Front Page Titles (by Subject) ARITHMETIC - Cyclopaedia of Political Science, Political Economy, and of the Political History of the United States, vol. 1 Abdication-Duty
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ARITHMETIC - John Joseph Lalor, Cyclopaedia of Political Science, Political Economy, and of the Political History of the United States, vol. 1 Abdication-Duty 
Cyclopaedia of Political Science, Political Economy, and of the Political History of the United States by the best American and European Authors, ed. John J. Lalor (New York: Maynard, Merrill, & Co., 1899). Vol 1 Abdication-Duty.
Part of: Cyclopaedia of Political Science, Political Economy, and of the Political History of the United States, 3 vols.
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ARITHMETIC, Political. Three different meanings are attached to this word, which was more used during the last century, than in our day, and which is rarely found in contemporary political economy. Some use it in a rather vague way, applying it to reflections upon social economy in general, or more especially to researches on population, agriculture, etc.; others employ it as a synonym for the science of statistics, calling to its aid political economy, to explain the causes and significance of the facts established by figures; to others still, it means simply the calculations and processes, arithmetical or algebraic, by the aid of which, from these facts, inductions and conclusions are formed which have not been directly established, but which are admitted by way of analogy, proportionality or probability.
—Arthur Young published under this title a work in which there are scarcely any figures, and which treats of the causes which, in his time, had made agriculture flourish in Great Britain, and of the causes which stood in the way of the advance of that great industry in other lands. His French translator, Freville, compiled from a work of Arbuthnot, also translated from the English, a volume, under the same title, upon the utility of large farms, and another volume without the name of the author, likewise translated from the English, treating of the condition of agriculture in the British Islands. The term political arithmetic was therefore used by Young and his translator in the first sense.
—It is in the last sense, however, that it is used by J. B. Say, who has devoted a chapter to it in his Cours, (part 9, chap. 3.) It is in this last sense that it should be used in order to avoid confusion in the terminology of economical science.
—M. Moreau de Jonnès in his Eléments de statistique, made political arithmetic, understood in the sense of J. B. Say, one of the two methods of statistics. He terms it the method of induction in contradistinction to the method of exposition which he recommends by way of preference, and which consists in registering all the numerical data, that constitute the elements of a given subject, in grouping, combining and even reducing them, or, to speak more correctly, in co-ordinating without altering them.
—When Vauban, at the commencement of the 18th century, estimated the agricultural products and the revenue of France, upon the basis of the investigations which he had made in a small number of localities; when Lavoisier, in 1790, calculated from the number of plows the extent of land under cultivation, and the amount of production and consumption in France; when Lagrange estimated the consumption of food by the whole population on the basis of that of a soldier, by supposing that one-fifth of the inhabitants were under ten years of age, and that two children and one woman consumed only as much as one man; when Necker, not venturing to undertake a general census, in 1784, calculated the number of inhabitants from the number of births, by adopting the ratio of one birth to every 25 inhabitants; when Chaptal, in 1818, gave the extent of arable lands, of vineyards, meadows and forests of the whole of France, at a seventh of the surveyed territory, and starting from the hypothesis that the other six-sevenths were identical in extent, with the first, as well in natural quality as in the uses made of them. Vauban, Lavoisier, Lagrange, Necker and Chaptal were workers in political arithmetic. When Arthur Young hit upon the idea of cutting up the map of France, estimating the parts and drawing conclusions from the notes he had been able to make upon certain localities, he pushed this method to the limits of possibility. "When one studies," says M. Moreau de Jonnès "the results which Vauban and Lavoisier have obtained by these strange processes, we are astonished to find in them all the characteristics of truth, and we are tempted to believe that there are men of genius who are endowed with the prescience of numbers and whose penetrating minds reach their object even following a vicious method. We can not refuse this preëminence to Necker, who was guided by the example of two distinguished statisticians, Messance and Montyon, and who surrounded himself with all the data necessary to eliminate error."
—We can easily see to what errors these calculations applied to the facts established by statistics might lead, and understand by the use to which they have sometimes been put, the discredit into which the works of certain statisticians, quite unworthy of the name, have fallen. It would be very wrong to confound with such men those who collect facts with intelligence, perseverance and honesty; who correct one method by the other; who use the processes of induction and the rule of three only with the greatest circumspection; and reason solely upon facts or figures drawn from a good source; who draw conclusions only from the particular to the general, taking local or even accidental facts and applying them to a whole country or an entire epoch.
—A writer who respects himself should have nothing to do with political arithmetic, unless he has no other means of calculation, and in this case itself, it is his duty to be sure of the solidity and exactness of the bases upon which he grounds his reasoning. This, several writers or publicists, of our day, who have discussed facts relative to poverty or other delicate questions of social economy, seem to have forgotten.
—There is a branch of arithmetic which has been remarkably developed, and which to-day constitutes a science apart. We mean the calculus of probabilities, that is to say the application of calculation to questions of insurance, of life annuities.