arrangement capable of exhibiting directly the laws obeyed by them. The mathematician might as well expect to integrate his functions by a ballot-box, as the experimentalist to draw deep truths from haphazard trials. All induction is but the inverse application of deduction, and it is by the inexplicable action of a gifted mind that a multitude of heterogeneous facts are ranged in luminous order as the results of some uniformly acting law. So different, indeed, are the qualities of mind required in different branches of science, that it would be absurd to attempt to give an exhaustive description of the character of mind which leads to discovery. The labours of Newton could not have been accomplished except by a mind of the utmost mathematical genius; Faraday, on the other hand, has made the most extensive additions to human knowledge without passing beyond common arithmetic. I do not remember meeting in Faraday’s writings with a single algebraic formula or mathematical problem of any complexity. Professor Clerk Maxwell, indeed, in the preface to his new Treatise on Electricity, has strongly recommended the reading of Faraday’s researches by all students of science, and has given his opinion that though Faraday seldom or never employed mathematical formulæ, his methods and conceptions were not the less mathematical in their nature.2 I have myself protested against the prevailing confusion between a mathematical and an exact science,3 yet I certainly think that Faraday’s experiments were for the most part qualitative, and that his mathematical ideas were of a rudimentary character. It is true that he could not possibly investigate such a subject as magne-crystallic action without involving himself in geometrical relations of some complexity. Nevertheless I think that he was deficient in mathematical deductive power, that power which is so highly developed by the modern system of mathematical training at Cambridge.
Faraday was acquainted with the forms of his celebrated lines of force, but I am not aware that he ever entered into the algebraic nature of those curves, and I feel sure that he could not have explained their forms as depending on the resultant attractions of all the magnetic particles. There are even occasional indications that he did not understand some of the simpler mathematical doctrines of modern physical science. Although he so clearly foresaw the correlation of the physical forces, and laboured so hard with his own hands to connect gravity with other forces, it is doubtful whether he understood the doctrine of the conservation of energy as applied to gravitation. Faraday was probably equal to Newton in experimental skill, and in that peculiar kind of deductive power which leads to the invention of simple qualitative experiments; but it must be allowed that he exhibited little of that mathematical power which enabled Newton to follow out intuitively the quantitative results of a complicated problem with such wonderful facility. Two instances, Newton and Faraday, are sufficient to show that minds of widely different conformation will meet with suitable regions of research. Nevertheless, there are certain traits which we may discover in all the highest scientific minds.
The Newtonian Method, the True Organum.
Laplace was of opinion that the Principia and the Opticks of Newton furnished the best models then available of the delicate art of experimental and theoretical investigation. In these, as he says, we meet with the most happy illustrations of the way in which, from a series of inductions, we may rise to the causes of phenomena, and thence descend again to all the resulting details.
The popular notion concerning Newton’s discoveries is that in early life, when driven into the country by the Great Plague, a falling apple accidentally suggested to him the existence of gravitation, and that, availing himself of this hint, he was led to the discovery of the law of gravitation, the explanation of which constitutes the Principia. It is difficult to imagine a more ludicrous and inadequate picture of Newton’s labours. No originality,