PRELIMINARY DISSERTATION

ON THE

HARMONY OF THEORY AND PRACTICE IN MECHANICS.*

THE words, theory and practice, are of Greek origin: they carry our thoughts back to the time of those ancient philosophers by whom they were contrived; and by whom also they were contrasted and placed in opposition, as denoting two conflicting and mutually inconsistent ideas.

In geometry, in philosophy, in poetry, in rhetoric, and in the fine arts, the Greeks are our masters; and great are our obligations to the ideas and the models which they have transmitted to our times. But in physics and in mechanics their notions were very generally pervaded by a great fallacy, which attained its complete and most mischievous development amongst the medieval schoolmen, and the remains of whose influence can be traced even at the present day-the fallacy of a double system of natural laws; one theoretical, geometrical, rational, discoverable by contemplation, applicable to celestial, ætherial, indestructible bodies, and being an object of the noble and liberal arts; the other practical, mechanical, empirical, discoverable by experience, applicable to terrestrial, gross, destructible bodies, and being an object of what were once called the vulgar and sordid arts.

The so-called physical theories of most of those whose understandings were under the influence of that fallacy, being empty dreams, with but a trace of truth here and there, and at variance with the results of every-day observation on the surface of the planet we inhabit, were calculated to perpetuate the fallacy. The stars were celestial, incorruptible bodies; their orbits were circular and their motions perpetual; such orbits and motions being characteristic of perfection. Objects on the earth's surface were terrestrial

This Dissertation contains the substance of a discourse, "De Concordiâ inter Scientiarum Machinalium Contemplationem et Usum," read before the Senate of the University of Glasgow on the 10th of December, 1855, and of an inaugural lecture, delivered to the Class of Civil Engineering and Mechanics in that University on the 3d of January, 1856.

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and corruptible; their motions being characteristic of imperfection, were in mixed straight and curved lines, and of limited duration. Rational and practical mechanics (as Newton observes in his preface to the Principia) were considered as in a measure opposed to each other, the latter being an inferior branch of study, to be cultivated only for the sake of gain or some other material advantage. Archytas of Tarentum might illustrate the truths of geometry by mechanical contrivances; his methods were regarded by his pupil Plato as a lowering of the dignity of science. Archimedes, to the character of the first geometer and arithmetician of his day, might add that of the first mechanician and physicist, might, by his unaided strength acting through suitable machinery, move a loaded ship on dry land, he might contrive and execute deadly engines of war, of which even the Roman soldiers stood in dread, he might, with an art afterwards regarded as fabulous till it was revived by Buffon, burn fleets with the concentrated sunbeams; but that mechanical knowledge, and that practical skill, which, in our eyes, render that great man so illustrious, were, by men of learning, his contemporaries and successors, regarded as accomplishments of an inferior order, to which the philosopher, from the height of geometrical abstraction, condescended, with a view to the service of the State. In those days the notion arose that scientific men were unfit for the business of life, and various facetious anecdotes were contrived illustrative of this notion, which have been handed down from age to age, and in each age applied, with little variation, to the eminent philosophers of the time.

That the Romans were eminently skilful in many departments of practical mechanics, especially in masonry, road-making, and hydraulics, is clearly established by the existing remains of their magnificent works of engineering and architecture, from many of which we should do well to take a lesson. But the fallacy of a supposed discordance between rational and practical, celestial and terrestrial mechanics, still continued in force, and seems to have gathered strength, and to have attained its full vigour during the middle ages. In those ages, indeed, were erected those incomparable ecclesiastical buildings, whose beauty, depending, as it does, mainly on the nice adjustment of the form, strength, and position of each part, to the forces which it has to sustain, evinces a pre found study of the principles of equilibrium on the part of the architects. But the very names of those architects, with few and doubtful exceptions, were suffered to be forgotten; and the principles which guided their work remain unrecorded, and were left to be re-discovered in our own day; for the scholars of those times, despising practice and observation, were occupied in developing and magnifying the numerous errors, and in perverting and obscur

PRELIMINARY DISSERTATION.

ing the much more numerous truths, which are to be found in the writings of Aristotle; and those few men who, like Roger Bacon, combined scientific with practical knowledge, were objects of fear and persecution, as supposed allies of the powers of darkness.

At length, during the great revival of learning and reformation of science in the fifteenth, sixteenth, and seventeenth centuries, the system falsely styled Aristotelian was overthrown: so also was the fallacy of a double system of natural laws; and the truth began to be duly appreciated, that sound theory in physical science consists simply of facts, and the deductions of common sense from them, reduced to a systematic form. The science of motion was founded by Galileo, and perfected by Newton. Then it was established that celestial and terrestrial mechanics are branches of one science; that they depend on one and the same system of clear and simple first principles; that those very laws which regulate the motion and the stability of bodies on earth, govern also the revolutions of the stars, and extend their dominion throughout the immensity of space. Then it came to be acknowledged, that no material object, however small,-no force, however feeble, no phenomenon, however familiar, is insignificant, or beneath the attention of the philosopher; that the processes of the workshop, the labours of the artizan, are full of instruction to the man of science; that the scientific study of practical mechanics is well worthy of the attention of the most accomplished mathematician. Then the notion, that scientific men are unfit for business, began to disappear. It was not court favour, not high connection, not Parliamentary influence, which caused Newton to be appointed Warden, and afterwards Master, of the Mint; it was none of these; but it was the knowledge possessed by a wise minister of the fact, that Newton's skill, both theoretical and practical, in those branches of knowledge which that office required, rendered him the fittest man in all Britain to direct the execution of a great reform of the coinage. Of the manner in which Newton performed the business entrusted to him, we have the following account in the words of Lord Macaulay, an author who cannot be accused of undue partiality to speculative science or its cultivators :—

