neers, in Scotland, for 1867-68, says: "It had previously been ascertained by observation of the success and failure of actual chimneys, and especially of those which respectively stood and fell during the violent storms of 1856, that, in order that a rend chimney may be sufficiently stable, its weight should be such that a pressure of wind, of about 55 lbs. per sq. ft. of a plane surface, directly facing the wind, or 271⁄2 lbs. per sq. ft. of the plane projection of a cylindrical surface, shall not cause the resultant pressure at any bed-joint to deviate from the axis of the chimney by more than one quarter of the outside diameter at that joint,' According to Rankine's rule, the Lawrence Mfg. Co.'s chimney is adapted to a maximum pressure of wind on a plane acting on the whole height of 18.80 lbs. per sq. ft., or of a pressure of 21.70 lbs. per sq. ft. acting on the uppermost 141 ft. of the chimney. Steel Chimneys are largely coming into use, especially for tall chimneys of iron-works, from 150 to 300 feet in height. The advantages claimed are: greater strength and safety; smaller space required; smaller cost, by 30 to 50 per cent, as compared with brick chimneys; avoidance of infiltra tion of air and consequent checking of the draught, common in brick chimneys. They are usually made cylindrical in shape, with a wide curved flare for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is provided, to which the chimney is riveted, and the plate is secured to a massive foundation by holding-down bolts. No guys are used. F. W. Gordon, of the Phila. Engineering Works, gives the following method of calculating their resistance to wind pressure (Power, Oct. 1893): In tests by Sir William Fairbairn we find four experiments to determine the strength of thin hollow tubes. In the table will be found their elements, with their breaking strain. These tubes were placed upon hollow blocks, and the weights suspended at the centre from a block fitted to the inside of the tube. Edwin Clarke has formulated a rule from experiments conducted by him during his investigations into the use of iron and steel for hollow tube bridges, which is as follows: 1 Center break- Area of material in sq.in. x Mean depth in in. x Constant This shows a close approximation to the breaking weight obtained by experiments and that derived from Edwin Clarke's and D. K. Clark's rules. We therefore assume that this system of calculation is practically correct, and that it is eminently safe when a large factor of safety is provided, and from the fact that a chimney may be standing for many years without receiving anything like the strain taken as the basis of the calculation, viz., fifty pounds per square foot. Wind pressure at fifty pounds per square foot may be assumed to be travelling in a horizontal direction, and be of the same velocity from the top to the bottom of the stack. This is the extreme assumption. If, however, the chimney is round, its effective area would be only half of its diameter plane. We assume that the entire force may be concentrated in the centre of the height of the section of the chimney under consideration. Taking as an example a 125-foot iron chimney at Poughkeepsie, N. Y., the average diameter of which is 90 inches, the effective surface in square feet upon which the force of the wind may play will therefore be 7 times 125 divided by 2, which multiplied by 50 gives a total wind force of 23,437 pounds. The resistance of the chimney to breaking across the top of the foundation would be 3 14 X 1682 (that is, diameter of base) X .25 X 35,000+ (750 X 4) = 258,486, or 10.6 times the entire force of the wind. We multiply the half height above the joint in inches, 750, by 4, because the chimney is considered a fixed beam with a load suspended on one end. In calculating fts strength half way up, we have a beam of the same character. It is a fixed beam at a line half way up the chimney, where it is 90 inches in diameter and .187 inch thick. Taking the diametrical section above this line, and the force as concentrated in the centre of it, or half way up from the point under consideration, its breaking strength is: 8.14 X 902.187 X 35,000 (381 × 4) = 109,220; and the force of the wind to tear it apart through its cross-section, 74 × 62% × 50 ÷ 2 = 11,352, or a little more than one tenth of the strength of the stack. The Babcock & Wilcox Co.'s book "Steam" illustrates a steel chimney at the works of the Maryland Steel Co., Sparrow's Point, Md. It is 225 ft. in height above the base, with internal brick lining 13' 9" uniform inside diameter. The shell is 25 ft. diam. at the base, tapering in a curve to 17 ft. 25 ft. above the base, thence tapering almost imperceptibly to 14' 8" at the top. The upper 40 feet is of 14-inch plates, the next four sections of 40 ft. each are respectively 9/32, 5/16, 11/32, and 3⁄41⁄2 inch. Sizes of Foundations for Steel Chimneys. Weight of Sheet-iron Smoke-stacks per Foot. Sheet-iron Chimneys. (Columbus Machine Co.) THE STEAM-ENGINE. Expansion of Steam. Isothermal and Adiabatic.