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THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[NoVEMBEn, 



eaitli's surface, anil their perfdrmances observed witli extreme 

 CHution. The discrepancies observed between tliese results and 

 those of theory are so minute, that no one but a mathematician 

 would refjard them ; and he successfully ascertains that they 

 arise from incidental circumstances, wholly independent of theo- 

 retical computations. 



Such results are magnificent exhibitions of the powers of the 

 mechanical sciences. The tests of their accuracy are immea- 

 surably more varied, more numerous, and more minute, severer, 

 lonjrer continued, and executed on a ^-ander scale, than those 

 to which any other natural science is subjected. But the accu- 

 racy of a system is not absolutely proved by the circumstance 

 that in any finite number of instances it leads to rij;ht con- 

 clusions. It is possible — though excessively improbable — that 

 this accuracy is, in every case, merely the result of fortu- 

 nate guesses. And this view of the subject is not so very 

 unnatural, when it is remembered that such fortuitous anticipa- 

 tions, though very remarkable, are by no means uncommon, and 

 that some of the most important laws of mechanics were won- 

 derfully felicitous conjectures long before they were demonstrated 

 truths. 



The absolute certaintj-, then, of mechanical science must rest 

 on yet higher grounds. Its su))reme authority consists in this — 

 that all its conclusions are rigonmsly logical inferences from 

 indisputable elementary laws. The iihilosopher has a right to 

 deriiuiid unreserved credence so far, and only so far, as he can 

 establish such inferences. The demonstrative truth of his results 

 depends on the answers to these two questions — Are the ele- 

 mentary laws indisputable ? — Are the deductions from them 

 rigorously logical .'' These are the two bases of the whole evi- 

 pence. Let them be considered in their respective order, for the 

 right comprehension of them will gi-eatly facilitate the object 

 proposed in the present inquiry — namely, to explain tb.e prelimi- 

 nary difficulties of the study of mechanics. 



First, as to the elementary laws : their peculiar characteristics 

 constitute the very perfection of the science. In number they 

 are so few, that a priori it seems impossible to build upon them 

 any system of great extent : in nature they are so simple and 

 a]>j)arent, that the mere enunciation of them necessarily carries 

 with it immediate assent. These fundamental principles, regu- 

 lating the minutest and the grandest phenomena of the material 

 world, are yet detected at once on the most imperfect and careless 

 observation of the operations of nature. They are inductions, 

 either from the rudest, or from the most refined, experiments. 

 Indeed, it is sometimes difficult to perceive that our knowledge 

 of them is experimental at all, and not intuitive; — at this very 

 moment, there are controversialists who believe them to be mere 

 axioms or self-obvious truths, innately perceived in the mind, 

 and not acquired frqpi sources external to it. 



And here it is necessary to establish a distinction between these 

 fundamental laws and tlieir ultimate causes. With the lattei", the 

 mechanical philosopher has no concern : he seeks only to ascertain 

 and trace the effects of the rules by which material bodies are 

 observed to operate on eacli other ; but causation or speculation 

 .•as to the modus operandi, forms no part of his inquiry. That 

 heavy bodies are drawn towards the earth when unsupported, is a 

 fact, of which, notwithstanding its constant occurrence, no expla- 

 nation has ever yet been given. A\''ere we not so familiar with 

 this phenomenon, it would appear very wonderful, that one body 

 should approach another without any communication between tlie 

 two, or any visible cause of the motion. To say that it is due to 

 the earth's attraction or gravity, is merely to give a name to, 

 not an explanation of, the mystery. Again, who can tell what 

 mighty, unseen chain binds this ear,th to move for ever in a cer- 

 tain orbit round a body ninety-five millions of miles distant? 

 Planets and satellites, apparently isolated in space, separated from 

 all other bodies by distances M4iich the mind is utterly incapable 

 of recognising, move on from age to age in tlieir predestined 

 courses ; yet, so silently, that no moi-tal ear ever yet heard the 

 sound of their mighty mechanism. Man, indeed, discerns its 

 minutest operations, and from their regular recurrence learns 

 to jn-edict them with unfailing accuracy ; but the secret agency 

 which pervades and guides the wliole system, remains an un- 

 searched, an unsearchable, mystery for ever. 



The harmonious concord of nature, however — her consistency 

 and never-failing regularity — these are questions within the pro- 

 vince of mathematical reasoning, and these are the questions upon 

 which the evidences of mechanical science rest. Let it be ascer- 

 tained that the laws of matter are unchangeable and univer.sa], 

 and a system may be founded on those \a\\^, which can never 

 be shaken by speculations as to their ultimate causes. 



