RATION 437 RATIONALISM a — b::c+d:c — d is the mixed ratio or proportion. Prime and ultimate ratios, a method of analysis, devised and first successfully, employed by Newton in his "Principia." It is an extension and simplification of the method known among the ancients as the method of exhaustions. To conceive the idea of this method, let us suppose two variable quantities constantly ap- proaching each other in value, so that their ratio continually approaches 1, and at last differs from 1 by less than any assignable quantity; then is the ultimate ratio of the two quantities equal to 1. In general when two variable quantities, simultaneously approach two other quantities, which, under the same cir- cumstances, remain fixed in value, the ultimate ratio of the variable quanti- ties is the same as the ratio of the quantities whose values remain fixed. They are called prime or ulti- mate ratios, according as the ratio of the variable quantities is receding from or approaching to the ratio of the limits. This method of analysis is generally called the method of limits. Extreme and mean ratio, in geometry, the ratio where a line is divided in such a manner that the greater segment is a mean proportional between the whole line and the lesser segment: that is, that the whole line is to the greater segment as that greater segment is to the less. Composition of ratios, the act of com- pounding ratios. Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one. To find the ratio of a given pro- gression, divide any term by the preced- ing one. Ratio of exchange, a phrase used in political economy to denote the propor- tion in which a quantity of one com- modity exchanges for a given quantity of another. The expression can never be used with any degn^ee of accuracy, ex- cept in those cases where the commodi- ties are homogeneous in quality, and sus- ceptible of weight or measurement, as in the exchange of gold for silver, copper, iron, etc., or that of wheat for barley, oats, etc. RATION, a stated or fixed amount or quantity dealt out; an allowance. SpecL- fically, rations are the allowance of provisions given out to each oflScer, non- commissioned officer, soldier, or sailor. RATIONALISM, as a "system of belief regulated by reason/' might be ex- pected to mean the opposite of irration- ality, crass ignorance, and perverse' pre- judice; and the rationalism would then mean the progress of civilization, the de- velopment of the intellectual and moral nature of men and nations. It is nearly in this sense that Lecky uses the word; attributing to its wholesome influence the decay of the belief in magic, witch- craft, and other hideous superstitions, and the substitution of a kindly toler- ance in place of blind zeal for persecu- tion. But in ordinary English usage, gen- eral as well as theological, the connota- tion of the word is substantially differ- ent. It is generally employed as a term of reproach for those who, without ut- terly denying or attempting to overthrow the foundations of religion, make such concessions to the enemy as tend to sub- vert the faith; who admit the thin end of a wedge that pressed home will rend and destroy the fabric. They rely, more or less exclusively and blameworthily, on mere human reason instead of sim- ply, frankly, and fully accepting the dicta of the divine word. An atheist would not be spoken of as a rationalist nor would an irreligious, blaspheming freethinker. Rationalists in ordinary parlance are those v/ho are more "lib- eral" or "advanced" than the main body of the orthodox; in especial those who take a "low" view of inspiration, and minimize or explain away the miraculous details of the history of revelation and redemption. Rationalism is not so much a body of doctrine as a mood of mind, a tendency of thought shown in the attempt to apply to religious doc- trine, the sacred story, and the sacred Scriptures the same methods of research and proof as are used in mere human science and history, and the literatures of all times and peoples. This feature is also recognized, though with approval, by Lecky in his wider use of the word: "Rationalism," he says, "leads men on all occasions to subordinate dogmatic theology to the dictates of reason and conscience. ... It predisposes men in history to attribute all kinds of phen- omena to natural rather than to mirac- ulous causes; in theology to esteem suc- ceeding religious systems the expression of the wants and aspirations of that religious sentiment which is implanted in man ; and in ethics to regard as duties only those which conscience reveals to be such." Rationalism, not being a system but a temper or drift of mind, has different aims at different times; just as "liberalism" in polities was not the same thing before 1832 as it came to be after, or in 1832 what it was in 1867, 1885, or 1900. Opinions are heard in sermons and expounded in books by theological professors in 1902 without proving serious stumblingblocks to the majority, which in 1860 would by all but
