Catholicism minus Christianity.

The mathematical thermology created by Fourier may tempt us to hope that, as he has estimated the temperature of the space in which we move, me may in time ascertain the mean temperature of the heavenly bodies: but I regard this order of facts as for ever excluded from our recognition. We can never learn their internal constitution, nor, in regard to some of them, how heat is absorbed by their atmosphere. We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies.

After Montesquieu, the next great addition to Sociology (which is the term I may be allowed to invent to designate Social Physics) was made by Condorcet, proceeding on the views suggested by his illustrious friend Turgot.

In the final, positive state, the mind has given over the vain search after Abolute notions, the origin and destination of the universe, and the cause of phenomenon, and applies itself to the tudy of their laws, - that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of this knowledge. What is now understood when we speak of an explanation of the facts is simply the establishment of a connection between single phenomena and some general facts, the number of which continually diminishes with the progress of science.

Notwithstanding the eminent difficulties of the mathematical theory of sonorous vibrations, we owe to it such progress as has yet been made in acoustics. The formation of the differential equations proper to the phenomena is, independent of their integration, a very important acquisition, on account of the approximations which mathematical analysis allows between questions, otherwise heterogeneous, which lead to similar equations. This fundamental property, whose value we have so often to recognize, applies remarkably in the present case; and especially since the creation of mathematical thermology, whose principal equations are strongly analogous to those of vibratory motion. This means of investigation is all the more valuable on account of the difficulties in the way of direct inquiry into the phenomena of sound. We may decide the necessity of the atmospheric medium for the transmission of sonorous vibrations; and we may conceive of the possibility of determining by experiment the duration of the propagation, in the air, and then through other media; but the general laws of the vibrations of sonorous bodies escape immediate observation. We should know almost nothing of the whole case if the mathematical theory did not come in to connect the different phenomena of sound, enabling us to substitute for direct observation an equivalent examination of more favorable cases subjected to the same law. For instance, when the analysis of the problem of vibrating chords has shown us that, other things being equal, the number of oscillations is hi inverse proportion to the length of the chord, we see that the most rapid vibrations of a very short chord may be counted, since the law enables us to direct our attention to very slow vibrations. The same substitution is at our command in many cases in which it is less direct.

Language forms a kind of wealth, which all can make use of at once without causing any diminution of the store, and which thus admits a complete community of enjoyment; for all, freely participating in the general treasure, unconsciously aid in its preservation.

Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena. . . . but if the employment of mathematical analysis should ever become so preponderant in chemistry (an aberration which is happily almost impossible) it would occasion vast and rapid retrogradation....

Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.

A common monetary standard will be established, with the consent of the various governments, by which industrial transactions will be greatly facilitated. Three spheres made respectively of gold, silver, and platinum, and each weighing fifty grammes, would differ sufficiently in value for the purpose. The sphere should have a small flattened base, and on the great circle parallel to it the Positivist motto would be inscribed. At the pole would be the image of the immortal Charlemagne, the founder of the Western Republic, and round the image his name would be engraved, in its Latin form, Carolus; that name, respected as it is by all nations of Europe alike, would be the common appellation of the universal monetary standard.

All classes, therefore, must be brought under women’s influence; for all require to be reminded constantly of the great truth that Reason and Activity are subordinate to Feeling. Of their influence upon philosophers I have spoken. If they are men worthy of their mission, they will be conscious of the tendency which their life has to harden them and lead them into useless speculation; and they will feel the need of renewing the ardour of their social sympathy at its native source. Feeling, when it is pure and deep, corrects its own errors, because they clash with the good to which it is ever tending. But erroneous use of the intellectual or practical faculties, cannot be even recognized, much less corrected, without the aid of Affection, which is the only part of our nature that suffers directly from such errors. Therefore whenever either the philosopher or the people deviate from duty, it will be the part of women to remonstrate with them gently, and recall them to the true social principles which are entrusted to their special charge.