But granting M. Comte his six abstract sciences, he proceeds to arrange them according to what he calls their natural order or hierarchy, their places in this hierarchy being determined by the degree of generality and simplicity of the conceptions with which they deal.  Mathematics occupies the first, astronomy the second, physics the third, chemistry the fourth, biology the fifth, and sociology the sixth and last place in the series.  M. Comte’s arguments in favour of this classification are first—­

“Sa conformite essentielle avec la co-ordination, en quelque sorte spontanee, qui se trouve en effet implicitement admise par les savants livres a l’etude des diverse branches de la philosophie naturelle.”

But I absolutely deny the existence of this conformity.  If there is one thing clear about the progress of modern science, it is the tendency to reduce all scientific problems, except those which are purely mathematical, to questions of molecular physics—­that is to, say, to the attractions, repulsions, motions, and co-ordination of the ultimate particles of matter.  Social phaenomena are the result of the interaction of the components of society, or men, with one another and the surrounding universe.  But, in the language of physical science, which, by the nature of the case, is materialistic, the actions of men, so far as they are recognisable by science, are the results of molecular changes in the matter of which they are composed; and, in the long run, these must come into the hands of the physicist. A fortiori, the phaenomena of biology and of chemistry are, in their ultimate analysis, questions of molecular physics.  Indeed, the fact is acknowledged by all chemists and biologists who look beyond their immediate occupations.  And it is to be observed, that the phaenomena of biology are as directly and immediately connected with molecular physics as are those of chemistry.  Molar physics, chemistry, and biology are not three successive steps in the ladder of knowledge, as M. Comte would have us believe, but three branches springing from the common stem of molecular physics.

As to astronomy, I am at a loss to understand how any one who will give a moment’s attention to the nature of the science can fail to see that it consists of two parts:  first, of a description of the phaenomena, which is as much entitled as descriptive zoology, or botany, is, to the name of natural history; and, secondly, of an explanation of the phaenomena, furnished by the laws of a force—­gravitation—­the study of which is as much a part of physics, as is that of heat, or electricity.  It would be just as reasonable to make the study of the heat of the sun a science preliminary to the rest of thermotics, as to place the study of the attraction of the bodies, which compose the universe in general, 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.