Periodic law

“ Now natural science has long been accustomed to deal with periodicities observed in nature, to seize them with the vice of mathematical analysis, to submit them to the rasp of experiment. And these instruments of scientific thought would surely, long since, have mastered the problem connected with the chemical elements, were it not for a new feature which was brought to light by the periodic law, and which gave a peculiar and original character to the periodic function. ”

“ This method of illustrating the periodic law in the behaviour of elements, whether or not still a hypothesis in Chemistry, is a law in Occult Sciences. Every well-read Occultist knows that the seventh and fourth members—whether in a septenary chain of worlds, the septenary hierarchy of angels, or in the constitution of man, animal, plant, or mineral atom—that the seventh and fourth members, we say, in the geometrically and mathematically uniform workings of the immutable laws of Nature, always play a distinct and specific part in the septenary system. ”

“ While connecting by new bonds the theory of the chemical elements with Dalton's theory of multiple proportions, or atomic structure of bodies, the periodic law opened for natural philosophy a new and wide field for speculation. ”

“ This empirical generalization has exercised a wide influence on the development of chemistry, and the periodic law has been considered by many to indicate that all the atoms are composed of some elementary substance or protyle. It is only within the last few years that our knowledge of atoms has reached a stage to offer a reasonable explanation of this remarkable periodicity. ”

“ What now is the present position of the philosophy of matter from the light thrown upon it by the Periodic Law? In the first place, drawing our deduction from the marvelously accurate determinations of. the relative weights of the atoms of the different elements, to which chemists have been incited by the Periodic Law, it may be considered as absolutely settled that the elements are not groups of hydrogen atoms, nor are they composed of half or quarter hydrogen atoms. ”

“ Meantime the present situation will strengthen the feeling, by no means new, that, while the periodic law is a grand generalization containing much that is true, it is certainly not a complete or final expression of the relations which exist between the properties of the elements and their atomic weights, but rather a first approximation to the law which may ultimately be formulated. ”

“ Although a rigid application of the principles of the periodic law is not possible, yet its discovery and elaboration mark one of the great forward steps of chemical philosophy.
If we regard any material system by itself, i.e., independently of any other system or influence by which it may be surrounded, we recognize it as consisting of essentially two things,—matter and energy. A precise definition of either matter or energy is difficult, if not impossible ”

“ Before the periodic law was formulated the atomic weights of the elements were purely empirical numbers, so that the magnitude of the equivalent, and the atomicity, or the value in substitution possessed by an atom, could only be tested by critically examining the methods of determination, but never directly by considering the numerical values themselves ”

“ Under the periodic law they are difficult to classify; they seem to belong nowhere; they simply exist, unsocial, alone. Only by their density, their spectra, and some physical properties can these intractable new forms of matter be identified. ”

“ ⁠By these considerations, however, Kepler was led to enunciate his third law, that the squares of the periodic times of planets are proportional to the cubes of their mean distances from the sun.—Kepler, Prodromus Dissertationum Mathematicarum continens Mysterium Cosmographicum, etc. ”

“ Just as the period occupies a certain finite time, so the process occupies a certain finite space; and in the case of a light-wave travelling outward from a source of light, the finite space occupied by the process grows larger as it travels away from the source. For the purposes of stating the quantum principle, one period of a periodic process has to be treated as an indivisible whole. ”

“ Every periodic process arranges itself so as to have [Pg 140] achieved a certain amount by the time one period is completed. This seems to show that nature has a kind of foresight, and also knows the integral calculus, without which it is impossible to know how fast to go at each instant so as to achieve a certain result in the end. ”

“ All mechanical laws exhibit acceleration as a function of configuration, not of configuration and time jointly; and this principle of the irrelevance of the time may be extended to all scientific laws. In fact we might interpret the "uniformity of nature" as meaning just this, that no scientific law involves the time as an argument, unless, of course, it is given in an integrated form, in which case lapse of time, though not absolute time, may appear in our formulas. ”

“ It is only successful in the few cases where the general nature of a group appears without much trouble. The second method is to assume that the observations must run in series which are repeated after definite intervals of time. These intervals of time are in reality obtained from the general physical principle that if any force is periodic, that is, if its fluctuations are repeated after a definite period of time, then certain of its effects are also repeated after a definite period of time, which is the same as that of the force. ”

“ For instance, if in mechanics and astronomy we had selected at random some arbitrary definition of time, if we had defined as congruent the intervals separating the rising and setting of the sun at all seasons of the year, say for the latitude of New York, our understanding of mechanical phenomena would have been beset with grave difficulties. As measured by these new temporal standards, free bodies would no longer move with constant speeds, but would be subjected to periodic accelerations for which it would appear impossible to ascribe any definite cause, and so on. ”

“ We shall seldom find a body subject to a single periodic variation, and free from other disturbances. We may expect the periodic variation itself to undergo variation, which may possibly be secular, but is more likely to prove periodic ”

“ The recent experiments which indicate a change in the mass of an electron with the speed, together with the phenomenon of radioactivity, have in some minds created a doubt as to the exact validity of some of the most general laws of nature. In the following pages I shall attempt to show that we may construct a simple system of mechanics which is consistent with all known experimental facts, and which rests upon the assumption of the truth of the three great conservation laws, namely, the law of conservation of energy, the law of conservation of mass, and the law of conservation of momentum. ”

