This is obvious, whenever we undertake to apply the processes of arithmetic to the realities of life. Arithmetic, unsubjected to the impulses of passion and the accidents of created nature, holds on its course; but, in the phenomena of the actual world, "time and chance happeneth to them all." Thus it is, for example, in the arithmetical and geometrical ratios, set up in political economy by the celebrated Mr. Malthus. His numbers will go on smoothly enough, 1, 2, 4, 8, 16, 32, as representing the principle of population among mankind, and 1, 2, 3, 4, 5, 6, the means of subsistence; but restiff and uncomplying nature refuses to conform herself to his dicta. Dr. Price has calculated the produce of one penny, put out at the commencement of the Christian era to five per cent. compound interest, and finds that in the year 1791 it would have increased to a greater sum than would be contained in three hundred millions of earths, all solid gold. But what has this to do with the world in which we live? Did ever any one put out his penny to interest in this fashion for eighteen hundred years? And, if he did, where was the gold to be found, to satisfy his demand? Morse, in his American Gazetteer, proceeding on the principles of Malthus, tells us that, if the city of New York goes on increasing for a century in a certain ratio, it will by that time contain 5,257,493 inhabitants. But does any one, for himself or his posterity, expect to see this realised? Blackstone, in his Commentaries on the Laws of England, has observed that, as every man has two ancestors in the first ascending degree, and four in the second, so in the twentieth degree he has more than a million, and in the fortieth the square of that number, or upwards of a million millions. This statement therefore would have a greater tendency to prove that mankind in remote ages were numerous, almost beyond the power of figures to represent, than the opposite doctrine of Malthus, that they have a perpetual tendency to such increase as would infallibly bring down the most tremendous calamities on our posterity. Berkeley, whom I have already referred to on another subject, and who is admitted to be one of our profoundest philosophers, has written a treatise(48) to prove, that the mathematicians, who object to the mysteries supposed to exist in revealed religion, "admit much greater mysteries, and even falshoods in science, of which he alleges the doctrine of fluxions as an eminent example(49)." He observes, that their conclusions are established by virtue of a twofold error, and that these errors, being in contrary directions, are supposed to compensate each other, the expounders of the doctrine thus arriving at what they call truth, without being able to shew how, or by what means they have arrived at it. (48) The Analyst. (49) Life of Berkeley, prefixed to his Works.