of this rotation that the preservation of our standards of time depends.

Necessity for a Common Scale.

20. The existence of quantitative correlations between the various forms of energy, imposes upon men of science the duty of bringing all kinds of physical quantity to one common scale of comparison. Several such measures (called absolute measures) have been published in recent years; and a comparison of them brings very prominently into notice the great diversity at present existing in the selection of particular units of length, mass, and time.

Sometimes the units employed have been the foot, the grain, and the second; sometimes the millimetre, milligramme, and second; sometimes the centimetre, gramme, and second; sometimes the centimetre, gramme, and minute; sometimes the metre, tonne, and second; sometimes the metre, gramme, and second; while sometimes a mixture of units has been employed; the area of a plate, for example, being expressed in square metres, and its thickness in millimetres.

A diversity of scales may be tolerable, though undesirable, in the specification of such simple matters as length, area, volume, and mass when occurring singly; for the reduction of these from one scale to another is generally understood. But when the quantities specified involve a reference to more than one of the fundamental units, and especially when their dimensions in terms of these units are not obvious, but require careful working out, there is great increase of difficulty and of liability to mistake.

A general agreement as to the particular units of length, mass, and time which shall be employed-if not in all scientific work, at least in all work involving complicated references to units-is urgently needed; and almost any one of the selections above instanced would be better than the present option.

21. We shall adopt the recommendation of the Units Committee of the British Association (see Appendix), that all specifications be referred to the Centimetre, the Gramme, and the Second. The system of units derived from these as the fundamental units is called the C.G.S. system; and the units of the system are called the C.G.S. units.

The reason for selecting the centimetre and gramme, rather than the metre and gramme, is that, since a gramme of water has a volume of approximately 1 cubic centimetre, the former selection makes the density of water unity; whereas the latter selection would make it a million, and the density of a substance would be a million times its specific gravity, instead of being identical with its specific gravity as in the C.G.S. system.

Even those who may have a preference for some other units will nevertheless admit the advantage of having a variety of results, from various branches of physics, reduced from their original multiplicity and presented in one common scale.

22. The adoption of one common scale for all quantities involves the frequent use of very large and very small numbers. Such numbers are most conveniently written by expressing them as the product of two factors,

one of which is a power of 10; and it is usually advantageous to effect the resolution in such a way that the exponent of the power of 10 shall be the characteristic of the logarithm of the number. Thus 3240000000 will be written 324 × 109, and '00000324 will be written 3'24 × 10-6.

21

CHAPTER III.

MECHANICAL UNITS.

Value of g.

23. ACCELERATION is defined as the rate of increase of velocity per unit of time. The C.G.S. unit of acceleration is the acceleration of a body whose velocity increases in every second by the C.G.S. unit of velocity—namely, by a centimetre per second. The apparent acceleration of a body falling freely under the action of gravity in vacuo is denoted by g. The value of g in C.G.S. units at any part of the earth's surface is approximately given by the following formula,

8 = 980·6056 – 2·5028 cos 2λ — '000003,

A denoting the latitude, and the height of the station (in centimetres) above sea-level.

The constants in this formula have been deduced from numerous pendulum experiments in different localities, the length of the seconds' pendulum being connected with the value of g by the formula g = π2l.

Dividing the above equation by 2 we have, for the length of the seconds' pendulum, in centimetres,

7=99*3562-2536 cos 2 – 00000034.

At sea-level these formulæ give the following values for

I

(in the case of both g and 7) is about of the mean

value.

196

Force.

24. The C.G.S. unit of force is called the dyne. It is the force which, acting upon a gramme for a second, generates a velocity of a centimetre per second.

It may otherwise be defined as the force which, acting upon a gramme, produces the C.G.S. unit of acceleration, or as the force which, acting upon any mass for 1 second, produces the C.G.S. unit of momentum.

To show the equivalence of these three definitions, let m denote mass in grammes, v velocity in centimetres per second, t time in seconds, F force in dynes.

Then, by the second law of motion, we have