compound engine, the area of the low pressure cylinder is calculated as if all the power were to be developed in that cylinder, which therefore requires to be of the same area as the cylinder of a simple engine of the same power.

To find the Area of the Low-pressure Cylinder.-Rule: Multiply the number of horse-power the engine is required to indicate by 33,000, which will give the number of footpounds required per minute, divide this by the speed of the piston in feet per minute, and the result will be the total effective pressure on the piston at that speed to develop the given number of indicated horse-power; divide the quotient by the mean effective pressure per square inch on the piston, and the final quotient is the area in square inches of the low-pressure cylinder,

The speed of the piston in compound engines is usually 420 feet per minute.

The ratio of expansion is found by dividing the initial absolute pressure of the steam in the high-pressure cylinder by the final pressure in the lowpressure cylinder.

The mean effective Pressure on the piston throughout the stroke is found thus.-Rule: To the hyperbolic logarithm of the total number of expansions add 1, then divide by the total number of expansions, and multiply the quotient by the initial absolute pressure of the steam (that is the boiler pressure plus 15 lbs.) which will give the average pressure of the steam expanded the given number of times, from which deduct the back pressure, usually 3 lbs., and the result will be the mean effective pressure.

To find the Area of the High pressure Cylinder.-Rule: Multiply the initial absolute pressure of the steam in the high pressure cylinder by *042, with which result, divide the area of the low pressure cylinder. In order to provide for the loss due to the fall in pressure of the steam in passing between the two cylinders, their areas found by the above rules should be increased to the extent of from 10 to 20 per cent.

The steam should be cut off in the high pressure cylinder when the piston has moved 45 of its length of stroke, and in the low pressure cylinder at one half the length of stroke. The final pressure in the low pressure cylinder should be from 8 to 9 lbs. in theory, but in practice it is from 2 to 3 lbs. more than that, and the lowest economical final pressure is from 10 to 12 lbs.

As an example of these rules.-Required the area of the cylinders for a compound engine to indicate 100 horse-power: speed of piston 420 feet per minute: boiler pressure 86 lbs. per square inch-then allowing 5 lbs. for loss of pressure between the boiler and the cylinder, the initial pressure in the high pressure cylinder will be 81 lbs., and the initial absolute pressure 81+ 15 = 96 lbs. presuming the steam to be worked down to a final pressure of 12 lbs.-it will give

96 initial absolute pressure in high pressure cylinder 12 final pressure in low pressure cylinder

=

8, ratio of expansion.

The hyperbolic logarithm of 8 is 2'0794 + 1 = 3'0794

8

= '3849 × 96=

3695, the average pressure in lbs. per square inch of steam of 96 lbs. pressure expanded eight times, and if 3 lbs. be deducted for back pressure, it leaves 33'95 lbs. mean effective pressure per square inch; then 100 indicated horse-power required × 33,000

420 speed of piston in feet per minute

the piston at that speed; and

= 7857 14 gross pressure on

7857'14

= 23134 33'95 mean effective pressure area in square inches of large cylinder, and 96 × 042403, 23134 and = 57'4 area of small cylinder, then if 20 per cent. be 4:03 added to provide against loss by the pressure falling during the passage of the steam between the cylinders, the area of the low pressure cylinder will be 23134 + 46′26 = 277'6 square inches, and the area of the high pressure cylinder will be 574 + 11:48 = 68.88 square inches, or 18 inches diameter for the large, and 9 inches diameter for the small cylinder, being a cylinder ratio of 4 to 1, which agrees with the best modern practice for that pressure of steam. If the initial absolute pressure had been 75 lbs., the ratio of the areas of the cylinders would have been 75 × *042 = 3.15, and for 60 lbs. it would have been 60 × *042 = 252; and for a high absolute pressure of 125 lbs, it would have been 125 X '042 = 5°25.

THE INDICATOR.

The Indicator.-The action of steam in a cylinder can only be correctly ascertained by means of an indicator; it shews the pressure of the steam at each point of the stroke, the power and performance of the engine, the amount of back pressure or force opposed to the motion of the piston, and enables any imperfections to be detected in the construction of the valve ports and steam passages. The best indicator is that known as Richards' Indicator.*

Indicator Diagrams.—Supposing the indicator to be fixed to a cylinder, and that the drum is connected by means of a cord to some part of the engine, which has a motion co-incident with that of the piston, if the barrel be allowed to rotate before the indicator cock is opened, a horizontal line is traced, which is called the atmospheric line, and all portions of the diagram above that line, represent steam pressures and all portions below that line represent vacuum.

