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DYNAMICS. 



Dynamics.^ UVNAMICS is that branch of Mechanical Philosophy 

 *"^V*' which treats of the action of forces when they give rise 

 to motion, and consists of the two following problems, 

 viz. 



1. From some of the circumstances which we observe 

 in a motion, to determine the forces by which it is pro- 

 duced ; and, 2. Conversely, from the knowledge which 

 we have acquired of the forces, to determine all the 

 circumstances of the motion to which they give rise. 



It is customary, however, to give under Dynamics 

 only the more general doctrines, and to reserve the rest 

 for distinct articles. We shall, therefore, in this arti- 

 cle, 1st, Give a short history of dynamics ; 2dly, State 

 some preliminary views with regard to the nature and 

 measure of forces ; 3dly, Lay down the general rules 

 or laws according to which they act ; 4thly, Deduce 

 consequences with regard to their composition and re- 

 solution ; and, 5thly, Apply these general doctrines to 

 some of the most general cases of dynamics. 



HISTORY. 



History. THE ancients were extremely little acquainted with 



dynamics. The wants of society, indeed, from the ear- 

 liest times, required mechanical arts, and many of the 

 Roman machines explained in Vitruvius excite our as- 

 tonishment. But these inventions seem to have pro- 

 ceeded rather from numerous trials and natural sagaci- 

 ty, than from a proper acquaintance with the general 

 principles of motion. 



The ancients did not even know the first law of mo- 

 tion, and, instead of conceiving that the motion of a 

 body was naturally uniform and rectilineal, they suppo- 

 sed that a circle, being the most perfect of figures, was 

 that in which a body would naturally revolve. They 

 cultivated both astronomy and geometry with consi- 

 derable success; the former affording some of the finest 

 examples of motion, and the latter furnishing the best 

 assistance for the investigation of its properties ; but 

 they wanted our experimental method of inquiry. 



Aristotle. Hence Aristotle, profound and accurate in most sub- 

 jects, is extremely deficient when he treats of motion. 



Archime- Archimedes, it is true, who ranks at the head of ancient 



dL =- geometers as well as of ancient mechanicians, knew in 



some machines the true ratio of the power to the resist- 

 ance in the case of equilibrium; but none of his wri- 

 tings discovers an acquaintance with the principle of 

 the composition of forces, from which may be deduced 

 the conditions of equilibrium in all machines, and still 

 less does he appear to have been acquainted with the 

 general method of calculating the motion of bodies, 

 which forms the principal business of dynamics. In 

 short, dynamics, as a science, is of modern date. The 



6lilco. celebrated Galileo, about 200 years ago, laid the foun- 

 dation of it. In his treatise on the motion of falling 

 bodies, he shewed that he was acquainted with the two 

 first laws of motion, and likewise made a happy appli- 

 cation of them. The law of reaction was a discovery 



DM Cute*. f sti" later times. Des Cartes attempted to find out 

 the law that obtains in the mutual collision of bodies, 

 but failed, notwithstanding the acuteness of his genius. 

 At last the Royal Society of London, after making it 

 the subject of discussion at several of their meetings, 

 devolved the task on three of their members, highly dis- 



tinguished in that society, and throughout Europe, for History, 

 their skill in geometry and mechanics. These were **~~Y^"^ 

 Wren, Wallis, and Huygens. The result was, that Wren, 

 each separately made the happy discovery about the Wallis, and 

 same time, in the year 1661. These three laws are the Huygens. 

 general principles on which hinges the whole of dyna- 

 mical science, and indeed the whole science, whether 

 of equilibrium or of motion. 



Dynamics has continued to improve, by the happy 

 examples that have been given of the application of 

 these principles to the solution of particular problems ; 

 by deductions from these of other principles, less gene- 

 ral, but more convenient for particular classes of ques- 

 tions ; and likewise by every discovery in abstract ma- 

 thematics, that great instrument for penetrating the 

 secrets of nature. In all these respects, the contribu- 

 tions of Newton to dynamical science are beyond all 

 praise. D'Alembert furnished a powerful principle, D'Alem- 

 which will be given under MECHANICS; and our coun- bert. 

 tryman M'Laurin, in his Fluxions, was the first to re- 

 present the motion of a body, by resolving the force 

 that actuates it into directions parallel to fixed axis : a 

 method that has contributed not a little to the solution 

 of dynamical problems. 



SECTION I. 



Nature and Measure of Forces. 



1. Force defined. Any thing that causes, or tends to 

 cause motion, is called force. The term is in familiar 

 use ; and the meaning attached to it by philosophers 

 and the vulgar is the same. It is divided into two 

 kinds, impulse and pressure. The former produces its 

 whole effect almost instantaneously ; the latter continues 

 to act during a sensible portion of time. It compre- 

 hends pressures, properly so called, and also attractions 

 and repulsions. 



2. Measure of Weight. We naturally judge two 

 weights to be equal, when they produce exactly the 

 same effect in the same circumstances ; as when they 

 counterpoise one another at the extremities of a balance, 

 whose arms are precisely alike, or to whichever arm 

 they are respectively suspended. We also naturally 

 consider the parts of a body which are alike in every 

 other respect as alike in point of weight, and thus con- 

 clude the weight of such a body to be proportional to 

 its bulk. We actually find it to be so. Hence, by 

 assuming the weight pf a certain bulk of a certain body, 

 a cubic foot of water for example, as an unit, and ta- 

 king multiples and submultiples of that bulk, we ob- 

 tain convenient measures of all weights whatsoever. 



3. Measure of any other Pressure The pressure of 

 gravity being thus easily measured, and also being one 

 with which we are familiar, is well fitted to form a 

 standard for measuring all other pressures. It is pro- 

 per to bear in mind, that the specific gravity of a body 

 is the weight of a certain bulk of it, and hence w=BS. 



4. Mass or Quantity of Matter measured. Any thing 

 is best measured by some quality which is measurable, 

 which distinguishes it from every thing else, and which 

 always belongs to it in the same degree, or whose va- 

 riation, if there be any, is known. Weight possesses 

 some of these properties, but in others it seems to be 



Force de- 

 fined. 



Measure of 

 weight. 



Measure of 

 any other 

 pressure. 



Mass or 

 quantity of 

 matter mea 

 sured. 



. 



