mission may be measured by the number of British thermal units which pass through a square foot of tubular surface in one hour for each degree of difference in temperature between the water and the steam. The difficulties which attend experiments in this direction can only be appreciated by those who have attempted to make such experiments. Certain results have been reached, however, which point to what appears to be a reasonable conclusion. One set of experiments made quite recently gave certain results which may be set forth in the table herewith.

"In other words, when the water was brought to within 5° of the temperature of the heating medium, heat was transmitted through the tubes at the rate of 67 B.T.U. per square foot for each degree of difference in temperature in one hour. When the amount of water flowing through the heater was so largely increased as to make it impossible to get the water any nearer than within 18° of the temperature of the steam, the heat was transmitted at the rate of 139 B.T.U. per sq. ft. of surface for each degree of difference in temperature in one hour. Note here that even with the rate of transmission as low as 67 B.T.U. the water was still 5° from the temperature of the steam. At what rate would the heat have been transmitted if the water could have been brought to within 2° of the temperature of the steam, or to 210° when the steam is at 212° ?

"For commercial purposes feed-water heaters are given a H.P.rating which allows about one-third of a square foot of surface per H.P.-a boiler H.P. being 30 lbs. of water per hour. If the figures given in the table above are accepted as substantially correct, a heater which is to raise 3000 lbs. of water per hour from 60° to 207°, using exhaust steam at 212° as a heating medium, should have nearly 84 sq. ft. of heating surface-that is, a 100 H.P. feed-water heater which is to maintain a constant temperature of not less than 207°, with water flowing through it at the rate of 3000 lbs. per hour, should have nearly a square foot of surface per H.P. That feed-water heaters do not carry this amount of heating surface is well known."

THE STEAM-ENGINE.

Current Practice in Engine Proportions, 1897 (Compare pages 792 to 817.)-A paper with this title by Prof. John H. Barr, in Trans. A. S. M. E., xviii. 737, gives the results of an examination of the proportions of parts of a great number of single-cylinder engines made by different builders. The engines classed as low speed (L. S.) are Corliss or other long-stroke engines usually making not more than 100 or 125 revs. per min. Those classed as high speed (H. S.) have a stroke generally of 1 to 11⁄2 diameters and a speed of 200 to 300 revs. per min. The results are expressed in formulas of rational form with empirical coefficients, and are here abridged as follows:

Thickness of Shell, L. S. only.-t CD+B; D= diam. of piston in in.; B= 0.3 in.; C varies from 0.04 to 0.06, mean = 0.05.

Flanges and Cylinder-heads.-1 to 1.5 times thickness of shell, mean 1.2. Cylinder-head Studs.-No studs less than 34 in. nor greater than 1% in. diam. Least number, 8, for 10 in diam. Average number = 0.7D. Average diam. D/40+2 in.

Ports and Pipes.--a area of port (or pipe) in sq. in.; A = area of piston, sq. in.; V = mean piston-speed, ft. per min.; a= = AV/C, in which C mean velocity of steam through the port or pipe in ft. per min.

Ports, H. S. (same ports for steam as for exhaust).-C= 4500 to 6500, mean 5500. For ordinary piston-speed of 600 ft. per min. a = KA; K = .09 ̊to .13, mean .11.

Steam-ports, L. S.-C

5000 to 9000, mean 6800; K = .08 to .10, mean .09. Exhaust-ports, L. S.-C 4000 to 7000, mean 5500; K = .10 to .125, mean .11. Steam-pipes, H. S.-C 5800 to 7000, mean 6500. If d = diam. of pipe and D= diam. of piston, d= .29D to .32D, mean .30D. Steam-pipes, L. S.-C= 5000 to 8000, mean 6000; d= .27 to .35D, mean .32D. Exhaust pipes, H. S.-C= 2500 to 5500, mean 4400; d= .33 to .50D, mean .37D. Exhaust-pipes, L. S.-C 2800 to 4700, mean 3800; d= .35 to .45D, mean .40D,

Face of Pistons.-F face; D= diameter. F= CD. H. S.: C.30 to .60 mean .46. L. S.: C.25 to .45, mean .32.

Piston-rods.-d= diam, of rod; D = diam. of piston; L = stroke, in.; d = C√DL. H. S.: C.12 to .175, mean .145. L. S.: C.10 to .13, mean .11. Connecting-rods.-H. S. (generally 6 cranks long, rectangular_section): b = breadth; h height of section; L1 = length of connecting-rod; D:

diani.

of piston; b = CVDL1; C = .045 to .07, mean .057; h = Kb; K = 2.2 to 4, mean 2.7. L. S. (generally 5 cranks long, circular sections only): C = .082 to .105, mean .092.

