Having shown that M. Comte’s alleged law of progression does not hold among the several parts of the same science, let us see how it agrees with the facts when applied to separate sciences.  “Astronomy,” says M. Comte, at the opening of Book III., “was a positive science, in its geometrical aspect, from the earliest days of the school of Alexandria; but Physics, which we are now to consider, had no positive character at all till Galileo made his great discoveries on the fall of heavy bodies.”  On this, our comment is simply that it is a misrepresentation based upon an arbitrary misuse of words—­a mere verbal artifice.  By choosing to exclude from terrestrial physics those laws of magnitude, motion, and position, which he includes in celestial physics, M. Comte makes it appear that the one owes nothing to the other.  Not only is this altogether unwarrantable, but it is radically inconsistent with his own scheme of divisions.  At the outset he says—­and as the point is important we quote from the original—­“Pour la physique inorganique nous voyons d’abord, en nous conformant toujours a l’ordre de generalite et de dependance des phenomenes, qu’elle doit etre partagee en deux sections distinctes, suivant qu’elle considere les phenomenes generaux de l’univers, ou, en particulier, ceux que presentent les corps terrestres.  D’ou la physique celeste, ou l’astronomie, soit geometrique, soit mechanique; et la physique terrestre.”

Here then we have inorganic physics clearly divided into celestial physics and terrestrial physics—­the phenomena presented by the universe, and the phenomena presented by earthly bodies.  If now celestial bodies and terrestrial bodies exhibit sundry leading phenomena in common, as they do, how can the generalisation of these common phenomena be considered as pertaining to the one class rather than to the other?  If inorganic physics includes geometry (which M. Comte has made it do by comprehending geometrical astronomy in its sub-section—­celestial physics); and if its sub-section—­terrestrial physics, treats of things having geometrical properties; how can the laws of geometrical relations be excluded from terrestrial physics?  Clearly if celestial physics includes the geometry of objects in the heavens, terrestrial physics includes the geometry of objects on the earth.  And if terrestrial physics includes terrestrial geometry, while celestial physics includes celestial geometry, then the geometrical part of terrestrial physics precedes the geometrical part of celestial physics; seeing that geometry gained its first ideas from surrounding objects.  Until men had learnt geometrical relations from bodies on the earth, it was impossible for them to understand the geometrical relations of bodies in the heavens.