make this sufficiently clear. Angles are measured by readings of length along certain arcs; the ordinary measurement of time is the reading of an angle on a clock face or the space described by a revolving drum; force is measured by longitudinal extension of an elastic body or by weighing; pressure by reading the height of a column of fluid supported by it; differences of temperature by the lengths of a thermometer scale passed over by a mercury thread; heat by measuring a mass and a difference of temperature; luminous intensity by the distances of certain screens and sources of light; electric currents by the angular deflection of a galvanometer needle; coefficients of electro-magnetic induction also by the angular throw of a galvanometer needle.

Again, a consideration of the definitions of the various. physical quantities leads in the same direction. Each physical quantity has been defined in some way for the purpose of its measurement, and the definition is insufficient and practically useless unless it indicates the basis upon which the measurement of the quantity depends. A definition of force, for instance, is for the physicist a mere arrangement of words unless it states that a force is measured by the quantity of momentum it generates in the unit of time; and in the same way, while it may be interesting to know that 'electrical resistance of a body is the opposition it offers to the passage of an electric current,' yet we have not made much progress towards understanding the precise meaning intended to be conveyed by the words 'a resistance of 10 ohms,' until we have acknowledged that the ratio of the electromotive force between two points of a conductor to the current passing between those points is a quantity which is constant for the same conductor in the same physical state, and is called and is the resistance' of the conductor; and, further, this only conveys a definite meaning to our minds when we understand the bases of measure. ment suggested by the definitions of electromotive force and electric current.

When the quantity is once defined, we may possibly be able to choose a unit and make a direct comparison; but such a method is very seldom, if ever, adopted, and the measurements really made in any experiment are often suggested by the definitions of the quantities measured.

The following table gives some instances of indirect methods of measurement suggested by the definitions of the quantities to be measured. The student may consult the descriptions of the actual processes of measurement detailed in subsequent chapters :

Name of quantity measured

ELECTRICITY.

Electric current

Quantity of Electricity

Electromotive force

Resistance

Electro-chemical equivalent.

Measurements actually made

Quantity of magnetism, force, and length (§ 71).

Current and time (§ 72).

Quantity of electricity and work ($ 74).

Electric current and E. M. F. (§ 75). Mass and quantity of electricity ($ 72).

The quantities given in the second column of the table are often such as are not measured directly, but the basis of measurement has, in each case, already been given higher up in the table. If the measurement of any quantity be reduced to its ultimate form it will be found to consist always in measurements of length or mass. The measurement of time by counting 'ticks' may seem at first sight an exception to this statement, but further consideration will shew that it, also, depends ultimately upon length measurement.

As far as the apparatus for making the actual observations is concerned, many experiments, belonging to different subjects, often bear a striking similarity. The observing apparatus used in a determination of a coefficient of torsion, the earth's horizontal magnetic intensity, and a coefficient of electro-magnetic induction, are practically identical in each case, namely, a heavy swinging needle and a telescope and scale; the difference between the experiments consists in the difference in the origin of the forces which set the moving needle in motion. Many similar instances might be quoted. Maxwell, in the work already referred to ('Scientific Apparatus,' p. 15), has laid down the grounds on which this analogy between the experiments. in different branches of the subject is based. All the physical sciences relate to the passage of energy under its various forms from one body' to another,' and, accordingly,

The measurement of mass may frequently be resolved into that of length. The method of double weighing, however, is a fundamental measurement sui generis.

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

'1. 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 experiments, 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 experiment 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