all instruments, or arrangements of apparatus, possess the following functions:

'I. The Source of energy. The energy involved in the phenomenon we are studying is not, of course, produced from nothing, but enters the apparatus at a particular place which we may call the Source.

'2. The channels or distributors of energy, which carry it to the places where it is required to do work.

3. The restraints which prevent it from doing work when it is not required.

'4. The reservoirs in which energy is stored up when it is not required.

5. Apparatus for allowing superfluous energy to escape. '6. Regulators for equalising the rate at which work is done.

7. Indicators or movable pieces which are acted upon by the forces under investigation.

'8. Fixed scales on which the position of the indicator is read off.'

The various experiments differ in respect of the functions included under the first six headings, while those under the headings numbered 7 and 8 will be much the same for all instruments, and these are the parts with which the actual observations for measurement are made. In some experi ments, as in optical measurements, the observations are simply those of length and angles, and we do not compare forces at all, the whole of the measurements being ultimately length measurements. In others we are concerned with forces either mechanical, hydrostatic, electric or magnetic, and an experiment consists in observations of the magnitude of these forces under certain conditions; while, again, the ultimate measurements will be measurements of length and of mass. In all these experiments, then, we find a foundation in the fundamental principles of the measurement of length and of the measurements of force and mass. The knowledge of the first involves an acquaintance with

some of the elementary properties of space, and to understand the latter we must have some acquaintance with the properties of matter, the medium by which we are able to realise the existence of force and energy, and with the properties of motion, since all energy is more or less connected with the motion of matter. We cannot, then, do better than urge those who intend making physical experiments to begin by obtaining a sound knowledge of those principles of dynamics, which are included in an elementary account of the science of matter and motion. The opportunity has been laid before them by one-to whom, indeed, many other debts of gratitude are owed by the authors of this work-who was well known as being foremost in scientific book-writing, as well as a great master of the subject. For us it will be sufficient to refer to Maxwell's work on 'Matter and Motion' as the model of what an introduction to the study of physics should be.

CHAPTER II.

UNITS OF MEASUREMENT.

Method of Expressing a Physical Quantity.

In considering how to express the result of a physical experi ment undertaken with a view to measurement, two cases essentially different in character present themselves. In the first the result which we wish to express is a concrete physical quantity, and in the second it is merely the ratio of two physical quantities of the same kind, and is accordingly a number. It will be easier to fix our ideas on this point if we consider a particular example of each of these cases, instead of discussing the question in general terms. Consider, therefore, the difference in the expression of the result of two experiments, one to measure a quantity of heat and the second to measure a specific heat-the measurements

of a mass and a specific gravity might be contrasted in a perfectly similar manner-in the former the numerical value will be different for every different method employed to express quantities of heat; while in the latter the result, being a pure number, will be the same whatever plan of measuring quantities of heat may have been adopted in the course of the experiment, provided only that we have adhered throughout to the same plan, when once adopted. In the latter case, therefore, the number obtained is a complete expression of the result, while in the former the numerical value alone conveys no definite information. We can form no estimate of the magnitude of the quantity unless we know also the unit which has been employed. The complete expression, therefore, of a physical quantity as distinguished from a mere ratio consists of two parts: (1) the unit quantity employed, and (2) the numerical part expressing the number of times, whole or fractional, which the unit quantity is contained in the quantity measured. The unit is a concrete quantity of the same kind as that in the expression of which it is used.

If we represent a quantity by a symbol, that must likewise consist of two parts, one representing the numerical part and the other representing the concrete unit. A general form for the complete expression of a quantity may therefore be taken to be 9 [Q], where q represents the numerical part and [Q] the concrete unit. For instance, in representing a certain length we may say it is 5 [feet], when the numerical part of the expression is 5 and the unit [foot]. The number 9 is called the numerical measure of the quantity for the unit [Q].

Arbitrary and Absolute Units.

The method of measuring a quantity, 9 [q], is thus resolved into two parts: (1) the selection of a suitable unit [Q], and (2) the determination of q, the number of times which this unit is contained in the quantity to be measured. The second part is a matter for experimental determination, and

has been considered in the preceding chapter. We proceed to consider the first part more closely.

The selection of [Q] is, and must be, entirely arbitrarythat is, at the discretion of the particular observer who is making the measurement. It is, however, generally wished by an observer that his numerical results should be understood and capable of verification by others who have not the advantage of using his apparatus, and to secure this he must be able so to define the unit he selects that it can be reproduced in other places and at other times, or compared with the units used by other observers. This tends to the general adoption on the part of scientific men of common standards of length, mass, and time, although agreement on this point is not quite so general as could be wished. There are, however, two well-recognised standards of length': viz. (1) the British standard yard, which is the length at 62° F. between two marks on the gold plugs of a bronze bar in the Standards Office; and (2) the standard metre as kept in the French Archives, which is equivalent to 39'37079 British inches. Any observer in measuring a length adopts. the one or the other as he pleases. All graduated instruments for measuring lengths have been compared either directly or indirectly with one of these standards. If great accuracy in length measurement is required a direct comparison must be obtained between the scale used and the standard. This can be done by sending the instrument to be used to the Standards Office of the Board of Trade.

There are likewise two well-recognised standards of mass, viz. (1) the British standard pound, a certain mass of platinum kept in the Standards Office; and (2) the kilogramme des Archives, a mass of platinum kept in the French Archives, originally selected as the mass of one thousandth part of a cubic metre of pure water at 4° C. One

1 See Maxwell's Heat, chap. iv. The British Standards are now kept at the Standards Office at the Board of Trade, Westminster, in accordance with the Weights and Measures Act,' 1878.

or other of these standards, or a simple fraction or multiple of one of them, is generally selected as a unit in which to measure masses by any observer making mass measurements. The kilogramme and the pound were carefully compared by the late Professor W. H. Miller; one pound is equivalent to 453593 kilogramme.

With respect to the unit of time there is no such divergence, as the second is generally adopted as the unit of time for scientific measurement. The second is 86400 of the mean solar day, and is therefore easily reproducible as long as the mean solar day remains of its present length.

These units of length, mass, and time are perfectly arbitrary. We might in the same way, in order to measure any other physical quantity whatever, select arbitrarily a unit quantity of the same kind, and make use of it just as we select the standard pound as a unit of mass and use it. Thus to measure a force we might select a unit of force, say the force of gravity upon a particular body at a particular place, and express forces in terms of it. This is the gravitation method of measuring forces which is often adopted in practice. It is not quite so arbitrary as it might have been, for the body generally selected as being the body upon which, at Lat. 45°, gravity exerts the unit force is either the standard pound or the standard gramme, whereas some other body quite unrelated to the mass standards might have been chosen. In this respect the gallon, as a unit of measurement of volume, is a better example of arbitrariness. It contains ten pounds of water at a certain temperature.

We may mention here, as additional examples of arbitrary units, the degree as a unit of angular measurement, the thermometric degree as the unit of measurement of temperature, the calorie as a unit of quantity of heat, the standard atmosphere, or atmo, as a unit of measurement of fluid pressure, Snow Harris's unit jar for quantities of electricity, and the B.A. unit of electrical resistance