here the most abstract, simple, and obvious of all conceptions. The idea of space is the same, whether we regard the distance between the sun and the stars by which he is surrounded, or that between the mountains and ourselves. So, too, with number and form, which apply as readily to the sands of the sea-shore as to the gigantic trees of the forest, or to the various bodies seen to be moving through the heavens.

Next in order would come the desire, or the necessity, for comparing distances, numbers, and magnitudes, and the means for this would be at hand in machinery supplied by nature, and always at his command. His finger, or his arm, would supply a measure of magnitudes, while his pace would do the same by distance, and the standard with which he would compare the weights would be found in some one among the most ordinary commodities by which he was surrounded. In numerous cases, however, distances, velocities, or dimensions, are found to be beyond the reach of direct measurement, and thus is produced a necessity for devising means of comparing distant and unknown quantities with those that being near can be ascertained, and hence arises mathematics, or The Science-so denominated by the Greeks, because to its help was due nearly all the positive knowledge of which they were possessed.

The multiplication table enables the ploughman to determine the number of days contained in a given number of weeks, and the merchant to calculate the number of pounds contained in his cargo of cotton. By help of his rule, the carpenter determines the distance between the two ends of the plank on which he works. The sounding-line enables the sailor to ascertain the depth of water around his ship, and by help of the barometer the traveller determines the height of the mountain on which he stands. All these are instruments for facilitating the acquisition of knowledge, and such, too, are the formulæ of mathematics, by help of which the philosopher is enabled to determine the magnitude and weight of bodies distant from him millions of millions of miles, and is thus enabled to solve innumerable questions of the highest interest to man. They are the key to science, but are not to be confounded with science itself, although often included in the list of sciences, and even so recently as in M. Comte's well-known work. That such should ever have been the case has been due to the fact that

so much of what is really physics is discussed under the head of mathematics; as is the case with the great laws for whose discovery we are indebted to Kepler, Galileo, and Newton. That a body impelled by a single force will move in a right line and with a velocity that is invariable, and that action and reaction are equal and opposite, are facts, at the knowledge of which we have arrived in consequence of pursuing a certain mode of investigation; but when obtained, they are purely physical facts, obtained by help of the instrument to which we apply the term mathematics— and which is, to use the words of M. Comte, simply "an immense extension of natural logic to a certain order of deductions."*

Logic is itself, however, but another of the instruments devised by man for enabling him to obtain a knowledge of nature's laws. To his eyes the earth appears to be a plane, and yet he sees the sun rising daily in the east and setting as regularly in the west, from which he might infer that it would always continue so to do--but of this he can feel no certainty until he has satisfied himself why it is that it does so. At one time, he sees the sun to be eclipsed, while at another, the moon ceases to give light, and he desires to know why such things are—what is the law governing the movements of those bodies; having obtained which he is enabled to predict when they will again cease to give light, and to determine when they must have done so in times that are past. At one moment ice or salt melts; at another gas explodes; and at a third, walls are shattered and cities are hurled to the ground; and he seeks to know why these things are-what is the relation of cause and effect ? In the effort to obtain answers to all these questions, he observes and records facts, and these he arranges with a view to deduce from them the laws by virtue of which they occur-and he invents barometers, thermometers, and other instruments to aid him in his observation-but the ultimate object of all is that of obtaining an answer to the questions: Why are all these things? Why is it that dew falls on one day and not on another? Why is it that corn grows abundantly in this field and fails altogether in that one? Why is it that coal burns and granite will not? What, in a word, are the laws instituted by the Creator for the government of matter? The answers to these questions constitute science

* Positive Philosophy, Martineau's Translation, Vol. i. 33.

and mathematies, logic, and all other of the machinery in use are but instruments used by him for the purpose of obtaining them.

In discussing the subject of rational mechanics, under the head of mathematics, M. Comte informs his readers that we here encounter a perpetual confusion between the abstract and the concrete points of view; between the logical and the physical; between the artificial conceptions necessary to help as to general laws of equilibrium and motion, and the natural facts furnished by observation, which must form the basis of the science."* This, however, is only saying that as "the natural facts," furnished by observation, increase in number, there arises a necessity for endeavoring to perfect the machinery by the help of which they are to be studied, and that this is the case in the instance referred to by M. Comte, is shown in his admission that the science of which he treats is "founded on some general facts, furnished by observation, of which we can give no explanation whatever."+ As we pass from gate to gate of science, we pass from simple to compound locks, requiring additional wards in the keys by which they are to be opened; but the key still remains a key, and can never become a lock, even though the wards should become fifty-fold more numerous than those of any yet constructed by Bramah, Chubb, or Hobbs, and might require years of study before its proper management could be acquired. There might then arise what would be called the science of the key, but it would constitute no part of true science. When D'Alembert made, to use the words of Comte,

a discovery, by help of which all investigation of the motion of any body or system might be converted at once into a question of equilibrium," he merely opened a new ward in the key by which we were to unlock the cabinet of nature, and thus enlarge the boundaries of that department of knowledge which treats of the properties of matter and the laws by which it is governed, and known as physical science.

