To the same effect are remarks by Professor J. Hopkinson:—“Doubling the thickness of a cylinder by no means doubles its strength. Conversely, doubling the strength of the material will permit the thickness to be diminished to much less than one half. Until 1869 hydraulic presses were mostly made of cast iron. There was much astonishment at the great reduction in thickness and weight which became possible when steel was substituted for the weaker material. In the case of guns it is well-known that greater strength can be obtained if the outer hoops are shrunken on the inner ones. Mathematical theory tells us what amount of shrinkage should give the best results. A gun may have a shrinkage so great as to weaken it.”
He continues:—“Mathematical treatment of any problem is always analytical—attention is concentrated upon certain facts, and for the moment other facts are neglected. For example, in dealing with the thermodynamics of the steam engine, one dismisses from consideration very vital points essential to the successful working of the engine—questions of strength of parts, lubrication, convenience for repairs. But if an engineer is to succeed he must not fail to consider every element necessary to success; he must have a practical instinct which will tell him whether the engine as a whole will succeed. His mind must not be only analytical, or he will be in danger of solving bits of the problems which his work presents, and of falling into fatal mistakes on points which he has omitted to consider, and which the plainest, intelligent, practical man would avoid almost without knowing it. Again, the powers of the strongest mathematician being limited, there is a constant temptation to fit the facts to suit the mathematics, and to assume that the conclusions will have greater accuracy than the premises from which they are deduced. This is a trouble one meets with in other applications of mathematics to experimental science. In order to make the subject amenable to treatment, one finds, for example, in the science of magnetism, that it is boldly assumed that the magnetization of magnetizable material is proportionate to the magnetizing force, and the ratio has a name given to it, and conclusions are drawn from the assumption; but the fact is, no such proportionality exists, and all conclusions resulting from the assumption are so far invalid. Whenever possible the mathematical deductions should be frequently verified by reference to observation and experiment, for the very simple reason that they are only deductions, and the premises from which the deductions are drawn may be inaccurate or incomplete. We must always remember that we cannot get more out of the mathematical mill than we put into it, though we may get it in a form infinitely more useful for our purpose.”
Professor Alexander Bain in his “Senses and the Intellect” concludes:—“A sound judgment, meaning a clear and precise perception of what is really effected by the contrivances employed, is to be looked upon as the first requisite of the practical man. He may be meagre in intellectual resources, he may be slow in getting forward and putting together the appropriate devices, but if his perception of the end is unfaltering and strong, he will do no mischief and practice no quackery. He may have to wait long in order to bring together the apposite machinery, but when he has done so to the satisfaction of his own thorough judgment, the success will be above dispute. Judgment is in general more important than fertility; because a man by consulting others and studying what has been already done, may usually obtain suggestions enough, but if his judgment of the end is loose, the highest exuberance of intellect is only a snare.”
Judgment Moves to New Fields.
As applied science rises to higher and higher planes, a good many questions which were once matters of judgment, become subjects of estimate, often precise. A century ago the forms of ships were decided by sheer sagacity; to-day, as we have seen in this book, such forms are of definite approved types, each adapted to specific needs, and never departed from by a prudent designer except in slight and carefully noted variations. Such examples may be drawn from many another field where science and industry join hands, especially in every branch of modern engineering. A new power-plant, in every detail of its installation, is so standardized that a competent corps of erectors, from any part of the civilized world, can readily put it together. Its designers from first to last have sought to make operation easy, and every working part “fool-proof.” In case of accident any item of the structure broken or deranged can be supplied by the builders at once.
All this does not mean that science in its onward march is eliminating the need for judgment, but simply that judgment is constantly passing into territory wholly new. In devising gas-engines of novel principle, in combining chemicals for new economies of illumination, the faculty of judgment enters provinces vastly broader than those from which it has retired as its approximations have given place to exact measurements. Manual skill has of late undergone a similar change of scope. Many a modern machine performs hammering, punching, riveting more effectively and swiftly than human hands, so that here an operator of little skill replaces a mechanic of much skill. But in another and higher field, deftness was never more in request than to-day. In the final adjustments of a voltmeter, of a refractometer, in the last polish given to an observatory lens, a delicacy of touch is demanded compared with which the dexterity of an old-time planisher or file-grinder is mere clumsiness.
CHAPTER XXVI
NEWTON, FARADAY AND BELL AT WORK
Newton, the supreme generalizer . . . Faraday, the master of experiment . . . Bell, the inventor of the telephone, transmits speech by a beam of light.