pressure is supplied for the purpose of working hydraulic lifts, &c., and since the price paid for a given quantity of water is in these circumstances much higher than that for which the same quantity of water would be obtained at such pressures as are found in the ordinary supply mains, we infer that the purchaser thinks he is buying some "thing" besides the matter of which the water is composed.

From the foregoing considerations we are led to define Physics in its most general aspect as a discussion of the properties of matter and energy. It is, however, usual to restrict somewhat the definition so as to exclude the discussion of those properties of matter which depend simply on the nature of the different forms of matter (Chemistry), as also the properties of matter and energy as related to living things (Biology). The line of demarcation separating Physics and Chemistry has never been very clear, and of late years has practically vanished.

2. Matter. Of the numerous definitions of matter which have from time to time been given, we may at present adopt the following: Matter is that which can occupy space. This definition does not attempt to state what matter is, it only gives us a working definition, which in the present state of our knowledge as to the ultimate structure of matter is all that can be done.

We may speak of a limited portion of matter as a body, and of matter of a certain definite kind as a substance. Thus water, sugar, air, lead, are all matter, since they all occupy space or have dimensions. Since each of these things is a special kind of matter possessing distinct properties, they each form a distinct substance. A drop of water, a lump of sugar, the air enclosed in a given vessel, is each an example of a body.

3. Energy.-Energy may be defined as the capacity of doing work, where by work we mean the act of producing a change of the state of matter in opposition to resistance, which opposes any such change. The real meaning of this definition will be made clearer when we come to consider the various forms in which energy can exist.

4. General Maxim of Physical Science.-There is a maxim to the effect that the same cause will always produce the same effects, which is at the foundation of all our investigations in Physical Science. Since no event ever happens more than once, it is evident that the causes and effects spoken of above cannot be the same in all respects. What is meant is that if the causes only differ as regards the absolute time and place at which the event we are considering occurs, so the effects will also only differ as regards the absolute time and place. In order to meet this defect in the maxim, Maxwell has proposed to substitute the following: "The difference between one event and another does not depend on the mere difference of the times or the places at which they occur, but only on differences in the nature, configuration, or motion of

the bodies concerned.

It follows that if a certain event has happened under a certain definite set of conditions, then if at any time exactly the same conditions again arise, a similar event must necessarily follow.

The belief in the truth of this maxim is at the foundation of all experiments, for an experiment is simply the artificial arrangement of certain causes, so that we may determine how, when one or more of the causes is inoperative, the event differs from that observed when all the causes ordinarily present are effective. If, then, by experiment we find that certain causes are allied to certain effects, we feel sure that the same causes and the same effects will always be allied; while if in any experiment the effect observed varies when we keep constant all the causes that, as far as we know, are operative, then we may at once assume that there is some other cause besides those we have taken into account which is varying and causing the variation in the effects; and it is by investigating such causes that our knowledge of nature is gradually extended.

CHAPTER II

PHYSICAL QUANTITIES AND MEASUREMENTS

5. Physical Magnitudes.—Although in some cases we may not be able to measure it with any great accuracy, every physical quantity has a certain definite magnitude. Whatever the nature of the physical quantity may be, we employ to measure its magnitude a certain fixed amount of the same kind of physical quantity, which we call the unit of that particular quantity. The given quantity is then said to be equal to so many times the unit.

Thus, in order to measure the magnitude of a given length, we take as our unit some standard length, say the yard, and then find how many times this length will go into the given length. Say it goes r times, where may be a whole number or a proper or improper fraction, then the given length is said to be r yards. We see, therefore, that the complete statement of the result of a measurement of a physical quantity consists of two parts; first, a pure number, called the numeric, which states the number of times the unit is contained in the given quantity; and, second, the name of the unit which has been employed. Every statement of the magnitude of a physical quantity must consist of these two parts, or it will be ambiguous. Thus if we were to say that a certain length was three, it would be uncertain whether we meant three inches. or three feet, or three miles, &c.

6. Units. Since the magnitude of every physical quantity has to be measured in terms of a unit of its own kind, it follows that there will be as many units as there are different kinds of physical quantities to be measured.

As great inconvenience would be caused if different people used in their measurements different units, the magnitude of the unit has in most cases, either by usage or by law, been agreed upon. Such a unit is generally called a standard unit.

7. Fundamental and Derived Units.-The magnitude of the unit chosen in every case may, if we like, be quite arbitrary, and in fact until a comparatively recent time this was so. The advances of physical science have, however, shown that there are certain relations which exist between different kinds of physical magnitudes, and that by selecting the units in a certain number of cases it is possible, by making use of these relations, to fix the magnitude of the units for the rest of the

physical quantities. The units which are thus chosen as the basis for our system of units are called fundamental units, while those units, for the determination of the magnitude of which we make use of the relations which exist between the physical quantity in question and the fundamental units, are called derived units.

