eral,
before that of the particular terrestrial bodies, which alone we can
experimentally know. Astronomy, in fact, owes its perfection to the
circumstance that it is the only branch of natural history, the
phaenomena of which are largely expressible by mathematical conceptions,
and which can be, to a great extent, explained by the application of
very simple physical laws.

With regard to mathematics, it is to be observed, in the first place,
that M. Comte mixes up under that head the pure relations of space and
of quantity, which are properly included under the name, with rational
mechanics and statics, which are mathematical developments of the most
general conceptions of physics, namely, the notions of force and of
motion. Relegating these to their proper place in physics, we have left
pure mathematics, which can stand neither at the head, nor at the tail,
of any hierarchy of the sciences, since, like logic, it is equally
related to all; though the enormous practical difficulty of applying
mathematics to the more complex phaenomena of nature removes them, for
the present, out of its sphere.

On this subject of mathematics, again, M. Comte indulges in assertions
which can only be accounted for by his total ignorance of physical
science practically. As for example:--

"C'est donc par l'etude des mathematiques, _et seulement par elle_,
que l'on peut se faire une idee juste et approfondie de ce que
c'est qu'une _science_. C'est la _uniquement_ qu'on doit chercher a
connaitre avec precision _la methode generale que l'esprit humain
emploie constamment dans toutes ses recherches positives_, parce
que nulle part ailleurs les questions ne sont resolues d'une
maniere aussi complete et les deductions prolongees aussi loin avec
une severite rigoureuse. C'est la egalement que notre entendement a
donne les plus grandes preuves de sa force, parce que les idees
qu'il y considere sont du plus haut degre d'abstraction possible
dans l'ordre positif. _Toute education scientifique qui ne commence
point par une telle etude peche donc necessairement par sa
base._"[24]

That is to say, the only study which can confer "a just and
comprehensive idea of what is meant by science," and, at the same time,
furnish an exact conception of the general method of scientific
investigation, is that which knows nothing of observation, nothing of
experiment, nothing of induction, nothing