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of steel to exactly the same degree. A ing to the eye, but it can be produced by single test is of comparatively small hammering cold. The consumer of steel value, as a second rate quality of steel may be enraptured, if he be of a poetical may stand very well the first time of turn of mind, by the superb fracture of a hardening, but deteriorates much more bar of steel, reminding him of a picture rapidly every time it is re-hardened, than by Ruskin of the aguille structure of the is the case with high-quality steel. Nor Higher Alps; but, after all, this is only a am I at all sure that the breaking strain dodge, depending upon the inclination is a fair test of the quality of steel. For of the axis of the revolving hammer to many tools the capacity to withstand a the plane of the anvil. The practical high amount of breaking strain slowly consumer of steel must descend from the applied is not so much required as its heights of art and science, and take capacity to withstand a sudden shock. refuge in the commonplace of the rule of The appearance

of the fracture is very thumb, and buy the steel which his illusory. The fineness of the grain and workmed tell him is full of “nature" and the silkiness of the gloss is very captivat- “body."

EXPERIMENTS ON THE STRENGTH AND STIFFNESS OF

SMALL SPRUCE BEAMS.

By F. E. KIDDER.

From Proceedings of the American Academy of Arts and Sciences. The object of the following experi- the deflections at a distance of one-inch ments was to determine the Moduli of from the center; but the deflections used Elasticity and Rupture in small beams in calculating the values of the Modulus of white spruce (Abies alba); and such of Elasticity were corrected so as to give other information as might be derived the deflection at the center, supposing from the data obtained.

the curve assumed by the beam to be the The machine used for the purpose arc of a circle; from which, in fact, it consists of two solid wooden frames, deviates but little under such small loads. carefully leveled and placed forty inches In reading the micrometer, the principle apart. Upon the top of each frame is of electrical contact was taken advantage placed a movable plate of iron, which is of. carefully adjusted so that the two plates The greatest errors liable to occur in shall be directly opposite each other, and using the machine are as follows: exactly forty inches apart between the In measuring the deflections, one tenfaces. These plates form the supports thousandth of an inch. In the breaking for the beams.

load, possibly one pound; but in the The loads were applied by means of a small loads there could be no appreciable scale pan suspended from a three-quarter error. In measuring the dimensions of inch bolt, which rested upon the oenter the test pieces, two thousandths of an of the beam. By means of an iron strap inch. suspended from a horizontal beam placed The experiments were conducted with above the test piece, and resting on two the utmost care, and every possible prescrews, the bolt from which the load was caution was taken to prevent errors. suspended could be raised from or low In arranging for the experiments, and ered upon the test piece as easily and while making them, the writer gradually as could be desired.

greatly assisted by Mr. Holman of the The deflections of the beams were Institute, to whom he extends his measured by means of a micrometer acknowledgements. screw, reading to one ten-thousandth of The pieces of wood experimented on an inch. As the bolt from which the were sawn from a spruce plank that had load was suspended rested on the center been cut in eastern Maine in the spring of the beam, it was necessary to measure of 1880, and the following summer

Vol. XXIV.--No. 6.-33.

was

shipped to Boston, where it had lain in and had but few defects, and in testing the open air until it was cut up in Octo- the beams they were placed so that the ber. The pieces were carefully planed defects should bave the least possible to an approximate size of one and a half effect upon the strength of the beams. inches square and four feet long. The exact dimensions of the test pieces They were nearly all straight-grained are given in Table I:

TABLE I.

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In making the experiments, each beam After the piece had returned, or at was first subjected to a load of thirty least nearly returned, to its original pounds, and the deflection noted. The position, it was subjected to a load of weight was then left on the beam for a forty pounds in the same manner. period of time varying from one to four, Table II. gives the deflection of each and in one case forty-four hours, and the piece under the loads of thirty and forty deflection again noted. The load was pounds, both immediately after the then removed from the beam and the set weight was applied and after it had noted, after which the beam was allowed rested upon the beam the length of time a certain time to recover from the set. designated.

