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considered an improvement mechanically, deed, the three latter strongly resemble by somewhat lessening the friction. Pro- each other, and can only be distinguished fessor F. H. Holmes has succeeded in by trained ears. It has also been found rendering the rotation of this siren cy- useless to attempt to get differential sig. linder automatic, with perfect control nals by means of pitch of the note alone. of the speed and consequent pitch, and To employ a high note at one station, an apparatus of this kind has not long and a low note at another, would, in the since been fitted on board the light-ship present condition of the musical cultivaat the Seven-stones.

tion of mariners, generally, be more likeIt seems probable that before long the ly to lead to confusion and disaster; alsiren will be brought into more general though, as Sir Richard Collinson obuse for maritime purposes. Already it served, in 1875, it might be possible to has been introduced into the Royal obtain an effective distinction by soundNavy, for which service Professor Holmes ing a high and a low note in direct conhas supplied three small-sized instru- trast. It has been frequently proposed ments. Messrs. Sautter, Lemonnier & to introduce long and short blasts; but Co., of Paris, have also produced a steam here, again, experience has shown that siren, which they claim can be used not many difficulties and risks would attend only as a fog signal at lighthouse sta- such an arrangement, and might result tions, but also for ships, and, in a smaller in conveying wrong information to the form, for locomotives, in the place of mariner, and lead him into danger. For the whistle. Mr. Wigham, of Dublin, real practical utility it has been found has also designed a form of siren for that, for the present, it is best to trust to steamships, driven by a small turbine, the distinctions which may be obtained actuated by the current of steam or air by varying the number of blasts, and the by which the instrument is sounded, the length of the silent interval. This is a rate of rotation being controlled and system which is intelligible to the most rendered uniform by a simple governor. ordinary understanding; and, according

Messrs. Sautter, Lemonnier & Co. Ily, it is on this basis that the characterishave more recently introduced a double tics of sound signals are founded. siren, in which two sirens, having differ- making the blasts to occur in groups, ent numbers of orifices in their respect- and varying the length of the intervals ive cylinders, produce simultaneously between the groups, on the same princitwo notes in the trumpet, and by this ple as that now applied to the new class means the power of the instrument is of group-flashing lights, sixteen fundamore than doubled, and a characteristic mental distinctions may readily be obfeature is given to the sound.

tained, thus-commencing with an inIt now remains to offer a few general terval of half a minute: remarks upon the subject.

1 blast every 12 min. 3 blasts every 12 min It is obvious that, with the increasing use of sound signals, there is an increasing necessity for differentiating them.

2 blasts 12 4 blasts Something must be done to prevent one from being mistaken for the other: in fact, it is necessary that every signal should have its own characteristic. This The introduction of compulsory and essential element, as regards coast fog optional sound signals in the new regusignals, has by no means been over- lations for preventing collisions at sea, looked, and as each lighthouse is made has naturally much extended the use of to proclaim its own individuality, so sound signals on board ship, and there every fog signal, established on onr coast can be no doubt that such signals should has been made to particularly indicate be entirely different from those made at itself by some distinguishing feature. fixed fog signal stations. It is said that One great reason why explosive reports, already some difficulty has arisen in refwhether from guns or rockets, are made erence to the clause in the regulations, use of, is because their sound is so en- which enacts that in foggy weather a tirely different from that of the blast of steamer shall sound a prolonged blast at a siren, a reed horn, or a whistle. In- intervals of not less than two minutes,

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the fact being that several coast fog state, care to try to distinguish between sirens sound the blast every two min- them ? I venture to say he would have utes. Unless checked, this, perhaps, is a neither the time nor the inclination to do danger likely to go on increasing as so; and it must not be forgotten that, in ships' sound signals become more pow- making provisions of this kind, it is not erful and more generally used.

