again in his own inventions, which were in turn to give a further impulse to scientific work. A very large proportion of the engineer's success was due to his regarding infinitesimals; and in respect to this point it was appropriate for the speaker to show how greatly infinitesimals or "next-to-nothings" determine the strength, the fitness, and the durability of works and materials. Take the case of steel, which in times that are not very old was dealt with and tested in a "rule-of-thumb" fashion. It was known to be a compound of iron and carbon—
"but the importance of exactness in the percentage was but little understood, nor was it at all understood how the presence of comparatively small quantities of foreign matter might necessitate the variation of the proportions of carbon. The consequence was, that anomalous results every now and then arose to confound the person who had used the steel, and, falsifying the proverb 'true as steel,' steel became an object of distrust. Is it too much to say that Bessemer's great invention of steel made by the 'converter,' and that Siemens's invention of the open-hearth process, reacted on pure science, and set scientific men to investigate the laws which regulate the union of metals and of metalloids, and that the labors of these scientific men have improved the manufacture, so that steel is now thoroughly and entirely trusted? By its aid engineering works are accomplished which, without that aid, would have been simply impossible. The Forth Bridge, the big gun, the compound armor of the ironclad with its steel face—all equally depend upon the 'truth' of steel as much as does the barely visible hair-spring of the chronometer, which enables the longitude of the ship in which it is carried to be ascertained. Now, what makes the difference between trustworthy and untrustworthy steel for each particular purpose? Something which, until our better sense comes to our aid, we are inclined to look upon as ridiculously insignificant—a 'next-to-nothing.' Setting extraneous ingredients aside, and considering only the union of iron and carbon, the question whether there shall be added or deducted one tenth of one per cent of carbon is a matter of great importance in the resulting quality of the steel. This is a striking practical instance of how apparently insignificant things may be of the highest importance. The variation of this fraction of a percentage may render your boiler-steel untrustworthy, may make the difference between safety in a gun and danger in a gun, and may render your armor-piercing projectile unable to pierce even the thinnest wrought-iron armor."
So the effects upon steel of adding manganese—whether it shall improve or deteriorate the metal—are matters of rather delicate calculation—
"and the effects of the addition of even the very smallest percentages of aluminum upon the steel with which it may be alloyed are very striking and very peculiar, giving to the steel alloy thus produced a very much greater hardness, and enabling it to take a much brighter and more silver-like polish. Further, the one twentieth part of one per cent of aluminum, when added to molten wrought-iron, will reduce the fusing-point of the whole mass some five hundred degrees, and will render it extremely fluid."
The engineer engaged in electrical matters is also often compelled to realize the importance of the "next-to-nothing," as in the case of the influence which an extremely minute percentage of impurity has on the electrical conductivity of copper wire. This conductivity is, in some cases, reduced as much as fifty per cent, in consequence of the admixture of that which, under other circumstances, would be looked upon as insignificant.
The internal strain which a great gun may suffer in the process of oil-hardening, by the operation of which it may be self-ruptured months afterward, is gauged in the most minute fractions of an inch. The various degrees to which a tool is tempered according to the uses to which it is to be adapted, all depend upon the "next-to-nothing" differences in the temperature to which the metal is heated. Then—
"consider the bicycles and tricycles of the present day—machines which afford the means of healthful exercise to thousands, and which will probably, in a very short time, prove of the very greatest possible use for military purposes. The perfection to which these machines have been brought is almost entirely due to strict attention to detail; in
