relatively to the frame of the recording apparatus, traces a straight line on the band of paper as the latter travels below the pencil. That line is called the zero line, and corresponds to O X in fig. 3.

An arm fixed to the forward gland carries another pencil, whose position is adjusted before the experiment, so that when there is no tractive force its point rests on the zero line. During the experiment, this pencil traces on the paper band a line such as ERG, fig. 3, whose ordinate or distance from any given point in the zero line is the deflection of the pair of springs, and proportional to the tractive force, at the corresponding point in the journey of the vehicle.

The areas of the diagrams drawn by this apparatus, representing quantities of work, may be found either by the method described in Articles 11, 11 A, or by an instrument for measuring the areas of plane figures, called the Planimeter, of which various forms have been invented by Ernst, Sang, Clerk Maxwell, Amstler, and others.

A third pencil, actuated by a clock, is sometimes caused to mark a series of dots on the paper band at equal intervals of time, and so to record the changes of velocity.

When one vehicle (such as a locomotive engine) drags one or more others, the apparatus may, if convenient, be turned hind side before, and carried by the foremost vehicle. In such a case the motion of the band of paper ought to be derived, not from a driving wheel, which is liable to slip, but from a bearing wheel.

When the apparatus is used to record the tractive force and work performed in towing a vessel, the apparatus for moving the paper band may be driven by means of a wheel or fan, acted upon by the water; in which case, the ratio of the velocity of the band to that of the vessel should be determined by experiment.

Owing to the varieties which exist in the elasticity of steel, the relation between the deflections of the springs and the tractive forces can only be roughly calculated beforehand, and should be determined exactly by direct experiment-that is, by hanging known weights to the springs and noting the deflections.

The best form of longitudinal section for each spring is that which gives the greatest flexibility for a given strength, and consists of two parabolas, having their vertices at the two ends of the spring, and meeting base to base in the middle-that is to say, the thickness of the spring at any given point of its length should be proportional to the square root of the distance of that point from the nearest end of the spring. To express this by a formula, let e be the half-length of the spring;

the thickness in the middle;

x the distance of any point in the spring from the end nearest

The breadth of each spring should be uniform, and, according to General Morin, should not exceed from 1 to 2 inches. Let it be denoted by b.

The following is the formula for calculating beforehand the probable joint deflection of a given pair of springs under a given tractive force :

Let the dimensions c, h, b, be stated in inches, and the force P in pounds.

Let y denote the deflection in inches.

Let E denote the modulus of elasticity of steel, in pounds on the square inch. Its value, for different specimens of steel, varies from 29,000,000 to 42,000,000, the smaller values being the most common. Then

The deflection should not be permitted to exceed about onetenth part of the length of the springs.

41. Morin's Rotatory Dynamometer is represented in figs. 14, 14 a,

and is designed to record the work performed by a prime mover in transmitting rotatory motion to any machine. A is a fast pulley,

and C a loose pulley, on the same shaft. A belt transmits motion from the prime mover to one or other of those pulleys according as it is desired to transmit motion to the shaft or not.

A third pulley, B, on the same shaft, carries the belt which transmits motion to the machine to be driven. This pulley is also loose on the shaft to a certain extent, so that it is capable of moving relatively to the shaft, backwards and forwards through a small arc, sufficient to admit of the deflection of a steel spring by which motion is transmitted from the shaft to the pulley.

One end of that spring is fixed to the shaft, so that the spring projects from the shaft like an arm, and rotates along with it. The other end of the spring is connected with the pulley B near its circumference, and is the means of driving that pulley; so that the spring undergoes deflection proportional to the effort exerted by the shaft on the pulley.

A frame projecting radially like an arm from the shaft, and rotating along with it, carries an apparatus similar to that used in the traction dynamometer, for making a band of paper move radially with respect to the shaft with a velocity proportional to the speed with which the shaft rotates. A pencil carried by this frame traces a zero line on the paper band; and another pencil carried by the end of the spring, traces a line whose ordinates represent the forces exerted, just as in the traction dynamometer.

The mechanism for moving the paper band is driven by a toothed ring surrounding the shaft, and kept at rest while the shaft rotates by means of a catch. When that catch is drawn back, the toothed ring is set free, rotates along with the shaft, and ceases to drive the mechanism; and thus the motion of the paper band can be stopped if necessary. (See Addendum, page 80.)

