Heat. The unit of heat, the calorie, is the amount of heat required to warm one gramme mass of water from 0° to 1° (C.); and the dynamical equivalent of this amount of heat is 42 million ergs, which is the value of Joule's equivalent, as expressed in C.G.S. measure (see also Art. 439). These units are sometimes called "absolute" units; the term absolute, introduced by Gauss, meaning that they are independent of the size of any particular instrument, or of the value of gravity at any particular place, or of any other arbitrary quantities than the three standards of length, mass, and time. It is, however, preferable to refer to them by the more appropriate name of "C.G.S. units," as being derived from the centimetre, the gramme, and the second. 282. Electrical Units. - There are two systems of electrical units derived from the fundamental "C.G.S." units, one set being based upon the force exerted between two quantities of electricity, and the other upon the force exerted between two magnet poles. The former set are termed electrostatic units, the latter electro-magnetic units. The important relation between the two sets is explained in Art. 359. 283. Electrostatic Units. No special names have been assigned to the electrostatic units of Quantity, Potential, Capacity, etc. The reasons for adopting the following values as units are given either in Chapter I. or in the present chapter. Unit of Quantity. - The unit of quantity is that quantity of electricity which, when placed at a distance of one centimetre (in air) from a similar and equal quantity, repels it with a force of one dyne (Art. 262). Potential. Potential being measured by work done in moving a unit of + electricity against the electric forces, the unit of potential will be measured by the unit of work, the erg. Unit Difference of Potential.-Unit difference of potential Unit of Capacity. - That conductor possesses unit capacity is, in the absence of any knowledge of its absolute value, taken as unity. Electromotive Intensity is the electric force or intensity of an electric field at any point, and is measured by the force which it exerts on a unit charge placed at that point. It may be convenient here to append the rules for reducing to their corresponding values in terms of the practical (electro-magnetic) units values that may have been. expressed in terms of the electrostatic units, as follows: Potential. To bring to volts multiply by 300. Capacity. To bring to microfarads divide by 900,000. Quantity. To bring to coulombs divide by 3 × 109. Current. To bring to amperes divide by 3 x 109. Resistance. To bring to ohms multiply by 9 × 1011. Example. Suppose two equally charged spheres whose centres are 40 centimetres apart are found to repel one another with a force of 630 dynes (= about the weight of 10 grains). By the law of inverse squares we find that the charge on each is 1004 (electrostatic units. Dividing by 3 x 10° we find that this amounts to 0:0000003347 coulomb. 284. Dimensions of Units. It has been assumed above that a velocity can be expressed in centimetres per second; for velocity is rate of change of place, and it is clear that if change of place may be measured as a length in centimetres, the rate of change of place will be measured by the number of centimetres through which the body moves in unit of time. It is impossible, indeed, to express a velocity without regarding it as the quotient of a certain number of units of length divided by a certain number of units of time. In other words, a velocity a length = = L a time; or, adopting L as a symbol for length, and T as a symbol for time, V which is still more conveniently written V LXT-1. In a similar way acceleration being rate of change of velocity, we have A V L = LXT-2. L Now these physical quantities," velocity" and "acceleration," are respectively always quantities of the same nature, no matter whether the centimetre, or the inch, or the mile, be taken as the unit of length, or the second or any other interval be taken as the unit of time. Hence we say that these abstract equations express the dimensions of those quantities with respect to the fundamental quantities length and time. A little consideration will show the student that the dimensions of the various units mentioned above will therefore be as given in the table below. The dimensions of magnetic units are given in the Table in Art. 356, p. 348. TABLE OF DIMENSIONS OF UNITS. LESSON XXII. - Electrometers 285. In Lesson II. we described a number of electroscopes or instruments for indicating the presence and sign of a charge of electricity; some of these also served to indicate roughly the amount of these charges, but none of them save the torsion balance could be regarded as affording an accurate means of measuring either the quantity or the potential of a given charge. An instrument for measuring differences of electrostatic potential is termed an Electrometer. Such instruments can also be used to measure electric quantity indirectly, for the quantity of a charge can be ascertained by measuring the potential to which it can raise a conductor of known capacity. The earliest electrometers attempted to measure the quantities directly. Lane and Snow Harris constructed" Unit Jars" or small Leyden jars, which, in order to measure out a certain quantity of electricity, were charged and discharged a certain number of times. 286. Repulsion Electrometers. The torsion balance, described in Art. 18, measures quantities by measuring the forces exerted by the charges given to the fixed and movable balls. It can only be applied to the measurement of repelling forces, for the equilibrium is unstable in the case of a force of attraction. Beside the gold-leaf electroscope and others described in Lesson II., there exist several finer electrometers based upon the principle of repulsion, some of which resemble the torsion balance in having a movable arm turning about a central axis. Amongst these are the electrometers of Dellmann and of Peltier. In the latter a light arm of aluminium, balanced upon a point, carries also a small magnet to direct it in the magnetic meridian. A fixed arm, in metallic contact with the movable one, also lies in the magnetic meridian. A charge imparted to this instrument produces a repulsion between the fixed and movable arms, causing an angular deviation. Here, however, the force is measured not by being pitted against the torsion of an elastic fibre, or against gravitation, but against the directive magnetic force of the earth acting on the small needle. Now this depends on the intensity of the horizontal component of the earth's magnetism at the place, on the magnetic moment of the needle, and on the sine of the angle of its deviation. Hence, to obtain quantitative values for the readings of this electrometer, it is necessary to make preliminary experiments and to "calibrate" the degree-readings of the deviation. 287. Attracted - Disk Electrometers. Snow Harris was the first to construct an electrometer for measuring the attraction between an electrified and a nonelectrified disk; and the instrument he devised may be roughly described as a balance for weighing a charge of electricity. More accurately speaking, it was an instrument resembling a balance in form, carrying at one end a light scale pan; at the other a disk was hung above a fixed insulated disk, to which the charge to be measured was imparted. The chief defect of this instrument was the irregular distribution of the charge on the disk. The force exerted by an electrified point falls off inversely as the square of the distance, since the lines of force emanate in radial lines. But in the case of a uniformly electrified plane surface, the lines of force are normal to the surface, and parallel to one another; and the force is independent of the distance. The distribution over a small sphere nearly fulfils the first of these conditions. The distribution over a flat disk would nearly fulfil the latter condition, were it not for the perturbing effect of the edges of the disk where the surface-density is much greater (see Art. 38); for this reason Snow Harris's electrometer was very imperfect. Lord Kelvin introduced several very important modifications into the construction of attracted-disk electrometers, the chief of these being the employment of the "guard-plate" and the providing of means for working with a definite standard of potential. It would be beyond the scope of these lessons to give a complete |