considered an improvement mechanically, by somewhat lessening the friction. Professor F. H. Holmes has succeeded in rendering the rotation of this siren cylinder automatic, with perfect control of the speed and consequent pitch, and an apparatus of this kind has not long since been fitted on board the light-ship at the Seven-stones. deed, the three latter strongly resemble each other, and can only be distinguished by trained ears. It has also been found useless to attempt to get differential sig. nals by means of pitch of the note alone. To employ a high note at one station, and a low note at another, would, in the present condition of the musical cultivation 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, accordingMessrs. Sautter, Lemonnier & Co. have more recently introduced a double siren, in which two sirens, having different numbers of orifices in their respective cylinders, produce simultaneously two notes in the trumpet, and by this means the power of the instrument is more than doubled, and a characteristic feature is given to the sound. It now remains to offer a few general remarks upon the subject. ly, it is on this basis that the characteristics of sound signals are founded. By making the blasts to occur in groups, and varying the length of the intervals between the groups, on the same principle as that now applied to the new class of group-flashing lights, sixteen fundamental distinctions may readily be obtained, thus commencing with an interval of half a minute: 1 blast every 1⁄2 min. 3 blasts every min 66 66 66 66 66 66 4 blasts 2 blasts 66 66 It is obvious that, with the increasing use of sound signals, there is an increasing necessity for differentiating them. 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 our 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, 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 danger likely to go on increasing as ships' sound signals become more powerful and more generally used. One point occurs to me, in connection with those gentlemen who give much time, and trouble, and, probably, spend much money, in developing sound signals. I observe that they all take up some special code of signals, and then show how well their instrument is adapted for it. Now, if I might give a piece of advice to those gentlemen it would be, first look at the law, and see what signals are provided, then adapt your apparatus, whatever it may be, to making those signals. Don't require the law to be altered to suit your instrument that is putting a real difficulty in the way; but make your instrument suit the law as it now exists. neither the time nor the inclination to do so; and it must not be forgotten that, in making provisions of this kind, it is not the skilled, clear-headed, highly-educated, Royal Naval or merchant captain you have to consider, so much as the thousands of experienced, weather-beaten master mariners, who know well how to navigate their vessels under trying circumstances, but whose minds are not adapted for comprehending any system requiring accurate and attentive observation, to which is tacked on the necessity of finding out the meaning after the observation is made. As regards the present development of our coast fog signals, there is every reason for congratulation. This new branch of coast marking has been brought up to a very effective condition; no efforts 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, but they assume a vastly different aspect in the mind of an anxious and, perhaps, not over intelligent master mariner, on board his vessel, say in the Downs, in a thick fog. All around he hears horns and whistles blowing, and all he attempts to do is to keep clear of those vessels which, by the sounds, appear to be nearest. Of what use, then, would be the combinations of long and short sounds? Would he, in his bewildered them. sound signals, the mariner is now enabled to continue his voyage with comparative safety, even when his vessel is enshrouded with a thick pall impenetrable by the keenest vision; and there is little doubt that those who have their business in the great waters are ready gratefully to acknowledge the humane spirit which has prompted the development of these signals, as well as the practical benefit which they derive from 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 bars of the same dimensions, 100 millimeters (3.9 inches) long, and 7 milimeters (0.27 inch) on the side, and then on bars of the same length but of different sections. The results obtained are as follow : After hardening in cold water the density decreases, or in other words the volume increases; the thicker the bar the less the increase. After tempering the volume again diminishes, the increase being at "straw" reduced to one-half, and at "blue" to about one-fifth of the total increase gained after hardening, returning at "gray" to the original volume when soft. 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 der 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. We propose in this note to examine two problems, which are presented for solution whenever it is desired to estimate in an expeditious manner the area of a cross-section. 