stone, eleven arrow points, and five implements of bone (to be described) were deposited on the left side; and a few small beads, an ornamental sh.e.l.l pin, two small hatchets, and a sharp-pointed flint knife or lance, eight inches long, having a neck or projection at the base, suitable for a handle, or for insertion in a shaft, on the right side. The earth behind the skull being removed, three enormous conch sh.e.l.ls presented their open mouths. One of my a.s.sistants started back as if the ghost of the departed had come to claim the treasure preserved, in accordance with superst.i.tious notions, for its journey to the "happy lands." The alarm seemed to be a warning, for at the moment the embankment, overloaded on one side, caved in, nearly burying three workmen, myself, and a spectator. Our tools being at the bottom of the heap, and the wall on the other side, shaken by the falling earth, giving tokens of a change of base, our prospects of a ready deliverance were not very hopeful.

The bystanders, however, went to work with their hands, and we were soon relieved, not without casualty, the spectator having the worst of it. Struggling to extricate himself, instead of abiding his time, he dragged one leg out of the pile shorter than the other.

The occurrence of marine sh.e.l.ls in a burial depository, especially of the varieties pyrula and oliva, four or five hundred miles from the Gulf and that portion of the Southern coast where the mollusks exist, bears upon the question of migration and tribal intercourse, and the commercial value of these articles. Obtained from a distance and regarded as precious commodities, they were used in exchange, for the material of ornaments, and for choice utensils. Only two or three of these sh.e.l.ls have been found in a perfect condition, but defective ones are frequent, with fragments, "cuttings," and various trinkets made out of them--such as ornamental pins, needles, crosses, b.u.t.tons, amulets, engraved plates, and beads. From one of the specimens recovered from the mound sepulchre, the spire and columella had been removed, leaving a hollow utensil. It would have been suitable for a water vessel, but for a hole in the bottom, which had furnished a b.u.t.ton-shaped ornament, or piece of money, which was found with the relic, and exactly corresponded to the orifice. The twirled end of the sh.e.l.l, however, had been improved for a handle by shallow cavities, one on the inside slanting from the middle longitudinal line, and one crossing that line at right angles on the convex side, so as to be fitted to the thumb and fore finger of the left hand, suggesting a use of the implement as a shield, or a mask held before the face. Adair speaks of large sh.e.l.ls in use by the Indians of his time (1735), suspended about the neck for shields, and regarded as badges of priestly dignity.

A trench was dug on the east side of the mound, nearly corresponding in dimensions to the one on the west side, making the length of the whole excavation, including the central cavity, thirty-two feet.

In the last opening, eight skeletons were exhumed; the mode of burial was the same throughout. The only article of value recovered was a curiously wrought pipe of stone, having a "figure head" representing the human face, which I have put down in a list of "articles stolen,"

and which the thief can describe better than the writer. After filling up all the gaps, and levelling the surface to suit the taste of the proprietor, we closed our labors on the mound in the Bent.