-According to Mariotte's law, the volume of a perfect gas, the temperature being 1 kept constant, varies inversely as its pressure, or p«; pv = a constant, The curve constructed from this formula is called the isothermal curve, or curve of equal temperatures, and is a common or rectangular hyperbola. The relation of the pressure and volume of saturated steam, as deduced from Regnault's experiments, and as given in Steam tables, is approximately, according to Rankine (S. E., p. 403), for pressures not exceeding 120 lbs., px7 17, or pa v = a constant. Zeuner has 1 or puli = pv 1,0625 1 or found that the exponent 1.0646 gives a closer approximation. When steam expands in a closed cylinder, as in an engine, according to Rankine (S. E., p. 885), the approximate law of the expansion is p ∞ — បទ pxv, or py1.111. a constant. The curve constructed from this formula is called the adiabatic curve, or curve of no transmission of heat. Peabody Therm., p. 112) says: "It is probable that this equation was obtained by comparing the expansion lines on a large number of indicatordiagrams. There does not appear to be any good reason for using an exponential equation in this connection,... and the action of a lagged steamengine cylinder is far from being adiabatic. ... For general purposes the hyperbola is the best curve for comparison with the expansion curve of an indicator-card. . . ." Wolff and Denton, Trans. A. S. M. E., ii. 175, say: "From a number of cards examined from a variety of steam-engines in current use, we find that the actual expansion line varies between the 10/9 adiabatic curve and the Mariotte curve." Prof. Thurston (A. S. M. E., ii. 203), says he doubts if the exponent ever becomes the same in any two engines, or even in the same engines at different times of the day and under varying conditions of the day. Expansion of Steam according to Mariotte's Law and to the Adiabatic Law. (Trans. A. S. M. E., ii. 156.)-Mariotte's law Pm 1 pvp1v1; values calculated from formula = R 10 (1+hyp log R), in which R V2V1, P1 = absolute initial pressure, Pm = absolute mean pressure, initial volume of steam in cylinder at pressure p1, v1 = final volume of steam at final pressure. Adiabatic law: pu pv,; values calculated from formula = 10R Pm 1 9R Mean Pressure of Expanded Steam.-For calculations of engines it is generally assumed that steam expands according to Mariotte's law, the curve of the expansion line being a hyperbola. The mean pressure, measured above vacuum, is then obtained from the formula Pm Pi 1+ hyp log R or Pm Pt(1 + hyp log R), in which Pm is the absolute mean pressure, p, the absolute initial pressure taken as uniform up to the point of cut-off, Pt the terminal pressure, and R the ratio of expansion. Ifl length of stroke to the cut-off, L= total stroke. Pm= Pil+P1l hyp log L 1+ hyp log R R Pressures.-Mariotte's ; and if R =, Pm = p1 Mean and Terminal Absolute Law. The values in the following table are based on Mariotte's law, except those in the last column, which give the mean pressure of superheated steam, which, according to Rankine, expands in a cylinder according to the law pa v-. These latter values are calculated from the formula 17-16Rmay be found by extracting the square root of R four times. From the mean absolute pressures given deduct the mean back pressure (absolute) to obtain the mean effective pressure. Pm = R Ratio of Mean to Initial 1 Dry Steam. Calculation of Mean Effective Pressure, Clearance and Compression Considered.-In the above tables no account is taken of clearance, which in actual steam-engines modifies the ratio of expansion and the mean pressure; nor of compression and back-pressure, which diminish the mean effective pressure. In the following calculation these elements are considered. с C = poc(1 + hyp log *+€) = p(x+c)(1 + hyp log+c); D = (p1 — Pc)c = p1c — P¿(x+c). Area of A = p1(l+c) (1+ hyp log+c) − [po(L− x) + P¿(x + c)(1 + hyp log *+)+pe · log+)+P(x+c)] = P1(l+c)(1+hyp log+c) − p¿[(L − x) + (x + c) hyp log + - p1 EXAMPLE.-Let L= 1, 1 = 0.25, x = 0.25, c = 0.1, p1 = 60 lbs., P2 lbs. − 2 [(1 − .25) + .35 hyp log = 21(1 + 1.145) - 2[.75 + 35 × 1.253] - 6 2.377636.668 mean effective pressure. The actual indicator-diagram generally shows a mean pressure consider. ably less than that due to the initial pressure and the rate of expansion. The causes of loss of pressure are: 1. Friction in the stop-valves and steampipes. 2. Friction or wire-drawing of the steam during admission and cutoff, due chiefly to defective valve-gear and contracted steam-passages. 3. Liquefaction during expansion. 4. Exhausting before the engine has completed its stroke. 5. Compression due to early closure of exhaust. 6. Friction in the exhaust-ports, passages, and pipes. Re-evaporation during expansion of the steam condensed during admis sion, and valve-leakage after cut-off, tend to elevate the expansion line of the diagram and increase the mean pressure. If the theoretical mean pressure be calculated from the initial pressure and the rate of expansion on the supposition that the expansion curve fol |