Now, is this true of economic science? Within certain limits, it is apparently true: Ricardo used mathematical formulæ, though he kept to arithmetic, instead of algebra. When Malthus spoke of arithmetical and geometrical ratios, the statement, true or false, was, of course, capable of precise numerical expression, so soon as the ratios were assigned. So there was the famous formula proving a relation between the number of quarters of corn produced by a given harvest, and the number of shillings that would be given for a quarter of corn. If, again, we took the number of marriages corresponding to a given price of corn, we should obtain a formula connecting the number of marriages with the number of quarters of corn produced. The utility of statistics, of course, depends upon the fact that we do empirically discover some tolerably constant and simple numerical formulæ. Such statistical statements are useful, indeed, not only in economical, but in other inquiries, which are clearly beyond the reach of mathematics. The proportion of criminals in a given population, the number of suicides, or of illegitimate births, may throw some light upon judicial and political, and even religious or ethical problems. Nor are such formulæ useless simply because empirical. The law of gravitation, for example, is empirical. Nobody knows the cause of the observed tendency of bodies to gravitate to each other, and therefore no one can say how far the law which represents the tendency must be universal. Still, the fact that, so far as we have observed, it is invariably verified, and that calculations founded upon it enable us to bring a vast variety of phenomena under a single rule, is quite enough to justify astronomical calculation.