cooling was in this way suppressed, and the strokes much quicker. This important improvement, like many others which might be cited, was the result of a fortunate accident. I regret very much not being able here to point out which of the three associates it was whose inventive mind saw directly, in the unexpected event of which I have given an account, the principle of an improvement which is still found in the engines of the present time; but tradition gives us no information upon this subject. [TO BE CONTINUED.] Notices of the advancement of Mineralogy in 1837, from Berzelius (Continued from Vol. XXIV, page 367.) In the former report p. 206, I mentioned two of the new minerals analysed by Thomson, one of which was said to consist of 2 (Ca 0+ C 03) + (Ba 0+C 02) and the other of one atom of sulphate, and two atoms of carbonate of baryta. Johnston* repeating the analysis, found the former (Ca 0 + C 02) + (Ba 0+C 02) and the latter Ba 0+C 02 or a simple carbonate of baryta. Thomsont again repeated the analysis of the former, and although this formula differs from his first, yet it varies from that of Johnston, being represented by the formula (Mn 0+ CO2) + (4 Ca 0+ C 02) + (4 Ba 0+ C02), or one part carbonate of manganese with four parts each of the carbonates of lime and baryta. The identity of its crystaline form with that formerly given for the same compound, favors the results of Johnston. It will be interesting to see how many of the results of Thomson's analyses presented in my last report, will stand the test of the experiments of other chemists! Sheppard examined a protophosphate of cerium (Edwardsite) which oc curs in Gneiss, in Norwich, Connecticut. It forms crystals, with an oblique rhombic prism as its radical; the small prisms generally present pyramidal terminations. It is hyacinth red; gives a white streak; is translucent-transparent; sp. gr. 4.2-4.6. It is found in crystals from of an inch in breadth. Before the blow pipe it becomes pearl-gray with a yellowish tint, and fuses on the edges to a transparent glass. Analysis gave: The proportion of phosphoric acid to oxide of cerium is represented by (Ce 0)3 + (P2 05). Copper-mica from Goslar was examined by Borchers. It is a pale, sometimes gold-yellow, artificial mineral product of a metallic splendent lustre, in the form of very thin, micaceous, six sided tables, occurring in an inferior kind of copper, called by the workmen mica-copper, and remains after dissolving the copper in nitric acid. This peculiar product consists of: The oxides of copper and nickel together, appear to contain four times as much oxygen as that of antimony. Damur analyzed a vanadiate of lead, the locality of which was unknown. It sits on quartz, forming brownish-yellow warts, which are dark green on their fractured surface, but yield a pale yellow powder. It contains: Apjohnt analyzed a mineral from Africa, which occurs in snow-white fibres with silky lustre, about 6 inches in length, and ascertained its composition to be (Mg 0 + S 03) + (A12 03 + S309). It is therefore an alum, in which the potassa is replaced by protoxide of manganese. Von Holger has undertaken to enrich the science of mineralogy with an entirely distinct branch, of which no one would previously have dreamed, viz. with a "Pathology of the mineral kingdom." In order to have a Pathology, minerals should also possess vitality. "No one," says V. Holger, "Dow views minerals as lifeless bodies, in contradistinction to living, organic beings, but it is believed that they possess life like the latter, although it is of a different kind. They must then exert vital energy, &c." He proceeds from this introduction to the Diseases of minerals, which constitute mineral Pathology, and attempts to show that they may be diseased in regard to their composition, their form and their origin. What was said by a philosopher about 2000 years ago still holds good, that nothing is so absurd, but it may at some day be asserted and maintained by the learned! The present number closes the extracts from Berzelius' Report, for the year 1837, and should it be deemed of sufficient interest to the readers of the Journal, the committee will endeavor to introduce similar notices from the Report of 1838, which is at present in the course of publication in Germany. Civil Engineering. On the Mensuration of Excavation and Embankment, upon Canals, Roads, and Rail Roads. By ELLWOOD MORRIS, Civil Engineer. On directing the attention to Public Works, one is immediately struck with the vastness of the amount of money expended in Excavation, Embankment and Masonry: forming on the Roads and Rail Roads, usually the chief, and on the canals nearly the only items of outlay. We have the authority of the Chev. de Gerstner, that the 3000 miles of railway this year * Journ. für Pract. Chemie. XI, 134. † Annal. der Pharmacie, XXII, 272. ‡ Zeitschrift für Physik von Baumgärtner & Ritter, v. Holger, V. 159. Of in operation in the United States, cost sixty millions of dollars.