found relief in the charms of music, and strangely enough dreaded an exhaustion of it, just as many other people who have not the excuse of morbid ailment think that all the greatest possible discoveries have been made, and that all the finest things in prose and verse have been said. Such notions are denied by the laws which have been stated, as exemplified not only in the diversity and might of modern achievement, but also in the deep relations between the elements of natural action divulged by their very multiplication of effects; the generalizations of this age have never been equaled in scope and force—the persistence of force and the theory of evolution.
As sciences advance, their essential unity becomes more and more evident; methods that at first view would seem utterly unconnected are being constantly found to have a secret and helpful family tie. The comparative value of various types of bridges has been investigated by submitting glass models duly weighted to polarized light, which shows at once the distributions of strain and pressure. A common magnetic needle has been successfully employed in finding weak places in iron and steel axles by its unequal deflection at such points, due to internal heterogeneity in the mass examined. At Paris recently an underground pneumatic tube became obstructed at an unknown point; excavation was correctly guided by the adoption of an acoustic principle; a loud sound was made at the tube's entrance, and the time occupied before the reflected wave returned was carefully noted, from which was inferred the distance traversed by it to and from the obstacle. Many instruments at first made for purely philosophical study have been drafted into the world's practical uses. Applications of the rheostat and Wheatstone's bridge serve to locate the oft-recurring breaks in ocean-cables and telegraph-lines, and have very lately yielded the marvellous duplex and quadruplex telegraphs. The spectroscope, originally directed to the heavens, has now found uses on earth of great value; it detects adulteration, marks defectiveness in drainage, and points out impurities in water-supplies.[1]
- ↑ A proposition in pure mathematics may receive elucidation and extension by an illustration taken from optics. In Newton's "Principia," book i., section xii., prop. 70, he proves, in a manner very difficult to follow, that a corpuscle placed within a hollow sphere, if attracted as the square of the distance by all the points in the concave surface, will remain unmoved wherever placed, as the sums of attraction always balance.
This may be made clear not only of a spherical surface, but the closed interior of any surface whatever, provided it has no reëntrant angles, as a pyramid or an obliquely-truncated cone.
For, imagine the corpuscle to be luminous and to be bisected by any plane extended so as to cut the containing hollow surface into two parts, it is evident that equal amounts of light are radiated by each half of the corpuscle on each of the two parts of the surface containing it. Now, these rays diminish in intensity as the square of the distance, and so reciprocally correspond with a force emanating according to the same law from the surface and affecting the corpuscle. Hence, the area of the surface of any hollow body, having no reëntrant angles, varies as the square of its average distance from any point within it.
