Popular Science Monthly/Volume 11/October 1877/Molecular Magnitudes
By L. R. CURTISS.
IN entering upon an analysis of the subject of atomic and molecular magnitudes, it is desirable that we should have as clear an idea of the immeasurably small in Nature as possible. To the astronomer the size and relative distances of the celestial bodies are real magnitudes, and so also, to the molecular physicist, the magnitudes verging upon the infinitely small are just as much of a reality. The billionth part of an inch is just as much of a fact as a billion miles.
The mathematical definition of a point consists in stating it as a locality without length, breadth, or thickness; but we receive no very concise idea of the definition until we proceed graphically, and make a dot with a pencil or otherwise, which shall possess limited dimensions of length and breadth; then, by the metaphysical process of abstraction, we dispense with the linear dimensions of length and breadth, and thus purify our conceptions concerning physical magnitudes, and place ourselves in a way of realizing the entity or real existence of the invisibly small in Nature.
In the animal kingdom are found myriads of forms so minute that their bulk is reckoned by less than the millionth part of a cubic inch, yet each one is endowed with organs of sense or assimilation sufficient to serve the purpose in their sphere of life. The vegetable kingdom, also, offers abundant specimens of microscopic forms, calculated to excite our admiration by the beauty and minuteness of their organisms. Such is notably the case in several forms of Diatomaceæ. The striated markings of Pleurosigma fasciola aggregate to 64,000 to the inch, while Amphipleura pellucida often exhibit striæ exceeding 100,000 to the lineal inch. And yet the skeletons of these minute organisms are composed mainly of silex, the silex again being made up of silicon and oxygen. Notwithstanding the almost infinitesimal magnitudes of the organic world, human skill is able to compete in the matter of minuteness. Platinum wire has been drawn so fine as to rival in minuteness the smallest fibre of the spider's web. Gold has been deposited upon the surface of other metals, and drawn to such extreme thinness that a thousand-millionth part of a grain exhibited the visible characteristics of the metal. The oscillations of the horizontal pendulum can be measured to the 80000000 inch, by the aid of a small mirror, a beam of light, and a graduated scale for reading the vibrations. Nobert, with a mechanical skill unsurpassed, has repeatedly ruled with a diamond-point upon glass the nineteenth band of his test-plate, consisting of lines less than the 112000 apart, and it is claimed that he has succeeded in ruling plates covering 224,000 lines per inch, such as would aggregate in superficial areas to over 50,000,000,000 to the square inch! Such minute divisions are wholly beyond the resolving power of the most elaborate of modern microscopic appliances; for it has been shown by Sorby that the ultimate power of the microscope for distinct definition is limited to the examination of magnitudes not less than one-half of the average wave-length of the luminous spectrum; and it is shown, upon the authority of Helmholtz, that when the amplitude of the object is less than this half wave-length—or somewhat in excess of 80,000 to the inch—the dark interference-fringes impair the definition of the instrument, except in the case of striated markings, which may be clearly defined, or resolved, by so arranging the illumination as to mask the fringes, and bring out a good definition even in excess of 100,000 to the inch. Hence, the main difficulty attending the possible amplification of objects less than about the 100000 of an inch in diameter is a purely physical one, and depends upon the constitution of light itself.
The various phenomena of chemical physics teach us that matter is not homogeneous, but is made up of infinitesimal particles or atoms, the term atom meaning indivisible particle; and that the term molecule—meaning literally a little mass—refers to an aggregation of two or more atoms. Thus, a crystal of common salt may be pulverized until one of its fragments is barely discernible to the highest range of microscopic power, and still this fragment will retain all the characteristics of salt. This same microscopic portion is susceptible of a further subdivision by solution in water, when the spectroscope will detect its presence in the still minuter quantity of the one-hundred-millionth part of a grain. Here, in the case of salt, physical analysis ends, and, aside from chemical analysis, any further subdivision must be by the process of abstraction, until by its means we arrive at the mental conception of a portion so minute as to consist of an atom of sodium united by the bonds of chemical affinity to an atom of chlorine. This is now a molecule of common salt. Any further division destroys the entity of the compound, and results in the decomposition of the salt into the atoms of its elements. Hence a simple molecule is the smallest portion of any chemical compound that is not susceptible of subdivision without destroying its entity, or, in other words, the smallest number of atoms that can cohere to form a compound constitute the molecule of that compound. An atom is designated as the ultimate particle of any elementary body, and is not susceptible of any further division within the range of human analysis.
