this law fails at the 2762nd term. If we continue to observe, we shall discover another law then coming into action, which also is dependent, but in a different manner, on triangular numbers, called triangular, because a number of points agreeing with their term may be placed in the form of a triangle, thus

1, 3, 6, 10. This will continue through about 1430 terms, when a new law is again introduced over about 950 terms; and this too, like all its predecessors, fails, and gives place to other laws, which appear at different intervals."

Such a process renders it evident that all calculations, beyond what serve for the immediate guidance of our life and practical reliance on Nature's uniformity, may be and probably are subordinated to some higher law which, at various seasons, interrupts and changes it. How then can any philosopher assert-"There never has been, and never will be any intervention of natural laws?” 1 There must have been an intervention, a series of crises, on the formation of elements out of primeval atoms; grouping and giving them powers as solids, fluids, gases; combining the inorganic; organising it, doing that which no chemist can—vitalising it ; and building up the world in harmonious beauty. The development, whether by an almost infinitely extended process, or sharp abrupt, absolute, is inexplicable, except by intervention of an Eternal Power. During the historical era ordinary observation might discern no change; the procedure may have been uniform; but, in ages preceding, we know not what happened; nor can we, with certainty, forecast the future; the invisible and unknown are indisputably great factors in the universe.

Think of natural variety in other ways.

Well-nigh infinite change has been wrought since our planet began. No part of the surface has ever been at rest. There is a constant change in life, solar radiance is ever gaining or losing in intensity, the density and moisture of the air are continually increasing or diminishing. Take the molecular theory of gases-The particles fly about with very great velocity, impinge upon one another and against the

1 "Conflict between Religion and Science: " Prof. Draper.

Changes may be called Infinite. 359

sides of the containing vessel, thus producing gaseous pressure. At ordinary pressure, every particle has to move a distance, say, of something like 300,000th or 500.000th part of an inch, on the average, before it comes in contact with another particle, and is sent on a new path. The pressure may be decreased by partially exhausting the gas, so that there are fewer particles in a given space; or, by compression bringing them so much closer that, on the average, the particles are not more, say, than 10.000.000th part of an inch asunder. The average square of the velocity of the particles corresponds with the energy of heat in the gas or its temperature. When a gas is so far condensed as to approach the liquid state, its particles are scarcely ever free from collisions; in the solid state its particles are, practically, in a permanent state of collision one with another.1

We obtain by mathematical methods a faint conception of the complexity and mystery: for example; in a mass of hydrogen, at ordinary temperature and pressure, every particle has on an average 17,700,000,000 collisions per second with other particles; in every second its course is wholly changed 17,700,000,000 times; and the particle itself moves at the rate of 70 miles in a minute. In air the number of collisions is about half, and the velocity about one-fourth of that in hydrogen.2 In a cubic inch of air, in the ordinary state of the atmosphere, the number of particles is approximately about 3 × 1020, that is, 3 with 20 cyphers after it; and the effective diameter of a particle is not very different from one-250,000,000 part of an inch.3 Reality is infinitely more various than fiction.

Careering amidst the tumult and storm, are minute living creatures hustling one another, or keeping out of one another's way, feeding and propagating themselves; in every room, not myriads only, billions exist. We are told that distilled water is homogeneous, and a germ of life is absolutely structureless, because the microscope fails to distinguish difference or structure; but even the microscope is blind as to these things. What shall we say then to skyey particles, so small that the minutest "vibrios and "Recent Advances in Physical Science," pp. 245-247: P. G. Tait, M.A. 3 Ibid. p. 317.

2 Ibid. p. 324:

bacteria of the microscopic field are as behemoth and leviathan ?" The diamond and amethyst have structure, but no structure can be detected; particles of water, changed so as to be diametrically polar, twist a ray of light, yet present nothing for the microscope to reveal, and germs of life, which seem absolutely simple, surpass our powers of observation. Truth is ever fresh, more and more comprehensive.

We hardly have patience with men who, knowing the world to be mysterious, full of things baffling and transcending human intelligence at every step, tell us— "there never has been any Divine Interference." Divine Interference is continual matter, life, intelligence, are as a garment of the Living God: shall He not move it, lay aside, or change it, as He sees fit? Commonest things manifest incomprehensible peculiarities. Take a cold highly polished plate of metal, place a wafer on it, breathe on the wafer: when the moisture has disappeared, and the wafer been thrown off, no trace of wafer or breath will be seen; but breathe again, and a spectral image of the wafer comes to view. Tried again, after many months, the shadowy form once more emerges-a symbol of resurrection and life from the dead that grand opening of mysterious doors to universal knowledge.