"The ability, the industry, and the strict uprightness of the great philosopher, speedily produced a complete revolution throughout the department which was under his direction. He devoted himself to the task with an activity which left him no time to spare for those pursuits in which he had surpassed Archimedes and Galileo. Till the great work was completely done, he resisted firmly, and almost angrily, every attempt that was made by men of science, here or on the Continent, to draw him away from his official duties."

Vol. iv., p. 703.

Then the historian proceeds to detail the results of Newton's exertions, and shows, that within a short time after his appointment, the weekly amount of the coinage of silver was increased to eightfold of that which had been looked upon as the utmost practicable amount by his predecessors.

The extension of experimental methods of investigation, has caused even manual skill in practical mechanics, when scientifically exercised, to be duly honoured, and not (as in ancient times) to be regarded as beneath the dignity of science.

As a systematically avowed doctrine, there can be no doubt that the fallacy of a discrepancy between rational and practical mechanics came long ago to an end; and that every well-informed and sane man, expressing a deliberate opinion upon the mutual relations of those two branches of science, would at once admit that they agree in their principles, and assist each other's progress, and that such distinction as exists between them arises from the difference of the purposes to which the same body of principles is applied.

If this doctrine had as strong an influence over the actions of men as it now has over their reasonings, it would have been unnecessary for me to describe, so fully as I have done, the great scientific fallacy of the ancients. I might, in fact, have passed it over in silence, as dead and forgotten; but, unfortunately, that discrepancy between theory and practice, which in sound physical and mechanical science is a delusion, has a real existence in the minds of men; and that fallacy, though rejected by their judgments, continues to exert an influence over their acts. Therefore it is that I have endeavoured to trace the prejudice as to the discrepancy of theory and practice, especially in Mechanics, to its origin; and to show that it is the ghost of a defunct fallacy of the ancient Greeks and of the medieval schoolmen.

This prejudice, as I have stated, is not to be found, at the present day, in the form of a definite and avowed principle: it is to be traced only in its pernicious effects on the progress both of speculative science and of practice, and sometimes in a sort of tacit influence which it exerts on the forms of expression of writers, who have assuredly no intention of perpetuating a delusion. To exemplify the kind of influence last referred to, I shall cite a passage from the same historical work which I recently quoted for a differ ent purpose. Lord Macaulay, in treating of the Act of Toleration of William III., compares, metaphorically, the science of politics to that of mechanics, and then proceeds as follows :—

"The mathematician can easily demonstrate that a certain power, applied by means of a certain lever, or of a certain system of pulleys, will suffice to raise a certain weight. But his demonstration proceeds on the supposition that the machinery is such as no load will bend or break. If

PRELIMINARY DISSERTATION.

the engineer who has to lift a great mass of real granite by the instrumentality of real timber and real hemp, should absolutely rely on the propositions which he finds in treatises on Dynamics, and should make no allowance for the imperfection of his materials, his whole apparatus of beams, wheels, and ropes, would soon come down in ruin, and with all his geometrical skill, he would be found a far inferior builder to those painted barbarians who, though they never heard of the parallelogram of forces, managed to pile up Stonehenge."*

It is impossible to read this passage without feeling admiration for the force and clearness (and I may add, for the brilliancy and wit) of the language in which it is expressed; and those very qualities of force and clearness, as well as the author's eminence, render it one of the best examples that can be found to illustrate the lurking influence of the fallacy of a double set of mechanical laws, rational and practical.

In fact, the mathematical theory of a machine,—that is, the body of principles which enables the engineer to compute the arrangement and dimensions of the parts of a machine intended to perform given operations,-is divided by mathematicians, for the sake of convenience of investigation, into two parts. The part first treated of, as being the more simple, relates to the motions and mutual actions of the solid pieces of a machine, and the forces exerted by and upon them, each continuous solid piece being treated as a whole, and of sensibly invariable figure. The second and more intricate part relates to the actions of the forces tending to break or to alter the figure of each such solid piece, and the dimensions and form to be given to it in order to enable it to resist those forces: this part of the theory depends, as much as the first part, on the general laws of mechanics; and it is, as truly as the first part, a subject for the reasonings of the mathematician, and equally requisite for the completeness of the mathematical treatise which the engineer is supposed to consult. It is true, that should the engineer implicitly trust to a pretended mathematician, or an incomplete treatise, his apparatus would come down in ruin, as the historian has stated: it is true also that the same result would follow, if the engineer was one who had not qualified himself, by experience and observation, to distinguish between good and bad materials and workmanship; but the passage I have quoted conveys an idea different from these; for it proceeds on the erroneous supposition, that the first part of the theory of a machine is the whole theory, and is at variance with something else which is independent of mathematics, and which constitutes, or is the foundation of, practical mechanics.

The evil influence of the supposed inconsistency of theory and

• Vol. iii., p. 84.