Were it possible to magnify the atoms of matter to a diameter available for distinct vision, we should be met at the outset by a difficulty too astounding for realization. It is a matter of easy proof that the magnifying of any object while in motion will exhibit that motion increased in velocity just as many times as the diameter of the object is augmented. Suppose we had at our command an instrument competent to amplify the atoms to the one-fiftieth of an inch in diameter: in the case of the hydrogen-atom the necessary magnifying power would be 10,000,000 diameters, under which power the atoms would have their motions enhanced by the same multiple, and we should then be called upon to examine an image the fiftieth part of an inch in diameter plunging across the field of vision five hundred million times faster than the flight of a cannon-ball.
It follows, since human skill is incompetent to penetrate by any mechanical means into the internal structure of matter, that we shall be compelled to direct our labors to other modes of investigation if we would know more of the atomic structure of matter, possessing as it does a minuteness far surpassing the analytical power of the microscope; in fact, so hopelessly ultra-microscopic as to elude all other processes except that of mathematics and experimental investigation.
The question of the infinitely large and the immeasurably small has engaged the attention of philosophers since the days of Democritus. Modern investigators are, however, in possession of experimental data that aid them in arriving at facts with ever-increasing accuracy. We have the atomic theory first placed upon a substantial basis by Dalton, which treats of the atomic constituents of matter, and gives to each atom a definite size and weight, and establishes the proposition that atoms combine to form molecules, and that molecules aggregate to masses. We have also the kinetic theory of gases, which has been placed upon a purely mathematico-scientific footing, as has also the department of hydro-kinetics; and experiments within these departments are accumulating evidence concerning the atomic and physical structure of matter.
The kinetic theories are based upon the conception that these particles or atoms are in constant motion among themselves; and it assumes, also, that their movements have an infinite series of velocities in all conceivable directions, but with varying degrees of intensity. This idea of atomic and molecular motion puts us in possession of an important factor for determining the causation of all physical phenomena. Of course we do not presume to say that the atom is the primordial or ultimate constituent of matter, for there are many evidences to show that the present list of sixty-five elements of matter may not be elementary at all, but isomeric compounds of one or more simpler constituents.
The question might here be asked, "How does the physicist know anything of the relative size of atoms and their vibratory motions?" The answer is: by mathematical deductions, based upon the behavior of gases; by experimental evidence, principally in the domain of radiant heat; also in the interdiffusion of liquids and gases. Researches in these departments have determined, with a great deal of certainty, that the atoms and molecules of matter do not touch each other, and that the various velocities they may assume under different conditions are the causes of all the phenomena of light and heat. And, moreover, it has been determined by the most refined experiments, with special instruments of precision, that these atoms have a definite size and weight, and, under special conditions, a definite velocity and momentum. The pressure of gases has also been defined as the resultant of the molecular bombardment or impact of these flying projectiles against the sides of the containing vessel.
Some molecular data have been tabulated from the calculations of Clausius, Maxwell, Thomson, and others, but the figures given are wholly beyond human comprehension. Thus the number of atoms in one cubic inch of hydrogen-gas, at the temperature of freezing water and under the pressure of one atmosphere, is given in the neighborhood of three hundred millions of millions of millions, each atom possessing an initial velocity of over a mile per second, covering nearly eighteen billions of oscillations in different directions in the same second of time. That is to say, each particle of hydrogen, while moving at the rate of seventy miles per minute, has its course wholly changed something like 17,700,000,000 times in every second. Sir William Thomson concludes, from the data given by Clausius, that the diameter of the gaseous molecule is somewhere between the 250000000 and the 500000000 inch, and as the density of known liquids and solids is from 500 to 16,000 times that of common air, he concludes that the distance from centre to centre of contiguous molecules in solids is less than the 250000000 and greater than the 500000000 of an inch; and he illustrates by supposing "a drop of water to be magnified up to the size of the earth, each molecule to be amplified in the same proportion, these molecules will then be less in size than cricket-balls, but larger than small lead-shot."