Such, then, are the premises from which the mechanical philoso- 

 pher reasons. The only remaining (|uestion as to evidence is this 

 — are the inferences from tliem rigorously logical.' 



The premises are obtained by induction, the inferences by de- 

 duction. The premises, as has just been said, are arrived at by 

 comparing a great number of natural phenomena, and extracting 

 the simple principles common to them all. This is the process 

 of induction, which reasons by analogy from examples. All the 

 physical sciences derive their origin from this source ; for how 

 are we to contrive a physical science — that is, how are we to 

 reduce any class of natural phenomena to a regular system — 

 unless by ascertaining, from luiture hei'self, the primary laws 

 by which she acts.' It is clear, that if a man did not look out 

 of himself, into the external world, for this elementary know- 

 ledge, his system would be nothing more than an ingenious fig- 

 ment of liis own brain. 



But the appliration of the primary laws depends on another 

 kind of logic than that of induction. Now, we no longer reason 

 by analogy — no longer refer to examples — no longer, indeed, draw 

 knowledge from the external world. Nature has furnished the 

 premises ; the mind of man depends on itself alone for the in- 

 ferences. These are deductive from that application of logical syl- 

 logisms to abstract propositions, which is no other than the pro- 

 cess oi common-sense. — the very highest kind of reasoning of which 

 the human mind is capable. It is not within our present scope 

 to discuss the principle on which deductive reasoning depetids, 

 further than by explaining, that it may alwaj's be immediately 

 referred, or ultimately reduced, to the Aristotelian dictum, de 

 omni et nulla — what is universally true of a class of things, is 

 true of anything in that class. It is not necessary, however, 

 to examine minutely here this logical, or rather metaphy- 

 sical, question : it is enough for our purpose that there are 

 certain primary truths which the mind universally recognises, cer- 

 tain elementary methods of combining them, the validity of which 

 is as certain to every man as his own consciousness, — and that 

 on these primary truths and these elementary methods the in- 

 ferences of mechanical science exclusively depend. 



Of course, the full effect of these considerations' can be per- 

 ceived only in the actual study of the science itself. But we 

 are now in position to explain the difficulties which originally 

 retarded its progress, and which, even now, constitute the 

 greatest obstacles to the student's progress. Geometry, it was 

 mentioned, became a systematic science, while mechanics re- 

 mained obscure and confused. If the preceding attempt to 

 explain the foundations on which the latter science depends, have 

 been at all successful, the i-eason of the earlier development of 

 geometry will readily suggest itself. One of the elements of 

 mechanical investigation — experimental induction — was wholly 

 wanting in geometry. It is needless here to inquire whether 

 any of the primary ideas of this science also be derived from 

 experience : we may well be anxious to avoid a discussion of 

 those essential affinities and distinctions between the objective 

 sciences, respecting which such men as Bacpn, D'Alembert, 

 Diderot, Locke, Adam Smith, Dugald Stewart, Turgot, &c., 

 have been unable to agree. But this is readily seen, and is 

 of itself quite sufficient to exjilain the comparatively rapid 

 development of geometry — that its progress was not impeded 

 by difficulties incident to the advancement of mechanics — the 

 necessity of making experiments, and of selecting, from an 

 overwhelming abundance of results, those which, from their 

 universality and precision, might be made the foundations of 

 the new science. 



The same difficulties occur to the student now. He ap- 

 proaches the study of geometry with an unprejudiced mind : 

 whatever previous ideas of space, form, and distance he has 

 acquired, may be confused and imperfect, but they cannot 

 be positively erroneous. Geometry contains no secret principles, 

 detected only by their effects; all its subjects are so obvious 

 and palpable, that any direct mistake respecting them would 

 be certain to soon detect itself. But of mechanics, almost 

 every doctrine is unconsciously prejudicated before the com- 

 mencement of its systematic study : here is a secret principle, 

 undetected, except by its effects — an invisible agent, kobcu 

 of which the existence is ascertained only by experience of 

 its operations, :ind of which the ultimate nature is altogether 

 unknown. 



The great task, then, which the student of mechanics must 

 perform, is to refer every problem to first principles : to re 

 train from appealing to his own physical notions, acquired 

 accidentally and witliout method. Not that he is required to 

 give up the right of private judgment, or subject it, uncon- 