* which, perhaps, forty millions were laid out in the graduation and masonry alone. When to this, we add the immense expenditures for similar objects upon the Canals and Roads of the Union, will it be too much to say that near one hundred millions of dollars have been disbursed in the earth works, requisite to reduce the routes to proper levels, and the architectural constructions necessary to pass the streams. This large amount of work having been done chiefly by contract, and paid for by the cubic yard, or perch, the vast importance of accuracy and uniformity in calculating the contents of Excavation, Embankment, and Masonry solids, must be palpable to all. Unfortunately, great diversity has existed, and still continues to exist, in the modes of mensuration adopted by Engineers; they may, however, in a general way, be divided into two principal methods, and the modifications which flow from them; first, those which depend on arithmetical, and, second, those dependant on geometrical, average. When we state that neither of these modes is exact, except in a limited number of cases, we merely mention what is well known to every engineer: but which is a reason not the less powerful, to induce us to seek more perfect methods, The importance of this subject will, we trust, be a sufficient apology for laying before the readers of the Journal of the Franklin Institute a few observations, with the hope of drawing to it the attention of abler minds.t We are aware, that it is urged by some, that the modes of measurement are immaterial, provided, the values of the unit of measure computed in a particular mode were known, and that mode generally adopted; and this argument would have great force if any single rule or method of mensuration was used in general practice: But whilst on some works the mode of computation uniformly errs in excess, on others it probably errs in deficiency, or, otherwise, according to circumstances; and this brings us back to the importance of a uniform and more exact mode. The surface of the ground is regarded by the Engineer, as being composed of planes, variously disposed with relation to each other; so that any vertical section, will exhibit a rectilineal figure more or less regular. This supposition, though not strictly correct, is sufficiently accurate for practical purposes, and avoids any necessity of entering into the complex calculations pertaining to warped surfaces. The usual method of measuring excavation and embankment, is by taking vertical sections, perpendicular to the centre line of the canal or road, and at short distances apart, in which the elevation or depression of numerous points in the ground, above or below the bottom of canal or grade of road, is ascertained by the spirit level and rod, whilst their distances out, right and left, are measured (generally) with a tape line. These elevations or depressions are commonly called plus or minus cultings, or simply cuttings, and the distances of the several points from the centre line are denominated shortly distances out. The cuttings then are ordinates or perpendiculars drawn from the plane of grade or bottom, to intersect the surface of the ground; and the distances out, are the horizontal distances of those perpendiculars from the centre line, (measured at right *See Journal Franklin Institute for September 1839. A Treatise on the Mensuration of Excavation and Embankment, from the pen of a Northern Engineer, well able to manage such a subject, was lately announced as being in the press, it has not however (the writer believes) yet been published. angles) and which, by deduction, give the distances apart of the separate cuttings, or the abscissa of those ordinates. The details of the operation of taking the cuttings require great nicety, but are so well known to practical Engineers as to render unnecessary a description at length. We may, however, mention a general rule which must not be neglected if accurate results are desired; viz: At every change of slope transversely, single cuttings, and distances out, must be taken, and at every longitudinal change, sections of cuttings. Upon rough ground it is customary to make the lateral distances apart of the cuttings uniformly ten feet, which materially facilitates the subsequent calculations. We may here observe that the cuttings and distances out, are commonly taken in feet and tenths, and the regular stations of one hundred feet, are divided by cross sections (or sections of cuttings) into shorter lengths if the ground requires, as it almost always does. Some Engineers have suggested the division, and we believe some have had their rods and tapes divided, into yards and decimals; and some retaining the rod and tape as usual, have made their regular stations fifty four feet, and have spaced their cross sections where they required to be nearer, so that their distances apart should be some aliquot part of 54 feet. These methods, though they somewhat expedite the office work where the quantities are ascertained by the process of arithmetical average, are not, however, generally adopted by the profession: A foot being usually the unit of lineal measure, a hundred feet a regular station, and the cubic yard the unit of the solidity of excavations and embankments. The isometrical diagram, fig. 1, Plate 1, represents a regular station of embankment on irregular ground, with