Many other curious facts might be mentioned which when once noticed were explained as the effects of well-known laws. It was accidentally discovered that the navigation of canals of small depth could be facilitated by increasing the speed of the boats, the resistance being actually reduced by this increase of speed, which enables the boat to ride as it were upon its own forced wave. Now mathematical theory might have predicted this result had the right application of the formulæ occurred to any one.[446] Giffard’s injector for supplying steam boilers with water by the force of their own steam, was, I believe, accidentally discovered, but no new principles of mechanics are involved in it, so that it might have been theoretically invented. The same may be said of the curious experiment in which a stream of air or steam issuing from a pipe is made to hold a free disc upon the end of the pipe and thus obstruct its own outlet. The possession then of a true theory does not by any means imply the foreseeing of all the results. The effects of even a few simple laws may be manifold, and some of the most curious and useful effects may remain undetected until accidental observation brings them to our notice. .
Predicted Discoveries.
The most interesting of the four classes of facts specified in p. [525], is probably the third, containing those the occurrence of which has been first predicted by theory and then verified by observation. There is no more convincing proof of the soundness of knowledge than that it confers the gift of foresight. Auguste Comte said that “Prevision is the test of true theory;” I should say that it is one test of true theory, and that which is most likely to strike the public attention. Coincidence with fact is the test of true theory, but when the result of theory is announced before-hand, there can be no doubt as to the unprejudiced spirit in which the theorist interprets the results of his own theory.
The earliest instance of scientific prophecy is naturally furnished by the science of Astronomy, which was the earliest in development. Herodotus[447] narrates that, in the midst of a battle between the Medes and Lydians, the day was suddenly turned into night, and the event had been foretold by Thales, the Father of Philosophy. A cessation of the combat and peace confirmed by marriages were the consequences of this happy scientific effort. Much controversy has taken place concerning the date of this occurrence, Baily assigning the year 610 B.C., but Airy has calculated that the exact day was the 28th of May, 584 B.C. There can be no doubt that this and other predictions of eclipses attributed to ancient philosophers were due to a knowledge of the Metonic Cycle, a period of 6,585 days, or 223 lunar months, or about 19 years, after which a nearly perfect recurrence of the phases and eclipses of the moon takes place; but if so, Thales must have had access to long series of astronomical records of the Egyptians or the Chaldeans. There is a well-known story as to the happy use which Columbus made of the power of predicting eclipses in overawing the islanders of Jamaica who refused him necessary supplies of food for his fleet. He threatened to deprive them of the moon’s light. “His threat was treated at first with indifference, but when the eclipse actually commenced, the barbarians vied with each other in the production of the necessary supplies for the Spanish fleet.”
Exactly the same kind of awe which the ancients experienced at the prediction of eclipses, has been felt in modern times concerning the return of comets. Seneca asserted in distinct terms that comets would be found to revolve in periodic orbits and return to sight. The ancient Chaldeans and the Pythagoreans are also said to have entertained a like opinion. But it was not until the age of Newton and Halley that it became possible to calculate the path of a comet in future years. A great comet appeared in 1682, a few years before the first publication of the Principia, and Halley showed that its orbit corresponded with that of remarkable comets recorded to have appeared in the years 1531 and 1607. The intervals of time were not quite equal, but Halley conceived the bold idea that this difference might be due to the disturbing power of Jupiter, near which the comet had passed in the interval 1607–1682. He predicted that the comet would return about the end of 1758 or the beginning of 1759, and though Halley did not live to enjoy the sight, it was actually detected on the night of Christmas-day, 1758. A second return of the comet was witnessed in 1835 nearly at the anticipated time.
In recent times the discovery of Neptune has been the most remarkable instance of prevision in astronomical science. A full account of this discovery may be found in several works, as for instance Herschel’s Outlines of Astronomy, and Grant’s History of Physical Astronomy, Chapters XII and XIII.
Predictions in the Science of Light.
Next after astronomy the science of physical optics has furnished the most beautiful instances of the prophetic power of correct theory. These cases are the more striking because they proceed from the profound application of mathematical analysis and show an insight into the mysterious workings of matter which is surprising to all, but especially to those who are unable to comprehend the methods of research employed. By its power of prevision the truth of the undulatory theory of light has been conspicuously proved, and the contrast in this respect between the undulatory and Corpuscular theories is remarkable. Even Newton could get no aid from his corpuscular theory in the invention of new experiments, and to his followers who embraced that theory we owe little or nothing in the science of light. Laplace did not derive from the theory a single discovery. As Fresnel remarks:[448]
“The assistance to be derived from a good theory is not to be confined to the calculation of the forces when the laws of the phenomena are known. There are certain laws so complicated and so singular, that observation alone, aided by analogy, could never lead to their discovery. To divine these enigmas we must be guided by theoretical ideas founded on a true hypothesis. The theory of luminous vibrations presents this character, and these precious advantages; for to it we owe the discovery of optical laws the most complicated and most difficult to divine.”
Physicists who embraced the corpuscular theory had nothing but their own quickness of observation to rely upon. Fresnel having once seized the conditions of the true undulatory theory, as previously stated by Young, was enabled by the mere manipulation of his mathematical symbols to foresee many of the complicated phenomena of light. Who could possibly suppose, that by stopping a portion of the rays passing through a circular aperture, the illumination of a point upon a screen behind the aperture might be many times multiplied. Yet this paradoxical effect was predicted by Fresnel, and verified both by himself, and in a careful repetition of the experiment, by Billet. Few persons are aware that in the middle of the shadow of an opaque circular disc is a point of light sensibly as bright as if no disc had been interposed. This startling fact was deduced from Fresnel’s theory by Poisson, and was then verified experimentally by Arago. Airy, again, was led by pure theory to predict that Newton’s rings would present a modified appearance if produced between a lens of glass and a plate of metal. This effect happened to have been observed fifteen years before by Arago, unknown to Airy. Another prediction of Airy, that there would be a further modification of the rings when made between two substances of very different refractive indices, was verified by subsequent trial with a diamond. A reversal of the rings takes place when the space intervening between the plates is filled with a substance of intermediate refractive power, another phenomenon predicted by theory and verified by experiment. There is hardly a limit to the number of other complicated effects of the interference of rays of light under different circumstances which might be deduced from the mathematical expressions, if it were worth while, or which, being previously observed, can be explained. An interesting case was observed by Herschel and explained by Airy.[449]