CHAPTER II.

MEASUREMENTS IN ELECTRICITY.

We have said that the subject of electricity has made its great strides during the past fifty years by the intelligent application of the doctrine of the conservation of energy to it, and by the measurements of the heat equivalents of various forms of motion. In a popular treatise it is difficult to present the more or less dry details of exact measurements. I wish here merely to emphasize the fact that the mysterious force of gravitation—perhaps more mysterious in its manifestation than any electrical or magnetic force is used to measure all our electrical manifestations.

It has been suggested, it is true, that the time of vibration of a hydrogen molecule at a definite temperature and pressure would be an unalterable standard of time, and that the wave length in vacuum of sodium light would form a standard of length independent of any change in the force of gravitation and in the dimensions of the earth. Maxwell remarks in regard to this last suggestion that "it should be adopted by those who expect their writings to be more permanent than that body."

We have what is called an absolute system of electrical measurements-absolute in the sense that everything is referred to acceleration of a body falling to the

earth at a definite place through a certain space in a definite time. Absolute also in the sense that we do not deal with merely ratios.

We measure the efficiency of a dynamo which is producing the currents of electricity which are used in lighting our houses and propelling our cars by means of the mechanical equivalent of heat, which states that the work done in raising one pound of water one degree in temperature on the Fahrenheit scale is equivalent to raising 772 pounds one foot high against the attraction of gravitation. Our ultimate appeal, therefore, on the subject of the transformation of energy upon which we are entering is to gravitation, and it will be interesting at the opening stage of our study of electro-magnetism to consider gravitation as our measurer of electrical energy.

In general terms, we measure the quantity of electricity which is delivered along a wire by the current which is flowing multiplied by the time during which it flows. Now, the time is measured by a pendulum which depends for its action upon the force of gravitation. Our standard for the measure of time depends upon the pendulum, and this in turn upon the time of rotation of the earth. It is true that we may depend upon a tuning fork for the estimation of very short intervals of time, but the fork in turn is standardized by a second pendulum.

By means of measurements based upon the law of gravitation scientific men use constantly the only known universal language-that of absolute measurements. When an English-speaking physicist expresses the results of his measurements in centimetres, in grammes, and in seconds, he knows that he will be understood by a German, a Russian, a Frenchman, or an Italian; and

it can be said that no other realm of human endeavour has such a universal language. It is curious to note the disposition of the human mind to dwell upon the mysteries of electricity and magnetism, and to totally ignore the greater mystery of gravitation. We are beginning to have an inkling of the relations of electricity and magnetism to light and heat and to motion. Every day fresh evidences of the laws of the transformations of energy increases our knowledge upon electricity, but we are absolutely ignorant of the relationship of gravitation to the subject of electricity and magnetism, light, heat, and motion. Gravitating force, by means of which we measure electricity, is perhaps the greatest mystery in the subject of physical science, and its manifestation is so omnipresent, so silent and unsensational, that our mind rarely dwells upon its mysterious action.

The work we have to do to overcome the force of gravitation is our measure of it. When large masses are lifted against this force we become sensible of its potency. Yet the force of attraction between two small bodies, such as two cannon balls, is extremely difficult to detect and to measure. The direct determination of the attraction between two masses by means of the common balance is the simplest way of obtaining a realizing sense of the magnitude of this force. Prof. Poynting, by many refinements, has made it also one of accuracy. The method he at first adopted was to suspend a mass from one arm of a balance by a long wire and counterpoise it in the other pan; then by bringing under it a known mass, its weight would be slightly increased by the attraction of this mass. Prof. Poynting showed that this increase in weight would be the quantity sought if the attracting mass had no appreciable effect before its introduction beneath the hanging mass, and if, when

beneath it, the effect on the balance could be neglected. It was found that a mass of 453 grammes of lead hung on one arm of a chemical balance by a wire, and attracted by a mass of 154 kilogrammes of lead, showed an apparent increase of about 0.01 milligramme. We perceive from this how small the force is which is to be measured, and in order to determine it with accuracy Prof. Poynting adopted a differential method, which consisted in suspending an attracting mass from each arm of a balance instead of from one arm, and bringing another attracting mass first under one suspended mass and then under the other. By this differential method certain errors were eliminated. It was found that there was a tilting of the floor of the room in which the balance was placed,

B

which had to be allowed for in the discussion of the results. One of the details of Prof. Poynting's investigation illustrates a refinement of modern science due to Lord Kelvin. Since the attracting force is so small, it is evident that the movements of the long pointer of the ordinary balance which indicates the difference in weight in the balance pans would be too small to observe. To make these small movements perceptible and also measurable, a small arm or bracket, B, was fixed to the pointer of the balance. One end of a spider thread or quartz fibre by which the mirror was suspended was attached to this bracket, and the other end to a fixed support, S, independent of the balance. The angle through which the mirror, M, turns for a given motion of the

M

FIG. 1.

pointer is inversely as the distance between it and the fixed point, "so that by diminishing this distance the sensibility of the arrangement may be almost indefinitely increased." In Prof. Poynting's experiments,

taking 4 millimetres as the distance between the threads and supposing the bracket to be 600 millimetres below the knife edge of the balance, the mirror turns through an angle 150 times as great as that through which the beam turns. The observation of the angular movement of the mirror was observed by a telescope placed at a distance. The movement of the mirror, it is evident, sweeps a beam of light through space. A movement of of an inch could thus be detected in the motion of the attracting masses. An idea of the amount of the attraction between small bodies can also be gained from a recent investigation of Prof. C. V. Boys, who finds that the force with which two spheres weighing a gramme each (about centres 1 centimetre (about one another is nearly 10000000 of a dyne,* and that the mean density of the earth is 5·5270 times that of water.

of a pound) with their of an inch) apart attract

Although the force of attraction between bodies of small magnitude requires for its detection apparatus of extreme delicacy, yet when one of the attracting bodies is large, like the earth, the force of attraction between it and even minute bodies becomes appreciable to our senses. Take, for instance, the effect of gravitation in regulating, so to speak, the transformations of energy in our atmosphere. When water is heated, the warm water, being less dense and therefore having less

* A dyne is the force which, acting upon a gramme for a second, generates a velocity of a centimetre per second. The force of gravity acting upon a gramme generates a velocity of 981 centimetres per second.