1st Problem. To construct the profile of a cross-section of earth work, and obtain its area, by a simple method. Provide a series of sheets or cards representing the outline of the usual cut or embankment of a road or canal. These cards will bear certain lines and scales which result from what is to follow. Figure 1 shows, on a reduced scale, one of these sheets for the half profile of an embankment of a single track railroad. What is required to complete the profile thus far exhibited? It is clear that nothing more is necessary than to draw the profile of the original surface. This may be done in a ready manner by the aid of a prepared scale, graduated to the scale of trigonometrical tangents, as shown in Table, Fig. 2. This little instrument is then applied to the axis of the cross-section diagram at the cut or fill height, and inclined at the angle of the natural surface. It only remains to follow with a pen- It is required finally to determine the area TNMP. This is done in the following manner, which is only an application of a more general method for the measurement of areas. If we consider some point A arbitrarily chosen on the movable scale, but having a position mathematically defined, it follows that for each position of A, a corresponding point on the engraved sheet may be determined. We can, therefore, trace beforehand upon the prepared sheet a series of curves, giving the area of the half crosssections for each position of the point A, and the problem is then solved by a simple reading. the For reasons, which will be immediately apparent, the point A is taken at A, point of tangency of TN (original surface line), and the curve to which all the lines are tangent, which cut off areas equal to the area TNMP. To determine the nature of this curve we seek for the position of the point of tangency A, under the above conditions. This point will be at the intersection of TN and another line T'N', drawn infinitely near it in such way that the areas PMNT and PMN'T' are equivalent. 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 TN. To determine the equation of the curve of the locus of A, under the prescribed conditions. Let Ox and Oy be co-ordinate axes, and let OT-X and ON Y. The area PMNT being constant, the area ONT is also constant (so long as the line NT does not intersect the line PM within the angle axoy, a condition which is taken into account further on). Then we have area OTN= or face curves generated by the different positions of A corresponding to equal areas. The curves are generally of a degree above the second, but as we have already seen they become hyperbolas of easy construction when we take for auxiliaries points analogous to A,. But the simplicity of construction is not the only advantage arising from this selection; for it is clear that it is an advantage to diminish as much as possible the length of the curves of equal surface; in taking A, the minimum of ON. OT. sina XY sin a length is secured. 2 XY=4K' a constant. 2 Fig. 1 represents cross sections, comprised between the following limits: 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, of 10 meters. The prepared sheet would not be inconveniently large if both these limits I were extended. A single sheet might serve for cross sections of different The locus of A, is, therefore, a hyper-slopes. bola having for asymptotes the axes Ox and Oy. For different values of K' we may obtain a series of hyperbolas corresponding to different values of the half section PMNT. These curves may be termed curves of equal areas. The advantages arising from the selection of the point A, under the assigned conditions, are obvious. 1st. The curves of equal surfaces being hyperbolas drawn relative to the same point O, and to the same asymptotes, are easily traced. Any one is easily constructed by means of some one of its tangents, and others of the series are readily derived from this. The preparation of the table of areas is not all complicated. An area is calculated corresponding to one of the curves. Other areas are determined by the law of the dimensions of similar surfaces, and the numbers may be written upon the curves. The mode of proceeding to employ the system is as follows: 1st. Make a book of the cross sections, also a sufficient number of the proposed sheets to serve the purposes of the work in hand. 2d. Write within the profile of each cross section, the center cut or fill and the slope of the original surface (expressed as a ratio or tangent of the angle made with the horizon). 3d. Proceed to trace the lines TN by aid of the movable scale (the inclination being measured by aid of graduations on the lower edge as at O in fig. 2). 4th. Read the numbers upon the curves to which in each case the line falls tangent, and write these areas within the respective cross sections. It may be remarked here that the tangency of the line TN is easy to determine, and moreover that an error of the first order, in determining the point of tangency, results in an error of the second order only in getting the areas. 5th. Complete the calculations indicated for estimating the volumes. If the curves are traced in such a manner that they cut equal segments on one of the radii vectores from the point O, 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 |