ted. 'Tis this: a profound knowledge of mathematics always produces a spirit of modesty and humility, eminently adapted to receive the doctrines of the lowly Nazarene. This cannot be otherwise. The mathematician feels every day the limit of his power. He has done a little, but the infinite remains untouched; he has thrown up his little mole-hill, but it is at the foot of the mighty Alps. For three centuries the world has made no advances in the solution of equations. No general rules are known for solving an equation above the fourth degree. Numerical equations of high degrees can be solved in particular cases, but we have arrived no nearer a general solution than did Tartaglia and Cardan, in the sixteenth century. The softest Freshman can propose an equation that the greatest mathematician living cannot solve. How, then, can the Algebraist be proud of his powers? The geometrician must be equally humble. The trisection of an angle, the duplication of a cube, the quadrature of the circle, are problems which have been tried again and again for more than two thousand years. Robert Simson was probably the greatest geometrician the world has ever produced, but any stupid boy, who had just taken in the conception of an angle, could have proposed to him a problem which his geometry could not reach. Mere smatterers in science may be vain and conceited, but the profound scholar has been too often baffled and foiled in his efforts to feel otherwise than humble. Thus Newton said, "that when he compared his attainments with what yet remained to be learned, he felt like a child picking up pebbles on the sea-shore, with the vast ocean of truth before him." Laplace, when congratulated upon his vast stores of knowledge, replied, "what I know is little, what I do not know is immense. John Bernouilli was more honoured and flattered than any sovereign in Europe, and yet he had the modest simplicity that old writers tell us used to be the characteristic of children. Compare the humility of these men and that of all eminent mathematicians with the insolence of Voltaire, the vanity of Rousseau, the arrogance of Gibbon, the conceit of Hume, the coxcombry of Byron, Bulwer, etc. The feeling with literary gentlemen is too often "we are the people, and wisdom shall die with us." And this feeling they are by no means careful to conceal. We will now leave our five propositions to fall by their weakness, or stand by their strength, and come to the indebtedness of religion to science. The observed acceleration of the moon in its orbit, led the infidels of France to conclude that this satellite would eventually strike the earth, and supposing that there was a like acceleration throughout the solar system, they inferred that all the planets would eventually precipitate themselves on the central mass of the sun. They therefore most sapiently reasoned that either the heavens and earth are the result of chance, or that their great Architect could not control their movements. A child can see the falsity of their logic, but infidels are not remarkable for sense. A poet has embalmed their folly in most exquisite verse: Roll on, ye stars, exult in youthful prime, Mark with bright curves the printless steps of time; Star after star from Heaven's high arch shall rush, Laplace, however, showed by astronomical calculations, that the acceleration was merely periodic, that this noble funeral dirge is uncalled for, and that we may all go quietly to bed any night, without dread of being wakened by the man in the moon knocking at our doors. The infidels were sorely vexed with Laplace, but every true Christian will thank God that science enables him to say with the Psalmist, "How manifold are thy works, Lord God Almighty, in wisdom hast thou made them all." Again. Christianity has nothing to fear from sound reasoning upon sound premises: everything to fear from false conclusions drawn from admitted facts, and from just conclusions deduced from false premises. But we are indebted to the geometry of Egypt for the whole science of Logic. Aristotle is the Father of the logic of the schools of the present day. He was for twenty years the pupil of Plato, the greatest mathematician of his age, who always began his instructions with mathematics, because he called it "the purgative of the soul that cleansed it from error, and restored it to the natural exercise of those faculties, in which just thinking consists." How apt a scholar Aristotle was under the great mathematician, we may judge by his frequent allusions to geometrical reasoning, and by his system itself, which is strictly mathematical. Thus his dilemma was in common use among the geometricians of his day, it is in constant use now in geometry, and always will be used: his syllogism too, was employed by the mathematicians on the banks of the Nile, hundreds of years before he was born. Every one knows that the syllogism is to be met with everywhere in every treatise on geometry, and Leibnitz tells us that he had seen two books, in which the theorems of the first six books of Euclid were demonstrated by the syllogism. Two Schools of Logic preceded the Aristotelian, the School of Pythagoras, and the School of Thales. Both of these last philosophers made geometry