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between the marks which denote the freezing point and the boiling point may be divided into any number of equal parts which is convenient; these parts are called degrees. In the Centigrade thermometer the space is divided into 100 degrees, and 0 is put at the freezing point and 100 at the boiling point; this is the instrument commonly used for scientific purposes. In Fahrenheit's thermometer the space is divided into 180 degrees, and 32 is put at the freezing point and 212 at the boiling point: this is the instrument in popular use in England, and it is often called the common thermometer. In Reaumur's thermometer the space is divided into 80 equal parts, and 0 is put at the freezing point and 80 at the boiling point.

561. It is easy to pass from a reading on one thermometer to the corresponding reading on another. For instance, suppose that a Centigrade thermometer indicates 30 degrees, and that we require the corresponding reading on Fahrenheit's thermometer. The number 30 on the 3

30

Centigrade thermometer indicates that is

100'

10'

of the

whole space between the freezing point and the boiling point; now in Fahrenheit's thermometer this space is divided into 180 degrees, and of 180 is 54: thus the

3

10

reading in Fahrenheit's thermometer must be 54 above the freezing point, and as the reading for the freezing point is 32 the required reading is 32 +54, that is 86. Again, suppose that Fahrenheit's thermometer indicates 104 degrees, and that we require the corresponding reading on the Centigrade thermometer. Since 104-32=72, Fahrenheit's thermometer indicates 72 degrees above the freezing point. Now 72 degrees above the freezing point means that

2

72

180'

is of the whole space between the freezing point and 5' the boiling point. This space in the Centigrade thermo

2

5

meter is divided into 100 degrees; and of 100 is 40: thus the required reading is 40.

T. P.

16

562. The temperature of melting snow is always the same. The temperature of boiling water is different for different states of the pressure of the atmosphere: see Art. 531. The exact definition of the boiling point of the Centigrade thermometer is the boiling point when the

19

height of the barometer is of a metre at a place on the

25

19

of a

F

H

level of the sea in latitude 45 degrees North. The 25 metre is about 2923 inches. A variation of 1045 of an inch in the barometer from the standard height causes a change of about one degree centigrade in the temperature of steam. 563. The Atmospheric Steam Engine. AB is a hollow cylinder into which a pipe C passes from a boiler. D is a pipe which communicates with a vessel of cold water. E is a piston which works up and down in the cylinder. The piston is connected with one end of a lever FGH which can turn round a fixed point G. From the other end of the lever is suspended a rod HK, by

B

E

which the machinery connected with the steam engine is set in motion; this rod carries a weight Z which is equal to half the atmospheric pressure on the upper surface of the piston E. An apparatus connected with the lever opens a cock in C when the piston is in its lowest position, and closes it when the piston is in its highest position. A cock in D is opened when the piston comes to its highest position, and is closed soon after the piston begins to descend. Suppose that the piston is in its lowest position; and let the pressure of steam in the boiler be a little greater than that of the atmosphere. When the cock in C is opened steam rushes into the cylinder; thus the pressure on the two surfaces of the piston is about equal, and the piston is made to rise by means of the weight L attached

to the end H of the lever. When the piston is at its highest point the cock in Dopens, and a jet of cold water enters the cylinder; this condenses the steam and forms a vacuum below the piston. The piston is then forced down by the pressure of the atmosphere which is twice as great as the opposing weight L. The water introduced into the cylinder, together with that arising from the condensed steam, escapes through a valve provided for that purpose at the bottom of the cylinder; this valve opens when the piston is nearly at its lowest point.

564. The great defect of the atmospheric steam engine is that by the admission of the cold water the cylinder is cooled at every stroke, so that when steam again enters the cylinder part of it is condensed; this leads to a waste of fuel. Watt improved the engine by having the condensation carried on in a separate chamber. Thus instead of water entering through D to condense the steam in the cylinder, the steam escaped through D into a vessel of cold water and was there condensed. But further improvements were made, and thus the engine assumed the form now to be described.