Cross-head Slides.-Maximum pressure in lbs. per sq. in. of shoe, due to the vertical component of the force on the connecting-rod. H. S.: 10.5 to 38, mean 27. L. S.: 29 to 38, mean 40.

Cross-head Pins.-1 = length; d= diam.; projected area = a = dl = CA; A area of piston; l = Kd. H. S.: C.06 to .11, mean .08; K = 1 to 2, mean 1.25. L. S.: C= .054 to .10, mean .07; K = 1 to 1.5, mean 1.3.

Crank-pin.-HP = horse-power of engine; L= length of stroke; l = length of pin; 1= CX HP/L+B; d= diam. of pin; 4 = area of piston; dl = KA. H. S.: C.13 to .46, mean .30; B 2.5 in.; K = .17 to .44, mean .24. L. S.: C.4 to .8, mean .6; B = 2 in.; K = .065 to .115, mean .09.

Crank-shaft Main Journal.-d=CVHP+N; d= diam.; length; N= revs. per min.; projected area = MA; A area of piston. H.S.: C 6.5 to 8.5, mean 7.3; K = 2 to 3, mean 2.2; M = .37 to .70, mean .46. L. S.: C = 6 to 8, mean 6.8; K = 1.7 to 2.1, mean 1.9; M = .46 to .64, mean .56.

Piston-speed.-H. S.: 530 to 660, mean 600; L. S.: 500 to 850, mean 600. Weight of Reciprocating Parts (piston, piston-rod, cross-head, and onehalf of connecting-rod).-W = CD2 ÷ LN2; D diam. of piston; L = length of stroke, in.; N= revs per min. H. S. only: C= 1,200,000 to 2,300,000, mean 1,860,000.

=

product of width of belt in 21 to 40 mean 28; B = 1800.

Belt-surface per I.H.P.-S= CHP+B; S feet by velocity of belt in ft. per min. H. S.: C L. S.: SCX HP.; C = 30 to 42, mean = 35. Fly-wheel (H. S. only).-Weight of rim in lbs.: W = C× HP÷D1'N3;D1: diam. of wheel in in.; C = 65 X 1010 to 2 × 012 mean = 12 X 1011, or 1,200,000,000,000.

=

Weight of Engine per I.H.P. in lbs., including fly-wheel.-W = C × H.P. H. S.: C 100 to 135, mean 115. L. S.: C 135 to 240, mean 175.

Work of Steam-turbines. (See p. 791.)-A 300-H.P. De Laval steamturbine at the 12th Street station of the Edison Electric Illuminating Co. in New York City in April, 1896, showed on a test a steam-consumption of 19.275 lbs. of steam per electrical H.P. per hour, equivalent to 17.348 lbs. per brake H.P., assuming an efficiency of the dynamo of 90%. The steampressure was 145 lbs. gauge and the vacuum 26 in. It drove two 100-K.W. dynamos. The turbine-disk was 29.5 in. diameter and its speed 9000 revs. per min. The dynamos were geared down to 750 revs. The total equipment, including turbine, gearing, and dynamos, occupied a space 13 ft. 3 in. long, 6 ft. 5 in. wide, and 4 ft. 3 in. high.

The "Turbinia," a torpedo-boat 100 ft. long, 9 ft. beam, and 441⁄2 tons displacement, was driven at 31 knots per hour by a Parsons steam-turbine in 1897, developing a calculated I.H.P. of 1576 and a thrust H.P. of 946, the steam-pressure at the engine being 130 lbs. and at the boilers 200 lbs. The vacuum was 13 lbs. The revolutions averaged 2100 per minute. The calculated steam-consumption was 15.86 lbs. per I.H.P. per hour. On another trial the "Turbinia " developed a speed of 3234 knots.

Relative Cost of Different Sizes of Steam-engines.
(From catalogue of the Buckeye Engine Co., Part III.)

Horse-power 50 75 100 125 150 200 250 300 350 400 500 600 700 800 Cost per H.P, $20 17 16 15 14 13 13 1234 12.6 12.6 12.8 134 14 15

GEARING.

Efficiency of Worm Gearing. (See also page 898.)-Worm gearing as a means of transmitting power, has until recently, generally been looked upon with suspicion, its efficiency being considered necessarily low and its life short. Recent experience, however, indicates that when properly proportioned it is both durable and reasonably efficient. Mr. F. A. Halsey discusses the subject in Am. Machinist, Jan. 13 and 20, 1898. He quotes two formulas for the efficiency of worm gearing due to Prof. John H. Barr: E=

tan a (1-ƒ tan a)

tan a +f

(1)

E=

tan a (1-ƒtan a)
tan a +2f

approx.,

(2) in which E = efficiency; a = angle of thread, being angle between thread and a line perpendicular to the axis of the worm; f = coefficient of friction. Eq. (1) applies to the worm thread only, while (2) applies to the worm and step combined, on the assumption that the mean friction radius of the two is equal. Eq. (1) gives a maximum for E when tan a = √1 + ƒ2 - ƒ . . . (3) and eq. (2) a maximum when tan a = 1/2+4f2-2 ƒ.. (4) Using a value

.05 for f gives a value for a in (3) of 43° 34' and in (4) a value of 52° 49′.