an intermediate cross section at 50 feet or midway. Base or width of road surface = 30 feet, slopes 2 to 1, a, b, c, d, e, f, and g, are cuttings, minus cuttings, in this case: 1: 2: and 3: are the sections of cuttings, or cross sections. C, C, is the centre line. Earth work on Roads and Canals is usually laid off in divisions called sections of half a mile or more in length, and when a sufficient number of trans. verse sections of the ground have been obtained, or technically when the “cuttings are taken," the transverse profiles or cross sections are drawn upon paper, their areas calculated, and the solid contents of the excava tions and embankments computed; generally by one of two rules, viz: No. 1: By Arithmetical Average. Multiply the sum of the end areas by their distance apart, and divide the product by 6 and by 9; the result will give, approximately, the number of cubic yards in the given length of excavation or embankment. No. 2: By Geometrical Average.--Multiply the sum of the end areas, and the square root of their product, by the distance apart, and divide the product by 9 and by 9. The result will be, nearly, the number of cubic yards in the given length of excavation or embankment. Of these rules, No. 1: gives a result always in excess, except when the excavation or embankment solid, happens to be a prism or cylinder, or when the sums of the right and left distances out, are the same for both the end areas used. And, No. 2: though accurate when applied to prisms, cylinders, pyramids and cones, or their frustra, fails on application to the prismoid.or wedge, as well as to embankment or excavation solids, on irregular ground, where the difference is great between the areas of adjacent transverse sections. Such is a brief sketch of the modes in common use for measuring excava tion and embankment on roads and canals; of which we may observe, that the method, (No. 1,) and all others founded upon the same principles, necessarily lead to errors, often of magnitude, and particularly in deducing "deficient embankment," as is very well shown by Mr. Macneill, in the introduction to his excavation and embankment tables published in 1833. It is true, that Engineers in this country would seldom fail to arrive at much closer results than Mr. Macneill has instanced; because, being well aware, that this very convenient rule (No. 1,) always gives results which are in excess in some ratio to the difference of any two areas averaged, they take care to place their cross sections so near together that this difference may be small, and consequently by closely pursuing this course are enabled to reach results proportionally more exact. Indeed, the writer has often known sections of cuttings on sidehill, to be taken but 10 feet apart longitudinally, and in some extraordinary cases amongst rocks even at a less distance. The rule No. 2: though not liable to so many, nor such strong objections, is still obnoxious to some: and where greater, indeed almost precise, accuracy is attainable without much more labour, we cannot but think it highly desirable, and accordingly propose to develope a method much superior, as it appears to us. But before doing so, the writer distinctly disclaims any attempt at novelty, as to the principles employed; for they have been long known to those versed in mensuration, and have also been applied to the matter in hand by the eminent Engineer before alluded to (J. Macneill, Esq., C. E. &c.,) in his publication in 1833. It is believed, however, that as a general process, the mode about to be laid down has not yet been used on any work. Upon the general supposition that any given length of excavation or embankment is a solid bounded laterally by plane surfaces, and terminated at both ends by transverse sections, or planes, perpendicular to the centre or guiding line of the excavation or embankment; the contents of that solid may be accurately computed by aid of the "prismoidal formula," used by Mr. Macneill, who gives a very good demonstration of it as applied directly to one of the solids under consideration. Mr. Macneill's tables, though carefully made out, and undoubtedly useful in a level country, are unfortunately not of very ready application to common cases, owing to the variable transverse figure of the ground not having been (and which indeed is scarcely capable of being) taken into the account in the tabular arrangement employed by that distinguished practical writer. The "Prismoidal Formula" referred to, is as follows: Parallel sections each perpendicular to the guiding line of the excavation or embankment. Let b The area of the base, or of a cross section at one end of a given length of excavation or embankment. แ t= The area of the top, or other end section. 66 m = The area of a section midway between the two, and deduced from them. << h = The height of the solid, or perp. distance between the end sec tions. S The solidity. Then the General Formula b + 4 m + t × } h = S. This is the rule for the capacity of a prismoid, demonstrated in almost every treatise on mensuration. And it is also the General Formula for the mensuration of all solids, whose bases and tops, or edges, lie in parallel |