§ 2. The abstract mathematics necessarily took precedence of the more concrete physics, because they were the sole product of logic, and dependent upon those first principles which are in their

* Positive Philosophy, Martineau's Translation, Vol. i. p. 107.
† Ibid.

elements so nearly intuitive that when the boy commences the study of geometry, he finds that he had already acquired a knowledge of much that is now being given to him as science. Hence, too, it was that moral science, poetry, the fine arts, and metaphysics were so far advanced in Greece, while mechanical science had scarcely an existence.

In default of observation, men of speculative habits looked inwards to their own minds and invented theories that were given to the world as laws, but, as has well been said: "Man can invent nothing in science or religion but falsehood, and all the truths that he discovers are but facts or laws that have emanated from the Creator." The men of the Middle Ages-the philosophers of the schools-taught the theories that had been invented by their Grecian predecessors, and it was left for Bacon to teach the philosophy that leads to the search for truth among the facts of nature and not among the speculations of men. From his day to the present there has been a perpetual tendency towards the substitution of careful observation and induction for the dreams of theorists, and as the Cartesian doctrine of Vortices gave way to the discovery of gravitation, so the imaginary phlogiston of Stahl, and the Plutonian and Neptunian cosmogonies have yielded to the discoveries of modern science. The former was early displaced by the oxygen of Lavoisier, while the latter held their ground until disproved by the observations of geologists, whose branch of science dates its existence but little beyond the present century.

In physics, as has everywhere been the case, the more abstract and general has, in its development, taken precedence of that which is concrete and special. Astronomy, the science of the laws governing bodies exterior to our own planet, was studied at an early period, the shepherds of Chaldea having carefully noted the movements of the celestial bodies, and Babylonians having calculated eclipses thousands of years before the commencement of the Christian era. From a well of Syene, Eratosthenes obtained the observations required for determining the terrestrial meridian; and many centuries before Copernicus, Archimedes taught the double motion of the earth around its axis and around the sun. The precise length of the solar year was determined by Hipparchus, while Mexican and Etrurian observation led in this respect so nearly to the same result, that the difference between them was but ten minutes.

The motions of the celestial bodies were thus early studied and comprehended, yet was it left to Newton to discover the reason why the apple falls to the earth; to Franklin to discover the identity of lightning and electricity; to Cavendish to discover the composition of the air we breathe; to Black to discover the existence of latent heat; and to philosophers, even of our own day, to discover the laws in virtue of which we see and hear. Laplace's great work of Celestial Mechanics, was the product of the same period that witnessed the birth of a new science, having for its object to determine the composition of the globe on which we live and move, and from which we derive our daily bread. It is thus, that as we approach nearer to man, his uses and purposes, we find the greatest retardation of that positive knowledge so early attained in reference to the method to be pursued in the effort for its attainment. The study of the history of science leads inevitably to an agreement with Buffon in the opinion that, "however great may be our interest in knowing ourselves," we probably "understand better all that is not ourselves”—and with Rousseau in the belief that "much philosophy is required for observing the facts that are very near to us."

Passing from the more abstract and general laws governing the movements of distant bodies towards those determining the composition of the matter by which we are immediately surrounded, we find new laws, but all subordinate to, and in harmony with, those first obtained. Chemistry, following physics, which deals with masses, deals with the elements of which they are composed, all of which are, however, subject to the same laws by which the masses themselves are governed. The atoms produced by the analysis of Cavendish, were as obedient to the law of gravitation as were the earth, the satellites of Jupiter, and Jupiter himself. "The distinction between physics and chemistry," says M. Comte, "is much less easy to establish" than between chemistry and astronomy, and, as he continues, "it is one more difficult to pronounce upon from day to day, as new discoveries bring to light closer relations between them."* That such is the case, will readily be seen by the reader who reflects how much of the present great development of physical knowledge has been due to the labors

* Positive Philosophy, Martineau's Translation, vol. i. p. 216.