Imagine the particles of the air we breathe flying about at the rate of eighteen miles per minute—a velocity exceeding that of a cannonball—a velocity which, if the particles were all moving in one direction, would constitute a tornado ten times more violent than any terrestrial hurricane! How is it, then, that we can survive the incessant bombardment of such a storm of projectiles? Simply because the particles are moving in all directions, so as nearly to counterbalance each other's momentum. Were it not that the molecules are continually changing their direction by executing a sort of carrom upon their neighbors, the interdiffusion of liquids and gases would be almost instantaneous. If the molecules could project in straight lines without interference with each other, the opening of a bottle of perfumery would permit the diffusion of its odor to the distance of many hundred feet sooner than you could open and recork the bottle, or, in some instances, about one-third of a mile in one second of time. An instructive experiment may be made: First, finely pulverize indigo, charcoal, or carmine, and then mix either of them with water, and place under the microscope, when an incessant movement of the small granular particles will become apparent; and the smaller the particles, the more rapid and uniform will be their movements. These movements are chiefly of a vibratory kind; and it is when the particles are minutely divided, so as to approach the limits of microscopic range, that this vibratory motion, together with an irregular axial rotation, approaches a degree of perfection that is beautiful as well as suggestive. This experiment is well calculated to assist us in forming a mental conception of the magnitudes and the motions of those atoms and molecules which have for their realm the regions below and beyond the immeasurably small.
As to the shape and internal structure of atoms, there is no definite knowledge; but Helmholtz's studies of certain equations in hydro-kinetics, several years ago, gave rise to the idea that vortex-motion in a frictionless medium would exist forever—an assumption which is purely hypothetical; but since the proposition has been enlarged upon by Sir William Thomson—who conjectures that the atoms might be filaments or rings endowed with a vortex-motion—the subject assumes a shape better calculated to form the basis of a scientific theory. To be sure, mathematical formulas might show that the behavior of a vortex-filament in a non-resisting medium would answer to that ascribed to atoms—indestructible and unalterable through all time; still, at the same time, the means at hand for its complete mathematical verification are not adequate to place the subject beyond the regions of theory. Prof. Tait, in a review of this subject in his "Recent Advances of the Physical Sciences," remarks that, "with a little further development, it may be said to have passed its first trial, and, being admitted as a possibility, may be left to time and the mathematicians to settle whether it will really account for everything experimentally found."
Small as these atoms are, we are not permitted to stop here, but remember that there is a finer medium environing them all, embracing possibly a complexity of internal structure sufficient to baffle human investigation for all time. This cosmic or luminiferous ether is supposed to fill all space, intermolecular and interstellar, and to be the medium in which the atoms and molecules move like motes in the sunbeam.
Atoms and molecules may vibrate to and fro, or may execute various oscillations about each other, with a moderate velocity, or perform their motions with a rapidity beyond conception; and be the intensity of the vibrations ever so great or ever so small, these same vibrations determine the amplitude of the ethereal waves—those waves of greatest length giving rise to all the phenomena of radiant heat, while shorter ones constitute light in all its luminous and chromatic effects; as also the ethereal waves of still more rapid undulations and lesser length furnish the actinic force of light. And if the mathematical deductions of such as Maxwell and Boltzmann, together with the refined researches of many others in this border-land of science, are not at fault, we would not be surprised if, at some early day, the solution of the phenomena of electricity should be found in some way connected with ethereal vibrations, infinitely more rapid and minute than those which produce the actinism of the ultra-violet spectrum. The difficulties attending the solution of this problem may be more fully comprehended when we recollect that, in dealing with vibrations more rapid than those bordering the visible spectrum, we are leaving regions where the undulations comprise nearly one thousand million of millions in a second of time, only to be confronted with others of infinitely greater rapidity.
These ethereal and molecular actions are going on eternally about us. The photographer's sensitized plate may receive an image that maps out the constellations, or, through the prism of the spectroscope in lines of light, we may read of the constituents of the nebulae, and thus upon the waves of ether do we hold communion across the universe by that ethereal chain of motion which binds us to the stars!
- H. C. Sorby, F. R. S., in his anniversary address to the Royal Microscopical Society, in the Quarterly Journal of Microscopical Science for April, 1876.