where K has the same value as before, and both n′ and n″ are integers which can pass through a series of different values. For n″ = 2, the Balmer series is given; to n″ = 1, and n′ = 2, 3 ... ∞ there corresponds a second series which lies entirely in the ultra-violet region, and to n″ = 3, n′ = 4, 5 ... ∞ a series lying entirely in the infra-red. Lines have actually been found belonging to these series.
Formulæ, similar to the Ritz one, have been set up for the line spectra of other elements, and represent pretty accurately the distribution of the lines. The frequencies are each represented by the difference between two terms, each of which contains an integer, which can pass through a series of values. But while the hydrogen formula, except for the n′s, depends only upon one constant quantity K and its terms have the simple form K/n², the formula is more complicated with the other elements. The term can often be written, with a high degree of exactness, as K/(n + α)², where K is, with considerable accuracy, the same constant as in the hydrogen formula. For a given element α can assume several different values; therefore the number of series is greater and the spectrum is even more complicated than that of hydrogen.
All these formulæ are, however, purely empirical, derived from the values of wave-lengths and frequencies found in spectrum measurements. They represent certain more or less simple bookkeeping rules, by which we can register both old and new lines, enter them in rows, arrange them according to a definite system. But from the beginning there could be no doubt that these rules had a deeper physical meaning which it was not yet possible to know. There was no visible correspondence between the spectral line formulæ and the other physical characteristics of the elements which emitted the spectra; not even in their form did the formulæ show any resemblance to formulæ obtained in other physical branches.
CHAPTER III
IONS AND ELECTRONS
Early Theories and Laws of Electricity.
The fundamental phenomena of electricity, which were first made the subject of careful study about two centuries ago, are that certain substances can be electrified by friction so that somehow they can attract light bodies, and that the charges of electricity may be either “positive” or “negative.” Bodies with like charges repel each other, while those with unlike charges attract each other, and either partially or entirely neutralize each other when they are brought close together. Moreover, it had long ago been discovered that in some substances electricity can move freely from place to place, while in others there is resistance to the movement. The former bodies are now called conductors and include metals, while the latter are called insulators, glass, porcelain and air being members of this class.
In order to explain the phenomena some imagined that there were two kinds of “electric substances” or “fluids”; and since no change in weight could be discovered in a body when it was electrified, it was, in general, assumed that the electric fluids were weightless. In the normal, neutral body it was believed that these fluids were mixed in equal quantities, thereby neutralizing each other; on this account they were supposed to be of opposite characteristics, so one was called positive and the other negative. According to a second theory, there was assumed to be just one kind of electricity, which was present in a normal amount in neutral bodies; positive electricity was caused by a superfluity of the fluid; negative, by a deficit. In both theories it was possible to talk of the amount of positive or negative electricity which a body contained or with which it was “charged,” because the supporters of the one-fluid idea understood by the terms positive and negative a superfluity and a deficit, respectively, of the one fluid. In both theories it was possible to talk about the direction of the electric current in a conductor, since the supporters of the two-fluid theory understood by “direction” that in which the electric forces sent the positive electricity, or the opposite to that in which the negative would be sent. It could not be decided whether positive electricity went in the one direction or the negative in the other, or whether each simultaneously moved in its own direction. Both theories were quite arbitrary in designating the electric charge in glass, which was rubbed with woollen cloth, as positive. On the whole, neither theory seemed to have any essential advantage over the other; the difference between them seemed to lie more in phraseology than in actual fact.
That the positive and negative states of electricity could not be taken as “symmetric” seemed, however, to follow from the so-called discharge phenomena, in which electricity, with the emission of light, streams out into the air from strongly charged (positive or negative) bodies, or passes through the air between positive and negative bodies in sparks, electric arcs or in some other way. In a discharge in air between a metal point and a metal plate, for instance, a bush-shaped glow is seen to extend from the point when the charge there is positive, while only a little star appears when the charge is negative.
Naturally, we cannot discuss here the many electric phenomena and laws, and must be satisfied with a brief description of those which are of importance in the atomic theory.
In this latter category belongs Coulomb’s Law, formulated about 1785. According to this law, the repulsions or attractions between two electrically charged bodies are directly as the product of the charges and inversely as the square of the distance between them (as in the case of the gravitational attraction between two neutral bodies, according to Newton’s Law). The unit in measuring electric charges can be taken as that amount which will repel an equal amount of electricity of the same kind at unit distance with unit force. If we use the scientific or “absolute” system, in which the unit of length is one centimetre, that of time one second and that of mass one gram, then the unit of force is one dyne, which is a little greater than the earth’s attraction on a milligram weight. Let us suppose that two small bodies with equal charges of positive (or negative) electricity are at a distance of one centimetre from each other. If they repel each other with a charge of one dyne, then the amount of electricity with which each is charged is called the absolute electrostatic unit of electricity. If one body has a charge three times as great and the other has a charge four times as great, the repulsion is 3 × 4 = 12 times greater. If the distance between the bodies is increased from one to five, the repulsion is twenty-five times as small, since 5² = 25. If the charge of one body is substituted by a negative one of same magnitude the repulsion becomes an attraction of the same magnitude.