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