3. In these last expressions, we suppose the theory, not only to be tested, but also to be corrected when it is found to be imperfect. And this also is part of the business of the observing astronomer. From his accumulated observations, he deduces more exact values than had previously been obtained, of the Constants or Coefficients of these Inequalities of which the Argument is already known. This he is enabled to do by the methods explained in the [fifth] chapter of this book; the [Method of Means], and especially the [Method of Least Squares]. In other cases, he finds, by the [Method of Residues], some new Inequality; for if no change of the Coefficients will bring the Tables and the observation to a coincidence, he knows that a new Term is wanting in his formula. He obtains, as far as he can, the law of this unknown Term; and when its existence and its law have been fully established, there remains the task of tracing it to its cause.
4. The condition of the science of Astronomy, with regard to its security and prospect of progress, is one of singular felicity. It is a question well worth our consideration, as regarding the interests of science, whether, in other branches of knowledge also, a continued and corrected system, of observation and calculation, imitating the system employed by astronomers, might not be adopted. But the discussion of this question would involve us in a digression too wide for the present occasion. 236
5. There is another mode of application of true theories after their discovery, of which we must also speak; I mean the process of showing that facts, not included in the original induction, and apparently of a different kind, are explained by reasonings founded upon the theory:—extensions of the theory as we may call them. The history of physical astronomy is full of such events. Thus after Bradley and Wargentin had observed a certain cycle among the perturbations of Jupiter’s satellites, Laplace explained this cycle by the doctrine of universal gravitation[50]. The long inequality of Jupiter and Saturn, the diminution of the obliquity of the ecliptic, the acceleration of the moon’s mean motion, were in like manner accounted for by Laplace. The coincidence of the nodes of the moon’s equator with those of her orbit was proved to result from mechanical principles by Lagrange. The motions of the recently-discovered planets, and of comets, shown by various mathematicians to be in exact accordance with the theory, are Verifications and Extensions still more obvious.
[50] Hist. Ind. Sc. b. vii. c. iv. sect. 3.
6. In many of the cases just noticed, the consistency between the theory, and the consequences thus proved to result from it, is so far from being evident, that the most consummate command of all the powers and aids of mathematical reasoning is needed, to enable the philosopher to arrive at the result. In consequence of this circumstance, the labours just referred to, of Laplace, Lagrange, and others, have been the object of very great and very just admiration. Moreover, the necessary connexion of new facts, at first deemed inexplicable, with principles already known to be true;—a connexion utterly invisible at the outset, and yet at last established with the certainty of demonstration;—strikes us with the delight of a new discovery; and at first sight appears no less admirable than an original induction. Accordingly, men sometimes appear tempted to consider Laplace and other great mathematicians as persons of a kindred genius to Newton. We must not 237 forget, however, that there is a great and essential difference between inductive and deductive processes of the mind. The discovery of a new theory, which is true, is a step widely distinct from any mere development of the consequences of a theory already invented and established.
7. In the other sciences also, which have been framed by a study of natural phenomena, we may find examples of the explanation of new phenomena by applying the principles of the science when once established. Thus, when the laws of the reflection and refraction of light had been established, a new and poignant exemplification of them was found in the explanation of the Rainbow by the reflection and refraction of light in the spherical drops of a shower; and again, another, no less striking, when the intersecting Luminous Circles and Mock Suns, which are seen in cold seasons, were completely explained by the hexagonal crystals of ice which float in the upper regions of the atmosphere. The Darkness of the space between the primary and secondary rainbow is another appearance which optical theory completely explains. And when we further include in our optical theory the doctrine of interferences, we find the explanation of other phenomena; for instance, the Supernumerary Rainbows which accompany the primary rainbow on its inner side, and the small Halos which often surround the sun and moon. And when we come to optical experiments, we find many instances in which the doctrine of interferences and of undulations have been applied to explain the phenomena by calculations almost as complex as those which we have mentioned in speaking of astronomy: with results as little foreseen at first and as entirely satisfactory in the end. Such are Schwerdt’s explanation of the diffracted images of a triangular aperture by the doctrine of interferences, and the explanation of the coloured Lemniscates seen by polarized light in biaxal crystals, given by Young and by Herschel: and still more marked is another case, in which the curves are unsymmetrical, namely, the curves seen by passing polarized 238 light through plates of quartz, which agree in a wonderful manner with the calculations of Airy. To these we may add the curious phenomena, and equally curious mathematical explanation, of Conical Refraction, as brought to view by Professor Lloyd and Sir W. Hamilton. Indeed, the whole history both of Physical Optics and of Physical Astronomy is a series of felicities of this kind, as we have elsewhere observed. Such applications of theory, and unforeseen explanations of new facts by complicated trains of reasoning necessarily flowing from the theory, are strong proof of the truth of the theory, while it is in the course of being established; but we are here rather speaking of them as applications of the theory after it has been established.
Those who thus apply principles already discovered are not to be ranked in their intellectual achievements with those who discover new principles; but still, when such applications are masked by the complex relations of space and number, it is impossible not to regard with admiration the clearness and activity of intellect which thus discerns in a remote region the rays of a central truth already unveiled by some great discoverer.
8. As examples in other fields of the application of a scientific discovery to the explanation of natural phenomena, we may take the identification of Lightning with electricity by Franklin, and the explanation of Dew by Wells. For Wells’s Inquiry into the Cause of Dew, though it has sometimes been praised as an original discovery, was, in fact, only resolving the phenomenon into principles already discovered. The atmologists of the last century were aware[51] that the vapour which exists in air in an invisible state may be condensed into water by cold; and they had noticed that there is always a certain temperature, lower than that of the atmosphere, to which if we depress bodies, water forms upon them in fine drops. This temperature is the limit of that which is 239 necessary to constitute vapour, and is hence called the constituent temperature. But these principles were not generally familiar in England till Dr. Wells introduced them into his Essay on Dew, published in 1814; having indeed been in a great measure led to them by his own experiments and reasonings. His explanation of Dew,—that it arises from the coldness of the bodies on which it settles,—was established with great ingenuity; and is a very elegant confirmation of the Theory of Constituent Temperature.
[51] Hist. Ind. Sc. b. x. c. iii. sect. 5.
9. As other examples of such explanations of new phenomena by a theory, we may point out Ampère’s Theory that Magnetism is transverse voltaic currents, applied to explain the rotation of a voltaic wire round a magnet, and of a magnet round a voltaic wire. And again, in the same subject, when it had been proved that electricity might be converted into magnetism, it seemed certain that magnetism might be converted into electricity; and accordingly Faraday found under what conditions this may be done; though indeed here, the theory rather suggested the experiment than explained it when it had been independently observed. The production of an electric spark by a magnet was a very striking exemplification of the theory of the identity of these different polar agencies.