“ The power of attraction which, according to the theory of gravity, each body possesses, is in proportion to the quantity of matter contained in that body. But the periodic time in which one body, at a given distance, revolves round another that attracts it, is shorter in proportion as this power is greater, and consequently as the quantity of matter in the attracting body. If the densities of Jupiter and Saturn were the same with that of the Earth, the periodic times of their several Satellites would be shorter than by observation they are found to be. ”

“ It thus appears that if a single valued monogenic function of z be periodic, either all its periods are real multiples of one of them, and then all are of the form MΩ, where Ω is a period and M is an integer, or else, if the function have two periods whose ratio is not real, then all its periods are expressible in the form NΩ + N′Ω′, where Ω, Ω′ are periods, and N, N′ are integers. ”

“ But in ordinary periodic functions one variable varies continuously, whilst the other increases to a limit, then a period of decrease begins, and having in turn reached its limit a period of increase again begins. ”

“ Now the theory of heat places us in the dilemma either of745 believing in Creation at an assignable date in the past, or else of supposing that some inexplicable change in the working of natural laws then took place. Physical science gives no countenance to the notion of infinite duration of matter in one continuous course of existence. And if in time past there has been a discontinuity of law, why may there not be a similar event awaiting the world in the future? Infinite ingenuity could have implanted some agency in matter so that it might never yet have made its tremendous powers manifest. ”

“ The structures thus produced have functions which are also analogous to those of living beings, a double current of diffusion, an evolutionary existence, and a latent vitality when desiccated or congealed.
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CHAPTER VI PERIODICITY
Periodic Precipitation.—A phenomenon is said to be periodic when it varies in time and space and is identically reproduced at equal intervals. We are surrounded on all sides by periodic phenomena; summer and winter, day and night, sleep and waking, rhythm and rhyme, flux and reflux, the movements of respiration and the beating of the heart, all are periodic. ”

“ This may be made more definite, if we express the second law in a mathematical form, as may be done by saying that in any reversible cyclic process which a body may undergo
where is an elementary portion of the heat imparted to the body, and the absolute temperature of the body, or the portion of it which receives the heat. Or, without limitation to cyclic processes, we may say that for any reversible infinitesimal change, where denotes a certain function of the state of the body, called by Clausius the entropy. ”

“ They resemble each other more than they do any one irreversible process. This is evident from an examination of the differential equations which control them; the differential with respect to time is always of an even order, because the essential sign of time can be reversed. ”

“ An atom is a clock, because the electrons go round the nucleus a certain number of times in a second; its properties as a clock are exhibited to us in its spectrum, which is due to light waves of various frequencies. The world is full of periodic occurrences, and fundamental mechanisms, such as atoms, show an extraordinary similarity in different parts of the universe. Any one of these periodic occurrences may be used for measuring time; the only advantage of humanly manufactured clocks is that they are specially easy to observe. ”

“ We may define a periodic phenomenon as one which, with the uniform change of the variable, returns448 time after time to the same value. If we strike a pendulum it presently returns to the point from which we disturbed it, and while time, the variable, progresses uniformly, it goes on making excursions and returning, until stopped by the dissipation of its energy. If one body in space approaches by gravity towards another, they will revolve round each other in elliptic orbits, and return for an indefinite number of times to the same relative positions. ”

“ In each of our half-century cycles we have seen that there are five maxima and five minima of sun-spots, whose periodic times average for the first cycle a little more than eleven and a half years, and for the last cycle a little less. We may reasonably conclude that the next half-century will witness no material change, but that the like phenomena will continue, with a mean period of about eleven years; also, that the temperature and the rainfall will continue to exhibit their dependent phenomena as before. On this basis let us construct our diagram for the coming years. ”

“ A knowledge of its variability is, therefore, of essential importance in studying the condition and behaviour of a system, and it is the great merit of the Phase Rule that the state of a system is defined entirely by the relation existing between the number of the components and the phases present, no account being taken of the molecular complexity of the participating substances, nor any assumption made with regard to the constitution of matter. It is, further, as we see, quite immaterial whether we are dealing with "physical" or "chemical" equilibrium ”

“ If the orbit of a binary system lies edgewise toward us, then one star will hide the other each revolution, moving across it and appearing on the other side. Several instances of this motion are known; the distant suns having made more than a complete circuit since discovery, the shortest periodic time known being twenty-five years. ”

“ Periodicity is, then, all into which the Tendency to Stability resolves itself for nature as we know it.
We perceive, in the actual universe, the fact of a certain imperfect periodicity. This wave form of movement in great and little plays, as Spencer has shown far more elaborately than Fechner, a large part in the universe.
But the evident fact of a present periodicity of imperfect form suggests another possible conception. We are under no necessity to regard the universe as finite either in space or time. ”

“ Similarly, when we consider the characters of the elements of the same families, their close resemblances to each other, and their minor resemblances to members of other families, the irregularities of the Periodic classification, etc., it is evident that we can coordinate these seemingly contradictory phenomena into a coherent whole on the basis of the evolution of the elements. The extraordinary relations disclosed by the Periodic classification are the outward and manifest signs of the process to which atoms, like organisms, owe their individual natures. ”