The physical quantities which are most commonly employed as fundamental units are those of length, mass, and time, although energy or force is sometimes employed as a fundamental unit in place of mass. In either case it is found that, with a few exceptions which are probably caused by our ignorance of the true nature of the phenomena considered, and which will be referred to later, it is possible to fix the magnitude of the unit to be employed in the case of all other physical quantities when we have fixed the value of these three fundamental units.

As examples of fundamental units we may take the yard, which is one of the British standard units of length, or the second, which is the unit of time. The gallon and pint, which are used as units of volume, have no connection with the unit of length. If, however, we take as our unit the volume of a cube, of which each edge is of unit length, then there is a direct connection between the unit of volume, which is in this case a derived unit, and the unit of length, a fundamental unit. Again, the velocity with which light traverses interstellar space is sometimes taken as the unit of velocity; this unit has no direct connection with the units of length and time. If the unit velocity, however, is defined as such that a body travelling with this velocity passes over the unit of length in the unit of time, then we have a direct connection between these three units, so that being given the magnitude of the two fundamental units of time and of length, we can at once say what is the unit of velocity.

8. Absolute Systems of Units.-A system of units in which certain units are chosen as fundamental, and all the others are derived units connected with these by fixed physical relations, is called an absolute system; measurements made in terms of these units being said to be in absolute units. The word absolute is sometimes used in a slightly different sense, i.e. as an antithesis to relative. For example, if a velocity is measured by comparing it with some known velocity, we are said to make a relative measurement. If, however, the velocity is measured by determining the length passed over by the body in the unit of time-i.e. if the quantities we actually measure are the fundamental quantities, length and timewe are said to make an absolute measurement. It must be carefully borne in mind that the word absolute has here no reference whatever to the accuracy or inaccuracy of the observations.

The term "absolute system of units" was first introduced by Gauss in 1832, in connection with his measurements of the strength of the earth's magnetic field at Göttingen. Instead of measuring, as had been done up to that date, this quantity in terms of the strength of the earth's field at some fixed place (such as London) taken as the unit, Gauss expressed

it in terms of the units of length, mass, and time, and thus the value of the unit did not change as the strength of the earth's field changed at the standard place, as was the case before.

There are several absolute systems of units possible according (1) to what we take as the fundamental units, (2) to the magnitude we adopt for the fundamental units chosen, (3) to the physical relation we employ for obtaining the derived units from the fundamental units. Thus we may take as our fundamental units those of length, mass, and time, or of length, force, and time, or of length, energy, and time, or length, mass, and force, &c. &c. Again, we may take as our unit of length the yard, the inch, the mile, or the metre. Finally, we might define the unit of volume as the volume of a cube, each edge of which is of unit length, or as the volume of the sphere whose radius is of unit length.

With the exception of the electrical units, it is with reference to the first two of these three possible modes of variation that all practical absolute systems differ amongst, themselves. By far the most usual system in all physical investigations is that in which the fundamental units are those of length, mass, and time, and in which the unit of length is the centimetre, the unit of mass the gram, and the unit of time the second. This system is referred to as the c.g.s. (centimetre, gram, second) system. This is the system that will be almost exclusively used in this volume, though occasionally, where there are other units in common use, they will be referred to, in order to familiarise the reader with the actual magnitude of the c.g.s. units.

An absolute system, which till quite lately was employed in all English Observatories, and is in fact still employed in some, is that in which the unit of length is the foot, the unit of mass the grain, and the unit of time the second. Again, the foot, the pound, and the second are sometimes (chiefly, let it be said, in text-books on mechanics, and in examination papers) used as the fundamental units.

A more important system of absolute units is that in which the fundamental units are those of length, force, and time, for this system, which will be referred to later as the gravitational system, is almost exclusively used by engineers (at any rate in this country).

Finally, there is the system proposed by Ostwald, in which the fundamental units are those of length, energy, and time.

9. Dimensions of Derived Units. - The relation by means of which we derive the magnitude of the unit of any quantity, in terms of the fundamental units, is indicated by what is called the dimensions of the unit in question. The easiest way to see how this is done will be to con sider some simple examples.

As has been stated in § 5, the record of any quantity, say a length. must consist of two parts, a pure number and a term giving the name of the unit employed. Thus we may indicate any length by the symbol [L], where represents the numerical part of the expression, ¿.e. the