On plotting equations (1) and (2) the curves show the striking influence of the pitch-angle upon the efficiency, and since the lost work is expended in friction and wear, it is plain why worms of low angle should be short-lived and those of high angle long-lived. The following table is taken from Mr. Halsey's plotted curves:

RELATION BETWEEN THREAD-ANGLE SPEED AND EFFICIENCY OF WORM GEARS. Angle of Thread.

Velocity of
Pitch-line,

feet per
minute.

The experiments of Mr. Wilfred Lewis on worms show a very satisfactory correspondence with the theory. Mr. Halsey gives a collection of data comprising 16 worms doing heavy duty and having pitch-angles ranging between 4° 30′ and 45°, which show that every worm having an angle above 12° 30' was successful in regard to durability, and every worm below 9° was unsuccessful, the overlapping region being occupied by worms some of which were successful and some unsuccessful. In several cases worms of one pitch-angle had been replaced by worms of a different angle, an increase in the angle leading in every case to better results and a decrease to poorer results He concludes with the following table from experiments by Mr. James Christie, of the Pencoyd Iron Works, and gives data connecting the load upon the teeth with the pitch-line velocity of the worm:

LIMITING SPEEDS AND PRESSURES OF WORM GEARING.

Double

Revolutions per minute. Velocity at pitch-line in feet per minute..

Doublethread Worm 24"

Pitch, 2

Pitch. 4

Pitch Diam. Pitch Diain.

128 201 272 425 128 201 272 201 272 425

96 150 205 320 96 150 205 235 319 498 Limiting pressure in pounds... 1700 1300 1100 700 1100 1100 1100 1100 700 400

APPROXIMATE HYDRAULIC FORMULA.
(The Lombard Governor Co., Boston, Mass.)

Head (H) in feet. Pressure (P) in lbs. per sq. in. Diameter (D) in feet. Area (4) in sq. ft. Quantity (Q) in cubic ft. per second. Time (T) in seconds.

Time (T) to acquire spouting velocity in a vertical pipe, or (T2) in a pipe on an angle (e) from horizontal:

T1 = 8.02 √H÷32.17, T1 = 8.02 √ H+ 32.17 sin 0.

Head (H) or pressure (P) which will vent any quantity (Q) through a round orifice of any diameter (D) or area (A):

Quantity (Q) discharged through a round orifice of any diameter (D) or area (4) under any pressure (P) or under any head (H):

Q = √P× 55.3 × A2, Q = VP-84.1 × D1;

Q = √H× 23.75 × A2, Q = √H× 14.71 × Da.

Diameter (D) or area (4) of a round orifice to vent any quantity (Q) under any head (H) or under any pressure (P):

Time (7) of emptying a vessel of any area (4) through an orifice of any area (a) anywhere in its side:

T = .416A √H + a.

Time (T) of lowering a water level from (H) to (h) in a tank through an orifice of any area(a) in its side. Area of tank is (4).

Kinetic energy (K) or foot-pounds in water in a round pipe of any diameter (D) when moving at velocity (V):

K = .76 × D2 × L × V.

Time-average-pressure (A. P.) in a pipe of any length (L) with water moving at any velocity (V).

A.P. 0.1324LV + T.

Note.-This must not be confused with water-hammer pressure, which is always many times greater than A.P. and for which no simple formula may be written.

Area (a) of an orifice to empty a tank of any area (A) in any time (7) from any head (H):

a = T÷0.409A VH.

Area (a) of an orifice to lower water in a tank of area (A) from head (H) to (h) in time (T):

a = T+0.409 × × × ( √H− √ñ).

SPECIFICATIONS FOR TIN AND TERNE PLATE.

(Penna. R. R. Co., 1902.)

Each sheet must (1) be cut as nearly exact to size ordered as possible, (2) must be rectangular and flat and free from flaws, (3) must doubleseam successfully under all circumstances, (4) must show a smooth edge with no sign of fracture when bent through an angle of 180° and flattened down with a wooden mallet, (5) must be so nearly like every other sheet in the shipment, in thickness, uniformity, and amount of coating, that no difficulty will arise in the shops due to varying thickness of sheets, and (6) must correspond for the different grades to the figures in the following table: