1848.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



325 



vinced, to a fixed standard. Thus far only is he called upon 

 to yield to the experience of his predecessors in the same 

 pursuit — to give credence to their assertion that all the know- 

 ledere which he requires may he deri-\-ed from the elementary 

 principles which they lay down. The accuracy of those prin- 

 ciples, and the legitimacy of the inferences from them, he must 

 determine for himself hv the effort of his own mind, indepen- 

 dently of— if he please,' in defiance of— the influence of stan- 

 dard authorities. 



By adopting- the method, here insisted upon as all-important, 

 of referring every question to a few first principles, his science 

 becomes a connected chain of reasoning, and acquires the two 

 great advantages of method, certainty and facility — certainty of 

 the accuracy of his knowledge, facility in applying it. This 

 power, however, of tracing the mutual connection of the 

 several parts of mechanics, and the ultimate dependence of 

 each part upon elements common to them all, is to he ac- 

 quired only hy long-continued habit. There are certain prac- 

 tical difficulties however in the exercise of it, of which the student 

 ought to be forewarned, and Mhich act as snares upon his judg- 

 ment ; oftentimes inducing him to believe that he traces a logical 

 consequence where none in reality exists. 



Of these sources of error in the pursuit of mechanical science, 

 the most important are included among Bacon's idola fori— idols or 

 fallacies, of which the power arises in the forum or common inter- 

 course of mankind — the defects of words — the names c* non-exist- 

 encies, or confused names of existencies. Language can never be 

 so perfectly refined as to avoid entirely this disadvantage, for while 

 the subtlety of nature is infinite, the subtlety of words is finite, 

 and, in general, serves only to nominate general ideas, and not 

 their minutest distinctions. In erecting the lofty edifice of science 

 on so narrow a basis as a few elementary definitions and axioms, 

 extreme exactness in the use of words is therefore requisite ; and 

 beautifully is it said, that when we attempt to rear a temple to 

 heaven, we must not be unmindful of the confusion of languages. 



Of no science have the principles been subject to more vehement 

 and learned debate than mechanics ; yet most of these debates 

 have been ultimately discovered to be mere logomachies — disputes 

 about words — which, it is therefore reasonable to suppose, would 

 never have arisen had it been possible originally to give sti-ict de- 

 finitions of the terms involved. Perhaps the most instructive 

 example of a learned controversy turning out to be a mere strife 

 of words, is that resi)ecting Vis Viva — a term retained in modern 

 science as a mere technicality, of which the interpretation does not 

 depend on any mechanical knowledge, but is purely conventional 

 and arbitrary. The following account of the controversy is taken 

 from AValton's " Mechanical Problems," a work, the value of which 

 to the English student of the physical applications of mathe- 

 matics, it would be difficult to over-estimate : — 



" Leibnitz contended, in opposition to the received doctrines of 

 the Cartesians, that the proper measure of the \'is Viva, or 

 Moving Force of a body, is the product of the mass into the square 

 of the velocity; the measure adopted by the disciples of Descartes 

 having been the same as that of the Quantity of Motion — namely, 

 the product of the mass and the first power of the velocity. This 

 contrariety of opinion in respect to the estimation of Moving 

 Force, gave rise to one of the most memorable controversies in the 

 annals of philosophy ; almost all the mathematicians of Europe 

 ultimately arranging tliemselves as partisans, either of the Car- 

 tesian or Leibnitzian doctrine. Among the adlierents of Leibnitz 

 may be mentioned John and Daniel Bernouilli, Poleni, 'sGrave- 

 sande, Camus, Muschenbroek, Papin, Hermann, Bulfinger, Koenig, 

 and eventually Madame du Chatelet ; while in the opposite ranks 

 may be named' Maclaurin, Clarke, Stirling, Desaguliers, Catalan, 

 Robins, Mairan, and Voltaire. * * « * The memorable 

 controversy of Vis Viva, after raging for the space of about thirty 

 years, was finally set at rest by the luminous observations of 

 D'Alembert, in the preface to his ' Di/namique,' who declared the 

 whole dispute to be a mere question of terms, and as having no 

 possible connection with the fundamental principles of mechanics. 

 Since tlie publication of D'Alembert's work, the term Vis Viva has 

 been used to signify merely the algebraical product of the mass of 

 a mo\'ing body and the square of its velocity ; while the words 

 Moving Force have been universally employe'd, agreeably to the 

 definition given by Newton in the ' Principia,' in the signification 

 of the product of the mass of a body and the accelerating force 

 to which it is conceived to be subject: 'no physical theory whatever, 

 in regard to the absolute nature of the force, being supposed to be 

 involved in these definitions." 



