DISCOVERY BY MEANS OF INFERENCE.

605

inheritance, selection, and adaptation. Whilst persons in general consider incredible the hypothesis that, during an immense number of years, man was gradually developed from the form of an ape, they are familiar with and believe the far more wonderful fact that, even in the comparatively short space of twenty years, each individual man is developed from a mere speck of albuminous matter. It is intrinsically no more incredible that, during an immense series of ages, inorganic, inanimate matter gradually becomes organised, acquires animation, and, by means of the processes of inheritance, selection, and adaptation, gradually developes, and passes through a whole series of vegetable and animal forms of life, up to that of a man, than that dead matter, partly organic and partly inorganic, taken as food and air by a woman, becomes in a few hours a part of her living structure, in a few months an embryo child, which by further assimilation of dead material becomes in a few years a full-grown human being.

In mental physiology, as well as in the physical and chemical sciences, in biology, &c., discoveries have been made, not only by means of experiment, observation, and comparison, but also by means of inference; and those made by the latter method have usually been the most abstruse and important. The process of inference, based upon comparisons of the actions of mental power and of those of the physical forces, leads us to conclude that even the human mind acts in accordance with all the chief laws and principles of those forces; also that neither the conscience nor the will is a separate or distinct mental power or faculty, and that the latter is simply a conscious mental effort to effect an object, the idea of which is already present to the mind.1

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CHAPTER LIX.

DISCOVERY BY MEANS OF NEW OR IMPROVED METHODS

OF INTELLECTUAL OPERATION.

A VERY large number of the most recondite and important discoveries have been more or less effected in this way. Every new logical or mathematical process of working in algebra or geometry, and every development and extension of logarithms, fluxions, the differential calculus, &c., has been followed by new discoveries in subjects to which these new or improved intellectual processes have been applied.

It was by the application of the peculiar mathematical methods which Laplace had invented for solving the problem of the figure of the planets, that Biot was enabled, about the year 1801, to give an exact solution of the problem of the distribution of electricity on a spheroid, to which Coulomb had only been able to approximate roughly by means of the previously-known methods of mathematical analysis, the state of mathematical knowledge being at the time behind that of electrical science. Poisson also, in 1824, by employing the mathematical artifices of Laplace and Legendre, was enabled to obtain general expressions for the attractions and repulsions of a body of any form whatever, magnetised by influence upon a given point, and in the case of spheroidal bodies was able to solve completely the equations which determine these forces.1

It is not improbable, that by invention of new or improved methods of intellectual operation (as by that of

1 Whewell, History of the Inductive Sciences, vol. iii. p. 45.

DISCOVERY BY NEW MODES OF INTELLECTUAL OPERATION. 607

new scientific instruments) the power and extent of action of man's mind may be as much enlarged beyond its present condition, as its present state is beyond what it was thousands of years ago. That such new methods are really possible appears to be proved by their invention in the past, as well as by the very rapid way in which calculating boys arrive at their conclusions.

Openings for extending the range of man's intellectual influence appear to lie in investigations of the physical conditions of mental action1-also in the invention of instruments for combining, dividing, multiplying, and permutating ideas; for drawing conclusions (as in Jevons's logical machine); or for calculating periodic phenomena and solving differential equations, as in the Integrating Machine' of Professor J. Thomson,2 and the Harmonic Analyser' of Sir W. Thomson.3

CHAPTER LX.

DISCOVERY BY MEANS OF CALCULATIONS BASED UPON

KNOWN TRUTHS.

AN immense number of discoveries have been made by this method, but as this book is simply a treatise on qualitative research, I will only refer to a few instances. The method is applicable chiefly in the exact sciences, and in those parts of other sciences which are based upon exact and known quantitative conditions. It has been largely used in mathematics, the mechanics of solids,

608

SPECIAL METHODS OF DISCOVERY.

liquids, and gases, including astronomy, hydrostatics, hydraulics, pneumatics, and acoustics, in the sciences of light and radiant heat, and to a less extent in those of electricity, magnetism, chemistry, and vital and mental

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action.

1

Many astronomical discoveries in particular have resulted from its use. It was by means of calculations, based upon known truths, that the effects of precession of the equinoxes were discovered by Hipparchus, 128 B.C., by comparison of his own observations with those of Timocharis, made 155 years previously. By calculation also, Newton appears to have discovered the method of demonstrating that a body might describe an ellipse, when acted upon by a force residing in the focus, and varying inversely as the square of the distance.' By similar means he discovered the specific gravity of the planets, and that the density of Saturn is almost nine times less than that of our earth; also that our earth could not be a perfect globe, and ascertained almost exactly how much it was flattened at the poles. He also found, by similar means, that the precession of the equinoxes was due to the earth not being a perfect sphere, and that the cause of it was the greater attraction of the sun and moon upon the extra mass of matter existing around it at the equator. About the year 1770, Lagrange, by means of mathematical calculation, discovered why it was that the moon always presents nearly the same surface towards the earth, and that what Newton had suggested was really the cause, viz., the attraction of the earth upon the swelling or extra quantity of matter at the lunar equator. In making this discovery, he also arrived at another, viz., the cause of the libration of the moon, i.e., why she always has a little

1 Whewell, History of the Inductive Sciences, 3rd. edit. vol. ii. p. 452.

DISCOVERY BY MEANS OF CALCULATIONS.

609

swaying motion of the axis, and exhibits to us continually first a little of one side, and then of the other.

The astronomer Encke, having, by calculation, predicted that his comet would return every 3 years, a Frenchman named Pons, at Marseilles, observed it in 1819, and found that it arrived 24 hours earlier than the calculated time. By calculating the effects of the different planets upon his comet, Encke also discovered that Mercury is smaller, and Jupiter much larger, than previous astronomers believed. By similar means Biela's comet was discovered by Biela, an Austrian officer, in 1826; Claussen computed its orbit, and found that the comet appeared every 6 years and 8 months, and subsequent re-appearances of it proved the correctness of the calculation. Its expected return in the year 1832 caused great consternation, especially in France, because it would then cross the earth's orbit, and people thought it would destroy the earth; but the latter was in a distant part of her orbit at the time. The alarm was so great in Paris, that Arago, at the request of the French Academy of Sciences, wrote a popular essay explaining the circumstances, in order to pacify the public. On November 26, 1845, it returned in accordance with the calculations, and Lieutenant Maury then discovered by observation that it had split into two portions, each a perfect comet. The two pieces returned in company, at the same distance apart, in the year 1852, but have never been seen again. It was by working out mathematical calculations that both Adams and Le Verrier, in 1846, were enabled to affirm the existence of the undiscovered planet Neptune, and whereabouts it might be found. It was also by means of calculations that Schiaparelli, in the years 1862-3, discovered, and confirmed his suggestion, that a comet which was seen in 1862 travelled along the same

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