The farina of flowers appears to the naked eye like simple dust, but when magnified is seen to possess beautiful shapes of great variety, according to the character of the plant. Leaves are among the most delicate and gorgeous forms of Nature. The leaf of the Box is supposed to have 344,180 pores, and the back of a Rose leaf is diapered as with silver. "The Crowberry of our moors (Empetrum nigrum) habitually exhibits a peculiar mode of variation in the arrangement of its leaves on different parts of the same twig. Out of fifty Crowberry twigs, taken at random, only four (and these fragments) preserved the same arrangement throughout. In the remaining forty-six the leaf arrangement was found to undergo a progressive change in ascending from the base of the twig to the summit-a change from a simpler order to others more complex." "" 1 It seems that complex spiral leaf-order "is the result of condensation operating on some

1 "Leaf-Arrangement of the Crowberry. Proceedings of the Royal Society," 1876, No. 172. Hubert Airy, M.A., M.D.

Death subjected to Life.

361 earlier and simpler order or orders, the successive stages of that condensation being ruled by the geometrical necessities of mutual accommodation among the leaves and axillary shoots under mutual pressure in the bud.1 It is supposed that the original form of leaf-arrangement was two-ranked; that this two-ranked form gave rise to forms with 2, 3, 4, 5, 6, 7, etc., ranks by sporting; that of the orders so formed, those with an even number, except 2, became whorled; and those with 2 or an odd number assumed an alternate arrangement; and that all orders have been subject to vertical condensation under the need of vertical economy of space.2 These are not trifles; or, if so, into every trifle infinity extendeth.

Some consider that the sun is the only source of the energy exhibited in these and all other vital actions, but when mushrooms are grown in Paris Catacombs there is no light. It is more correct to say-Life is peculiar to organism, all life proceeds from former life; the material constituents of living substances cannot by mere combination and interaction produce life, nor can the sun give-it only stimulates and favours. Yeast will increase indefinitely in the dark. There are organisms, beneath two or three thousand fathoms of water, almost if not wholly deprived of light. Aided by solar influence, or apart from solar influence, the structureless colourless life-fluid transforms itself, groups the transformations into molecules so marvellously that though the life-wave in two consecutive moments is never composed of the same particles, similar living creatures are continually and unerringly produced this germ proceeding to the plant, that to the animal; but both, while agreeing in general parallelism and analogy, develop into different and opposing forms of structure, subjecting death to life.

How is it all wrought? Light in plant life enables the leaflets to shake apart the carbonic acid of the air and build up the plant. Oxygen is exhaled as an incident in plant nutrition. The proteids which nourish protoplasm are probably constructed by the plant from a carbohydrate and ammonia. Plant protoplasm contains less nitrogen than animal protoplasm. The fact being that the plant exhibits

1 "Leaf-Arrangement of the Crowberry. Proceedings of the Royal Society," 1874, No. 152, p. 301. Hubert Airy, M.A., M.D. 2 Ibid. 1874, No. 152, p. 307.

little physical activity as a mass, and has the minimum of protoplasm distributed throughout its framework, needful to sustain vitality. The animal, compared with the plants, brings into play a far larger aggregate of protoplasm, on the contractility of which the movements exhibited by animals depend. Again, the protoplasm of plants is contained in inelastic chambers (cells), the walls of which are composed of an inert substance (cellulose), of which nitrogen is not a constituent. The walls of animal cells, where they can be said to exist, are more of the nature of inert protoplasm, and are therefore nitrogenous. Bulk for bulk, plant tissues contain less nitrogen than animal, mainly because they contain less protoplasm-this fact being correlated with the absence of any power of movement en masse. It is well to lift our thoughts high as we can, above the mire and clay whence life is brought; to the eternal power, the highest Life of lives, who fashions creatures so marvellous.

Some suppose that by means of electrical agency form is imparted to organisms, and that the leaves and twigs of plants all terminate in angles or sharp edges by electrical operation. Among Phanerogamous Plants, a certain number of organs, either developed or rudimentary, is always present; and the rudimentary are capable of development. Flowers, bearing stamens on one stalk and pistils on another, can be made to produce both. Where and when a new function is required, Nature provides—not a new origin-but a modification of the common one by metamorphism. Some plants, if transferred to the sea-shore, produce thick fleshy leaves; the same plants, placed in a dry hot locality, get thin hair leaves. Out of the wild acrid sloe, some say the almond, have been produced our rich variety of plums, peaches, nectarines. Individual peculiarities are more accurately transmitted by non-sexual than by sexual propagation. When, for instance, a tree with stiff and upright branches accidentally produces down-hanging branches, the gardener, as a rule, must obtain a weeping tree by planting cuttings or slips seedlings would generally have the stiff and upright form. A species of Aloe is said to blossom once in a century. Not less wonderful is a bamboo that grows among the hills in the south-east of Mysore: the natives report that it seeds once every sixty years, and the product, marvellously abundant, is called bamboo rice. In the husk it resembles