A

B

E

565. Watt's Steam Engine. AB is a hollow cylinder closed at both ends; C and D are openings at the ends. A piston E works up and down in the cylinder by means of a rod which passes through a steam-tight collar in the upper end of the cylinder. A vessel of cold water, called the condenser, is placed near the cylinder. The openings at C and D are connected with appropriate pipes furnished with cocks, so that steam may be alternately admitted and expelled. When the piston is in its lowest position steam from the boiler enters through D, and at the same time a communication is made between C and the condenser, so that the steam above the piston passes away and is condensed while the piston is forced up by the pressure beneath it. When the piston is in its highest position steam from the boiler enters through C, and the steam below the piston passes

away through D to the condenser, so that the piston is forced down by the pressure of the steam above it. This engine is sometimes called the double-acting steam engine from the circumstance that the force of steam drives the piston alternately up and down.

The con

566. The High-pressure Steam Engine. struction is much the same as in Watt's steam engine, but there is no condenser. The steam has a pressure many times greater than that of the atmosphere, and instead of being condensed after each stroke it is permitted to escape into the open air. This is the form of steam engine used on railways.

567. We have given only a brief sketch of the steam engine; there are many important details connected with the subject, for an account of which the student must consult special treatises. One of the most remarkable contrivances due to Watt is called the Parallel Motion. In the atmospheric steam engine the ends of the lever are arched, and chains passing round them are connected with the ends of the rods which move up and down; thus the piston E can pull the end F down, but cannot push it up. Watt devised a system of jointed bars which allowed the piston rod to move vertically and F to describe an arc of a circle, while the piston rod could push as well as pull the end of the lever. The motion is very important not only in the steam engine but in various cases where motion in a right line is to be transformed, as it were, into motion in a circular arc, and the contrary; attention has recently been drawn to this transformation by some fine researches of Professor Sylvester in relation to a method invented by M. Peaucellier.

LI. FAMILIAR APPLICATIONS.

568. In this Chapter the principles which have been already explained will be applied to some familiar examples, in some cases taken from well-known toys of children.

569. The Kite is memorable as having been a favourite toy with Newton; and the younger Euler, a well-known

mathematician, has devoted to it a memoir in the Transactions of the Berlin Academy for 1756. It is unnecessary to describe an object so well known as the kite; we will suppose it floating in the air and at rest. There are three forces which act and maintain equilibrium; the weight of the kite, including the tail; the force of the wind; and the tension of the string. The weight acts vertically downwards. The wind may be taken to blow horizontally, but its force must be supposed to be resolved into two components, one along the surface of the kite, and the other at right angles to the surface; it is only the latter which produces any effect on the kite, for the former would be like a wind gliding over the surface of the kite and not pressing it see Art. 473. The tension of the string acts in the direction of the string at the point where it leaves the kite; but usually the string near the kite is, as it were, divided into two, one going to a point near the upper end of the kite, and the other to a point near the lower end: in this case the tensions of the two strings are equivalent to the tension of a single string the direction of which is that of the kite-string at the point where it is divided into two. The three forces which thus act on the kite must fulfil the proper conditions in order to produce equilibrium; this will require that their directions should meet. at a point, and that their magnitudes should be in the proper proportion.

570. The kite then adjusts itself to a suitable inclination, and the tail adjusts itself to a suitable position, so as to bring about the precise circumstances necessary for equilibrium; but it would not be easy to state in words exactly what these must be. If we consider the kite alone we can find the situation of its centre of gravity by the experimental method of Art. 170; but when the tail is attached the situation of the centre of gravity of the whole will depend on the position taken by the tail. The weight of the kite alone, or of the kite and the tail, can easily be ascertained. If we consider the kite alone, the points at which the force of the wind on it may be supposed to act can be found. For we may conceive the force of the wind to consist of parallel pressures on all the portions of the face of the kite, the pressures being equal on equal

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