If the indicator cock be opened at the beginning of the stroke, when

Richards' Indicator is made by Messrs. Elliot Brothers, 449, Strand, London, who sell Richards' work on the Indicator, published by Longman & Co., to which the Author is indebted for some of the above information on Indicator Diagrams.

steam enters the engine cylinder, the pencil moves upwards and traces a vertical line, and as the piston moves forward the indicator barrel rotates and a horizontal line is traced until the steam is cut off; then, as the expanding steam increases in volume, it declines in pressure, which causes the pencil to gradually fall and describe a curved line until the exhaust port is opened, when the pencil immediately falls and describes the "toe" of the diagram. On the return stroke the pencil traces the bottom or exhaust line of the diagram until the closing of the exhaust port, when cushioning commences, then the pressure rises and moves the pencil up and completes the diagram.

Theoretical Indicator Diagram.-The rules for the expansion of steam are based upon the approximately correct law of gases, viz. that the pressure of gas varies inversely as the volume, or the product of the pressure and volume of a gas is always a constant, other conditions being unaltered; and in order to ascertain the varying pressure and volume of

steam during expansion, it is necessary to construct a theoretical diagram according to this law, the descending curve of which represents the decreasing force of the steam as it expands in volume. This curve is called a hyperbolic curve, and is the standard by which the character of all expansion curves in indicator diagrams is determined. To draw the theoretical curve upon a diagram as shewn in Fig. 13, draw the line A F, representing the line of perfect vacuum, parallel with the atmospheric line, and at the proper distance below it to represent 14'7 lbs.; and perpendicular to the line A F draw A O, representing the clearance space; draw the line C D, representing the period of admission of the steam; from the point D draw the vertical line D B; draw the line D E; from A to F represents the full length of stroke; divide the distance D E into a number of parts, from

which points draw diagonal lines to the point A; from the points where the diagonal lines cut the vertical line D B, draw horizontal lines; and the points where the vertical lines drawn from the points in the line DE meet these horizontal lines, will be the points of the hyperbolic curve, which may be drawn in by hand.

Indicator Diagrams, Fig. 14.-The lines forming the outline of a diagram during one revolution of the engine are as follows:

admitted a little before the beginning of the steam stroke, due to the lead of the valve, to ensure having the full pressure of steam in the cylinder at the beginning of the stroke.

Admission Line, Fig. 14.-A to B is the admission line. This line is formed by the rise of pressure in the cylinder as the port is opened for the admission of steam; the full pressure of the steam should come on to the

piston at the beginning of the stroke, and the admission corner should be sharp. When it is rounded as at A in Fig. 15, or when it slants, as at B,

it shows that the steam is admitted too late and the momentum of the piston at the commencement of the stroke is imparted by the engine. To remedy this the valve requires more lead. When the valve has excessive lead, and steam enters too soon, it will produce a slanting line like C, Fig. 16; to remedy this the valve requires less lead.

Steam Line.-B to C, Fig. 14, is the steam line or period of admission of the steam. This line is formed by the advance of the piston while the port remains open for the admission of steam; the full pressure of steam should be maintained in the cylinder during the whole period of admission, and the steam line should be straight and horizontal, or parallel with the atmo

spheric line up to the point of cut off; when this line falls, like D in Fig. 17, the fall is due either to condensation in the cylinder, or to the ports and steam pipes being too small, which wiredraws and reduces the pressure of the steam.

The Point of Cut Off, Fig. 14.-C is the point of cut off or suppression. As expansion does not properly commence until the port is closed, the action of the valve in cutting off the steam should be sharp and sudden, and the pressure should fall as little as possible during the closing of the port. The point of cut off should be sharp and clear. When this corner is rounded, like E in Fig. 18, it shows that the valve does not close quickly enough, and that the expansion arrangements are defective. When the steam is cut off slowly it causes a fall of pressure in the cylinder before the port is completely closed. When this corner shows a gradually descending line like F in Fig. 18, it shows that some steam has entered the cylinder after it was supposed to have been cut off.

The Expansion Curve.-C to D, Fig. 14, is the expansion curve or period of expansion. In a condensing engine this curve is partly above and partly below the atmospheric line, but in a non-condensing engine the whole of the curve is above the atmospheric line. This curve should approach as nearly as possible in form to that of the theoretical diagram, unless it be filled up by leaky valves, or diminished by steam leaking past the piston. When the cylinder is not properly protected, there will be great loss of heat from radiation, and fall of pressure during expansion, which will cause the expansion curve to fall below the theoretical curve. When the curve rises above the theoretical curve, it is generally due to