case of the scales, the law of equilibrium of which was familiar to the earliest nations known, Archimedes advanced to the more general case of the unequal lever with unequal weights; the law of equilibrium of which includes that of the scales.  By the help of Galileo’s discovery concerning the composition of forces, D’Alembert “established, for the first time, the equations of equilibrium of any system of forces applied to the different points of a solid body”—­equations which include all cases of levers and an infinity of cases besides.  Clearly this is progress towards a higher generality—­towards a knowledge more independent of special circumstances—­towards a study of phenomena “the most disengaged from the incidents of particular cases;” which is M. Comte’s definition of “the most simple phenomena.”  Does it not indeed follow from the familiarly admitted fact, that mental advance is from the concrete to the abstract, from the particular to the general, that the universal and therefore most simple truths are the last to be discovered?  Is not the government of the solar system by a force varying inversely as the square of the distance, a simpler conception than any that preceded it?  Should we ever succeed in reducing all orders of phenomena to some single law—­say of atomic action, as M. Comte suggests—­must not that law answer to his test of being independent of all others, and therefore most simple?  And would not such a law generalise the phenomena of gravity, cohesion, atomic affinity, and electric repulsion, just as the laws of number generalise the quantitative phenomena of space, time, and force?

The possibility of saying so much in support of an hypothesis the very reverse of M. Comte’s, at once proves that his generalisation is only a half-truth.  The fact is, that neither proposition is correct by itself; and the actuality is expressed only by putting the two together.  The progress of science is duplex:  it is at once from the special to the general, and from the general to the special:  it is analytical and synthetical at the same time.

M. Comte himself observes that the evolution of science has been accomplished by the division of labour; but he quite misstates the mode in which this division of labour has operated.  As he describes it, it has simply been an arrangement of phenomena into classes, and the study of each class by itself.  He does not recognise the constant effect of progress in each class upon all other classes; but only on the class succeeding it in his hierarchical scale.  Or if he occasionally admits collateral influences and intercommunications, he does it so grudgingly, and so quickly puts the admissions out of sight and forgets them, as to leave the impression that, with but trifling exceptions, the sciences aid each other only in the order of their alleged succession.  The fact is, however, that the division of labour in science, like the division of labour in society,