42. Morin's Integrating Dynamometers record simply the work performed in dragging a vehicle or driving a machine, without recording separately the force and the motion. The general principle of the method by which this is effected is shown by fig. 15, in

K

B

Р

which A represents a plane circular disc, made to rotate with an angular velocity proportional to the speed of the motion of the vehicle or machine, and B a small wheel driven by the friction of the disc against its edge, and having its axis parallel to a radius of the disc. The wheel B, and some mechanism which it drives, are carried by a frame which is carried by one of the dynamometer springs, and so adjusted that the distance of the edge of B from the centre of A is equal to the deflection of the springs, and proportional to the effort.

Fig. 15.

The velocity of the edge of B at any instant being the product of its distance from the centre of A into the angular velocity of A, is proportional to the product of the effort into the velocity of the vehicle or machine-that is, to the rate at which work is performed; therefore the motion of the wheel B, in any interval of time, is proportional to the work performed in that time; and that work can be recorded by means of dial plates, with indexes moved by a train of wheelwork driven by the wheel B.

43. Indicator-Application to the Steam Engine. This instrument was invented by Watt, and has since been improved by M'Naught, Richards, and other inventors. Its object is to record, by means of a diagram, the intensity of the pressure exerted by steam against one of the faces of a piston at each point of the piston's motion, and so to afford the means of computing, according to the principles of Article 6 and Article 11, first, the energy exerted by the steam in driving the piston during the forward stroke; secondly, the work lost by the piston in expelling the steam from the cylinder during the return stroke; and thirdly, the difference of these quantities, which is the available or effective energy exerted by the steam on the piston, and which, being multiplied by the number of strokes per minute and divided by 33,000 foot-pounds, gives the INDICATED HORSE-POWER.

The indicator in its present form is represented by fig. 16. It consists essentially of a small cylinder, fitted with a piston, which cylinder, by means of the screwed nozzle at its lower end, can be fixed in any convenient position on a tube communicating with that end of the engine cylinder where the work of the steam is determined. The communication between the engine cylinder and the indicator cylinder can be opened and shut at will by means of a cock. When it is open, the intensity of the pressure of the steam on the engine piston and on the indicator piston is the same, or nearly the same.

Fig. 16.

The upper part of the cylindrical case contains a spiral spring, one end of which is attached to the piston or to its rod, and the other to the top of the casing. The indicator piston is pressed from below by the steam, and from above by the atmosphere. When

the pressure of the steam is equal to that of the atmosphere, the spring retains its unstrained length, and the piston its original position. When the pressure of the steam exceeds that of the atmosphere, the piston is driven outwards, and the spring compressed; when the pressure of the steam is less than that of the atmosphere, the piston is driven inwards, and the spring extended. The compression or extension of the spring indicates the difference, upward or downward, between the pressure of the steam and that of the atmosphere.

The indicator piston rod is connected by links and parallel motion with a pencil.

F (fig. 16) is a brass drum, which rotates backward and forward about a vertical axis, and which, when about to be used, is covered with a piece of paper called a "card." It is alternately pulled round in one direction by the cord H, which wraps on a pulley, and pulled back to its original position by a spring contained within itself. The cord H is to be connected with the mechanism of the steam engine in any convenient manner which shall insure that the velocity of rotation of the drum shall at every instant bear a constant ratio to that of the steam engine piston: the back and forward motion of the surface of the drum representing that of the steam engine piston on a reduced scale. This having been done, and before opening the cock K, the pencil is to be placed in contact with the drum during a few strokes, when it will mark on the card a line which, when the card is afterwards spread out flat, becomes a straight line. This line, whose position indicates the pressure of the atmosphere, is called the atmospheric line. In fig. 17, it is represented by A A.

C

A

Then the cock K is opened, and the pencil moving up and down

B

G

AK

A

E

with the variations of the pressure of the steam, traces on the card during each complete or double stroke a curve such as B C D E B. The ordinates drawn to that curve from any point in the atmospheric line, such as HK and HG, indiIcate the differences between the -v pressure of the steam and the atmospheric pressure at the corresponding point of the motion of the piston. The ordinates of the part BCDE represent the pressures of the steam during the forward stroke, when it is driving the piston; those of the part EB represent the pressures of the steam when the piston is expelling it from the cylinder.

F

Fig. 17.

L

To found exact investigations on the indicator diagrams of steam