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The values of the Modulus of Elas- weight would, probably, break the beam ticity calculated from these deflections if applied long enough. are also given. The Moduli of Elasticity Table I. gives the values of the obtained from the deflection of the beams Modulus of Rupture of each piece, comimmediately after the weight was ap

3 WI

in which plied have been denoted by E. and puted by the formula R=

2 BD” those obtained from the deflection of R denotes the Modulus of Rupture; W the pieces after the weight had been the breaking weight of the beam, and applied one or more hours, by E. Table the other letters have the same signifiI. gives the values of E and E, for each cance as in the formula for E. The load piece, obtained by taking the average of which would break a beam of the same the values given in Table II.

wood, one inch square and one foot beThe values of E were computed by tween supports, if applied at the center,

W! the formula E=

in which w de- is also given in the same table. This 4 ABD"

load is one eighteenth of the Modulus of notes the weight in pounds producing Rupture. the deflection; Ithe clear span in inches; When the weight of 400 lbs. was A the deflection of the beam at the applied to piece No. 7, it immediately center; B the breadth of the beam, and cracked at a knarl in one of the lower D the depth, both in inches.

edges, about three-fourths of an inch After all the beams had been treated from the center of the beam. As it was in this way, piece No. 3 was again put in thought that the beam would soon break the machine and subjected to a load of entirely, the load of 400 lbs. was allowed 100 lbs., which was allowed to remain i to remain on the beam; but at the end upon the beam for about two hours, the of one hundred hours the deflection had deflection being measured directly after only increased 0.2224 inches, and as it the weight was applied and just before was evident that it would, at that rate, it was removed. The beam was then take a long time for the beam to break, allowed a certain time to recover its set. the load was then gradually increased In two cases, the beams, after having until the piece broke at 550 lbs., giving a been subjected to a load of 100 lbs., Modulus of Rupture considerably above finally returned to their original posi. the average. It was noticed in this tion, and it appeared probable that all beam that the deflections under the would have done so had sufficient time loads above 500 lbs. were considerably been allowed for the purpose.

greater than in the other beams under After the piece had nearly recovered the same loads. from the effects of the load of 100 lbs., a Piece No. 5 gave a very high breaking load of 150 lbs. was put on the beam, weight, and broke very suddenly, more and gradually increased until the break- like the harder kinds of wood. The ing point was reached.

fracture was very perfect, the upper half The remaining pieces were tested with of the fibers being very evidently coma load of 100 lbs. in the same way, and pressed and the lower half suddenly then subjected to a load of 400 lbs. for pulled apart, with almost no splintering. one or two minutes, for the purpose of This piece had a small knot on the upper getting the deflection under that load, side, five inches from the center of the and immediately after subjected to the beam, but it appeared to have no effect full load of 500 lbs., which was gradually upon the strength of the beam. increased until the piece broke. As the Piece No. 4 broke in a rather peculiar load approached the breaking weight, it manner. While under a load of 575 lbs., was increased by the addition of only the lower fibers for about a depth of one or two pounds at a time, so that the one-tenth of an inch snapped apart, and breaking weight could be obtained with the beam gradually settled down until sufficient accuracy. In fact, the break- the next layer of fibers had apparently ing weight is so much modified by the the same deflection as did the lower ones time occupied in breaking the beam, that at the time of breaking, when they also it is difficult to ascertain exactly what it snapped, making a layer of about the really is.

For any load over three- same thickness. In this way the whole fourths of what is called the breaking lower half of the beam seemed to divide

itself into layers of about one-tenth of before. The beam was thus subjected an inch thick, and to break separately to a weight of 275 lbs. for three hundred under about the same deflection, so hours in all, after which it was broken in that the beam was a long time in break- the same manner as the others. It was ing.

expected that the effect of such a severe Observing that under every load that strain for so long a time would diminish had been applied the deflection kept in- its strength; but, on the contrary, it creasing with the length of time the appeared to increase it, as the beam weight remained on the beam, piece No. gave a higher Modulus of Rupture than 7 was subjected to a load of 275 lbs. for any of the others, although it did not ninety-eight hours, during which time appear to be of as good quality as many the deflection increased 0.079 inches. of them. The ultimate deflection of this The weight was then taken off and the beam greatly exceeded that in any of the beam allowed to recover for twenty-four others. hours, when it had a set of .0446 inches. Table III. shows the deflection of The same weight was again applied, and each beam under loads of 30, 40, 100, it was found that the deflection, obtained 400, 500, and 550 lbs., immediately after by taking the difference between the the load was applied, and at a distance readings of the micrometer just before of one inch from the center. The small and after the weight was applied, was figures under each deflection show what less than it was the first time the weight it would be if Hooke's Law held true, was applied, and the rate of increase of taking the deflection under 30 lbs. as the the deflection was about the same as starting point.