the skilled, clear-headed, highly-eduOne point occurs to me, in connection cated, Royal Naval or merchant captain with those gentlemen who give much you have to consider, so much as the time, and trouble, and, probably, spend thousands of experienced, weather-beaten much money, in developing sound sig- master mariners, who know well how to nals. I observe that they all take up navigate their vessels under trying cirsome special code of signals, and then cumstances, but whose minds are not show how well their instrument is adapted for comprehending any system adapted for it. Now, if I might give a requiring accurate and attentive observapiece of advice to those gentlemen it tion, to which is tacked on the necessity would be, first look at the law, and see of finding out the meaning after the obwhat signals are provided, then adapt servation is made. your apparatus, whatever it may be, to As regards the present development of making those signals. Don't require the our coast fog signals, there is every realaw to be altered to suit your instru- ison for congratulation. This new branch ment—that is putting a real difficulty in of coast marking has been brought up the way; but make your instrument suit to a very effective condition; no efforts the law as it now exists.

have been spared to cope with the seaI may remark it is not easy to see how man's greatest enemy,fog, and the remarks the system of long and short sounds can which I have had the honor to address at present be brought into satisfactory to you indicate with what success these operation. Such distinctions are ex- efforts have been attended. By the aid of tremely pretty and simple upon paper, sound signals, the mariner is now enbut they assume a vastly different aspect abled to continue his voyage with comin the mind of an anxious and, perhaps, parative safety, even when his vessel is not over intelligent master mariner, on enshrouded with a thick pall impenetraboard his vessel, say in the Downs, in a ble by the keepest vision; and there is thick fog. All around he hears horns little doubt that those who have their and whistles blowing, and all he at- business in the great waters are ready tempts to do is to keep clear of those gratefully to acknowledge the humane vessels which, by the sounds, appear to spirit which has prompted the developbe nearest. Of what use, then, would ment of these signals, as well as the be the combinations of long and short practical benefit which they derive from sounds ? Would he, in his bewildered them.

ON THE ALTERATION IN THE DENSITY OF STEEL

THROUGH HARDENING AND TEMPERING.

By C. FROMME.

From "Abstracts” of the Institution of Civil Engineers.

The experiments were made first on four volume increases ; the thicker the bar bars of the same dimensions, 100 milli. the less the increase. meters (3.9 inches) long, and 7 milime After tempering the volume again ters (0.27 inch) on the side, and then on diminishes, the increase being at "straw" bars of the same length but of different reduced to one-half, and at ”blue” to sections. The results obtained are as about one-fifth of the total increase follow :

gained after hardening, returning at After hardening in cold water the "gray" to the original volume when soft. density decreases, or in other words the The molecular condition must, however, be

different, as the steel retains twice as of the bar, the Author proceeded to much permanent magnetism in the determine by eating off successive layers

grey” temper as in the soft. If the by acid, and determining the specific bar is heated to a bright red and cooled gravity of the remainder ; but as a fissure slowly, the volume is larger than in was ultimately discovered inside the the original state before hardening, bar, the results must be considered unthe difference being about one-sixth the trustworthy. Further experiments in this total increase gained after hardening. direction are certainly desirable.-AnnaThe question as to whether the density len iler Physik und Chemie. varies from the exterior to the interior

A GRAPHIC METHOD FOR MEASURING CROSS-SECTIONS

OF EARTHWORK.

Par M. H. WILLOTTE.

Translated from Annales des Ponts et Chaussées.

The employment of graphical meth- cil the edge of the protractor, in order ods of solving problems tends to become to complete the half profile TNMP. more and more general. Every day The length of the slope and the methods are invented or improved, and breadth of base are read at once from the progress already made only calls the inclined scale drawn on the prepared more strongly for the attention of engi. card. neers to this subject.

It is required finally to determine the We propose in this note to examine area TNMP. This is done in the followtwo problems, which are presented for ing manner, which is only an application solution whenever it is desired to esti- of a more general method for the measmate in an expeditious manner the area urement of areas. of a cross-section.

If we consider some point A arbitrari. 1st Problem. To construct the profile ly chosen on the movable scale, but havof a cross-section of earth work, and ing a position mathematically defined, obtain its area, by a simple method. it follows that for each position of A, a

Provide a series of sheets or cards corresponding point on the engraved representing the outline of the usual cut sheet may be determined. or embankment of a road or canal.