the basis of their systems, because they "were fearned in all the learning of the Egyptians." Many an unsophisticated Freshman has wished that Pythagoras had confined himself to his Logic, and had let alone the square upon the hypothenuse. The inductive philosophy, which has crushed infidelity, as the strong man crushes the loathsome reptile beneath his feet, is ascribed by some to Lord Verulam, and by others to Aristotle. Take either hypothesis that yon please, a mathematician is still the author of it. The theory of probabilities, invented by the French mathematicians, and employed by them in determining the chances of games of hazard, the value of testimony in courts of laws, the reliability of statistical facts, the present worth of annuities, etc., has had a higher and nobler application in the hands of the Christian philosopher, Olinthus Gregory, and of other pious men, who have shown the thousands of chances against the concurrent meeting in the person of Jesus Christ, of the nineteen circumstances predicted of the Messiah, without the special interference of Him "who rules in the armies of Heaven, and among the inhabitants of the earth." They have also applied the same theory to numerous prophecies, and shown that the chances against their fulfilment were so great, that even the soft-headed Atheist can scarcely have effrontery enough to deny the miraculous interposition of God. Mechanical Philosophy demonstrates on almost every page that "the Lord by wisdom hath founded the earth; by understanding hath he established the heavens."The poor, ignorant Atheist thinks, or at least says, that the planets began to revolve in their orbits by chance.But Mechanical philosophy teaches that curvilinear motion is due to an original projectile, as well as incessant force: yea, the very point, at which each shining orb was struck when hurled into boundless space, has been exactly determined. The chance of the Atheist must then have had "a mighty hand and an outstretched arm," thus to have projected with amazing velocity, bodies of such enormous and almost inconceivable magni tude. An elementary demonstration in Mechanics, shows that the centre of gravity is independent of the intensity and direction of the gravitating forces. Were it not independent of the first, ships could not navigate the ocean, because the slightest deviation from the parallel of latitude upon which they ballasted, would capsize them; were it not independent of the second, we could not change the position of our bodies without being liable to fall. 'Twas long a desideratum with mechanicians to know the solid angle of greatest strength. Maclaurin demonstrated by the Differential Calculus that this was the angle under which bees built their cells. Where did they get their science? Again, we learn from Mechanics that an increase of velocity in the motion of the earth upon its axis, would be accompanied by such a loss of weight on our part, that a translation to the upper regions of the air would not be improbable on any gusty day. Human Kites would be as common as Da guerreotype pictures. Who has ordered all things with such consummate skill and wisdom as we are thus taught prevails throughout all nature? Astronomy opened the gates of Ispahan and Teheran to the Missionary Henry Martin. The Persian mathematicians treated with deference and respect a man superior to themselves in the study, which was their special boast and pride. They could not answer him too, when he showed them that their Prophet was ignorant of the nature and laws of the heavenly bodies. Astronomy has always secured the Missionary a welcome from the Moslem, the Pagan and the worshipper of the Lama. May not that sublime science, which enables a worm of the dust to measure, as with a line, the bright worlds that encircle the Throne of the Eternal, be a chosen instrument in his hand for elevating lost and ruined men. from their low and degraded condition, "to shine as stars in the firmament forever and forever?" We have proved that the mathematician could not become an infidel without abandoning his usual mode of reasoning, and without being grossly false to the principles which he employs in all his scientific investigations. We have also shown that mathematical science has contributed much towards confounding Atheism, and establishing the claims of the religion of Jesus to be from God. We now propose to close the subject with an array of names of the profoundest mathematicians, who have also been the most humble and devoted followers of the Lamb of God. The Latin Fathers, Augustine, Tertullian, Clemens Alexandrinus, Origen, &c., were "learned in all the wisdom of the Egyptians," and must have been thorougly imbued with a knowledge of mathematics; for in the Egyptian school in which they were taught, Geometry was made the basis of all instruction. A treatise on Geometry, by Augustine, was for centuries the only text-book on that subject in all Europe. Origen tinged his religion with the mathematical philosophy of Plato. The four greatest mathematicians of modern times, Newton, Leibnitz, Euler and John Bernouilli, were eminent for their Christian faith and piety. We place Newton first, because all men agree that the inscription on |