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From these experiments I think we That even under very small loads, if may draw the following conclusions: applied for any length of time, there will

That the Modulus of Elasticity de- be a temporary set. pends not only upon the elasticity of the That knots and knarls in beams loaded material, but also upon the length of at the center, when not within onetime the load is applied.

eighth of the span of the center of the That when subjected to loads not ex. beam, do not materially affect the elasceeding one-sixth of the breaking weight, ticity under small loads. spruce beams do not take a permanent That the deflection is very nearly proset

portional to the load, far beyond the * Approximately.

customary limits of strain, and that the

Modulus is consequently very nearly taken at from 1,600,000 to 1,700,000 lbs., constant for all moderate deflections. and the Modulus of Rupture at about

That a high Modulus of Elasticity does 11,000 lbs. not always accompany high transverse The only other experiments on Ameristrength; for, as shown by Table I., can spruce with which the writer is piece No. 10, which had the greatest familiar are those made by Mr. R. G. transverse strength, gave next to the Hatfield on small beams, 1.6 feet belowest value of E.

tween supports, and some experiments That in spruce beams the upper fibers by Mr. Thomas Laslett, of England, on commence to rupture by compression pieces of Canada spruce, 2 inches square under about four-fifths of the breaking and 72 inches between supports. weight, and the neutral axis is

very near

1
Mr. Hatfield gives as the

average value the center of the beam as shown by the of the transverse strength of a unit beam, fracture.

612 lbs.. * which would give 11,016 lbs. That beams which are subjected to for the Modulus of Rupture. severe strains for a long time bend more From data given by Laslett † we obbefore breaking than those which are tain as the value of R, 9,045 lbs. broken in a comparatively short time. The value generally given for the

That the Modulus of Elasticity of Modulus of Elasticity of spruce is small spruce beams, of a quality such as 1,600,000 lbs. is used in the best buildings, may be

GAS AND ELECTRICITY AS HEATING AGENTS. *

By Dr. C. WILLIAM SIEMENS, F.R.S.

From “Iron."

On the 14th of March, 1878, I had the wood, is practically inert to oxygen at honor of addressing you “On the Utili- ordinary temperatures ; but if wood is zation of Heat and other Natural Forces.” heated to 295° C. (593 Fal.), or coal to I then showed that the different forms of 326° C. (617° Fah.) according to experienergy which Nature has provided for ments by M. Marbach, combination takes our uses had their origin, with the single place between the fuel and the oxygen exception of the tidal wave, in solar radi. of the atmosphere, giving rise to the ation; that the forces of wind and wa- phenomenon of combustion. It is not ter, of heat and electricity, were attrib- necessary to raise the whole of the comutable to this source, and that coal bustible materials to this temperature, formed only a seeming and not a real in order to continue the action ; the

very exception to the rule - being the embodi- ' act of combustion when once commenced ment of a fractional portion of the solar gives rise to a great development of heat, energy of former geological ages. more than sufficient to prepare additional

On the present occasion I wish to con- carbonaceous matter, and additional air fine myself to one branch only of the for entering into combination ; thus a general subject, namely, the production match suffices to ignite a shaving, and of heat energy. I shall endeavor to that in its turn to set fire to a building. prove that for all ordinary purposes of The first effect of combustion is, thereheating and melting gaseous fuel should fore to heat the combustible and the air be resorted to, but that for the attain- necessary to sustain combustion to the ment of extreme degrees of heat the temperature of ignition, but in dealing electric arc possesses advantages, un- with the combustible called coal other rivaled by any other known source of preparatory work has to be accomplished, heat.

besides mere heating in order to sustain Carbonaceous material such as coal or

* Hatfield's Transverse Strains, Table XLII.

+ Tiinber and Timber Trees, Native and Foreign, by * A lecture delivered before the Science Lecture As- Thomas Laslett, Inspector to the Admiralty, London, sociation, Glasgow.

1875.

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