We can, therefore, trace beforehand These cards will bear certain lines and upon the prepared sheet a series of scales which result from what is to fol- curves, giving the area of the half crosslow. Figure 1 shows, on a reduced sections for each position of the point scale, one of these sheets for the half A, and the problem is then solved by a profile of an embankment of a single simple reading. track railroad.

For reasons, which will be immediately What is required to complete the pro- apparent, the point A is taken at A, the file thus far exhibited ? It is clear that point of tangency of TN (original surnothing more is necessary than to draw face line), and the curve to which all the the profile of the original surface. This lines are tangent, which cut off areas may be done in a ready manner by the equal to the area TNMP. aid of a prepared scale, graduated to

To determine the nature of this curve the scale of trigonometrical tangents, we seek for the position of the point of as shown in Table, Fig. 2.

tangency A, under the above condi. This little instrument is then applied tions. This point will be at the interto the axis of the cross-section diagram section of TN and another line T'N', at the cut or fill height, and inclined at drawn infinitely near it in such way the angle of the natural surface.

that the areas PMNT and PMN'T are It only remains to follow with a pen-'equivalent.

Vol. XXIV.-No. 2-11.

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The two infinitely small triangles table of determinate form; and for each TA,T and NA N are equivalent. Hence table there exists a system of equal surthe point A, is at the center of the line face curves generated by the different TN.

positions of A corresponding to equal To determine the equation of the areas. The curves are generally of a curve of the locus of A, under the pre- degree above the second, but as we have scribed conditions. Let Ox and Oy be already seen they become hyperbolas of co-ordinate axes, and let OT=X and easy construction when we take for auxON=Y. The area PMNT being con. iliaries points analogous to A. stant, the area ONT is also constant (so But the simplicity of construction is long as the line NT does not intersect not the only advantage arising from this the line PM within the angle coy, a con- selection; for it is clear that it is an dition which is taken into account further advantage to diminish as much as possion).

ble the length of the curves of equal Then we have

surface; in taking A, the minimum of ON.OT.sina XY sin a length is secured. OTN=

Fig. 1 represents cross sections, com2

2

prised between the following limits: XY=4K’ a constant.

1st. Inclinations of surface varying As x and y are the co-ordinates of A, from —0.33 to +0.33. we have

2d. Depths or fillings at the center,
X
Y

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2
2

The prepared sheet would not be in-
XY

conveniently large if both these limits and

ay=
-=K?.

were extended. A single sheet might

for cross sections of different The locus of A, is, therefore, a hyper- slopes. bola having for asymptotes the axes Ox The mode of proceeding to employ the and Oy.

system is as follows: For different values of K’ we may 1st. Make a book of the cross sections, obtain a series of hyperbolas correspond- also a sufficient number of the proposed ing to different values of the half section sheets to serve the purposes of the work PMNT. These curves may be termed in hand. curves of equal areas.

2d. Write within the profile of each The advantages arising from the selec- cross section, the center cut or fill and tion of the point A, under the assigned the slope of the original surface (exconditions, are obvious.

pressed as a ratio or tangent of the an1st. The curves of equal surfaces gle made with the horizon). being hyperbolas drawn relative to the 3d. Proceed to trace the lines TN by same point 0, and to the same asymp- aid of the movable scale (the inclination totes, are easily traced. Any one is easily being measured by aid of graduations on constructed by means of some one of its the lower edge as at 0 in fig. 2). tangents, and others of the series are 4th. Read the numbers upon the readily derived from this.

curves to which in each case the line The preparation of the table of areas falls tangent, and write these areas withis not all complicated. An area is calcu- in the respective cross sections. lated corresponding to one of the curves. It may be remarked here that the tanOther areas are determined by the law gency of the line TN is easy to determof the dimensions of similar surfaces, ine, and moreover that an error of the and the numbers may be written upon first order, in determining the point of the curves.

tangency, results in an error of the secIf the curves are traced in such a man. ond order only in getting the areas. ner that they cut equal segments on one 5th. Complete the calculations indiof the radii vectores from the point 0, cated for estimating the volumes, the second differences of these numbers As the accuracy of the work depends are equal.

so largely upon the accuracy of the pre2nd. For each of the different methods pared sheets, it will suggest itself that of choosing the point, there is a graphic a shrinkage of the sheet would result in

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