Technicalities expressing the elementaiy ideas of mechanics are 



idola fori belonging to the commencement of the science : other 

 and different difficulties of language occur in its ultimate conclu- 

 sions. Among the remote results of elaborate investigation are 

 certain general theorems, exceedingly extensive and useful in their 

 application ; but which, if inaccurately enunciated, may be made 

 to include cases which do not belong to them, and exclude others 

 legitimately within their province. These difficulties may be 

 termed questions of jurisdictions. When the language of a general 

 theorem does not indicate with precision its jurisdiction over any 

 particular case, or its proper mode of application to it, the only 

 legitimate mode of arriving at a decision is by tracing the processes 

 by which the theorem itself has been arrived at, and considering 

 whether the particular case in question was contemplated in them. 

 The general mechanical theorems have so vast and varied applica- 

 tions, that the bare enunciation of them,howe\'er carefully expressed, 

 is utterly insufficient to convey to the student's mind an idea of 

 all their consequences. Their actual operation, and the boundaries 

 which define their power, qiios utra citruque nequit consistere rectum., 

 can be fully learned only by actual practice. In this respect, the 

 science of jurisprudence presents a striking analogy. We are accus- 

 tomed to reverence the common law of England as the accumulated 

 wisdom of ages — the combination of the most subtle sagacity and 

 the most extensive experience. But who does not know that a 

 bare acquaintance with the gener.al principles of law is practically 

 insufficient for the solution of particular cases — that amidst the 

 infinite variety of combinations to which the business of life gives 

 rise, the abstract rule cannot be successfully applied without a cer 

 tain intellectual dexterity, which long experience and constant 

 practice alone confer.'' 



The importance to the mechanical student of expertness 

 similarly acquired, can scarcely be o\'er-rated. His efforts 

 should be incessantly exerted in the application of mechani- 

 cal principles to the direct solution of problems ; and it is 

 scarcely too much to assert, that his knowledge of the science 

 will be proportional to the number of problems wliich he 

 ►solves. The most trivial incidents of his every-day life — every 

 weight which he moves, every action of his muscles, suggest 

 cases fruitful with instruction respecting the laws of force. 

 There is not a single spot in the material world, free from 

 the influence of force ; and he has hut to look around him, 

 to discern innumerable instances in which the rationale of 

 their action may be investigated, and the consequences of 

 them predicted. This unintermitted habit of ransacking the 

 stores of nature, of tracing the most trivial and tlie grandest 

 of her operations to first principles, strengthens and confirms 

 the power of investigation, and reduces those effects of the 

 material laws which on a superficial view appear confused and 

 disconnected, to one harmonious and simple system. 



Another class of errors peculiarly incident to our science, is 

 that arising from incorrectness of data — the neglect of operating 

 causes, either from absolute oversight or from an impression that 

 their effect is inconsiderable. The first of these mistakes will 

 seldom be made, except by an inexperienced student ; and may 

 be altogether avoided by practice and care in conceiving the 

 exact nature of the question before him. As a useful pre- 

 caution against this difficulty, he should habituate himself to 

 test the accuracy of his conclusions by particular instances, and 

 by varying this test within the widest legitimate limits. If, in 

 any one instance, his general investigations lead to an absurd 

 consequence, they are themselves erroneous ; and it «ill be ne- 

 cessary to re-exanvne them, and ascertain at what step the 

 error arose. 



There are more difficult cases, however, where the neglect 

 of data arises, not from oversight, but from necessity — where 

 the complexities of the question are such, as to render its 

 solution impracticable without hypothetical simplifications. In 

 all such instances, the in\ estigator must remember that he is 

 solving, not a question of real existence, but an artificial case — 

 making the nearest approach to it which his powers of inves- 

 tigation permit. In practical mechanics, this consideration is 

 especially important ; and, as a general rule, no such hypothe- 

 tical simplification should be admitted — or at least acted upon — 

 without some estimate of the limits of the error which it may 

 possibly induce. 



Complicated mathematical formulse are wholly unsuited for the 

 practical application of mechanics, on account of the refine- 

 ment and exactness of both workmanship and computation which 

 they require. The only formulse which the practical artisan 

 or mechanic will truist, are those which he can readily apply, 

 and which afford a margin for all the diversified circumstances 

 of practice, unavoidable and unknown imperfections of materials, 



