MOTIF 



MOTLEY 



329 



wardrobe, chest, &c. containing them should have 

 no cracks or crevices. Pieces of camphor, sprinkled 

 pepper, and strongly odoriferous ' moth-powder ' of 

 some sort will help to keep the adult moths away ; 

 but when a host of larvte have jxissessed the gar- 

 ment it may be immersed in tailing water, carbolic 

 acid, &c., or burned as hopelessly spoilt. Almost 

 the only directly useful form is the Silk-moth 

 (q.v.). There are separate articles on the Hawk 

 Moth, Death's- head Moth, Gooseberry Caterpillar, 

 &c. ; see also BUTTERFLY, CATERPILLAR, INSECTS. 



Motif, in a musical composition, means the 

 principal subject on which the movement is con- 

 structed, and which, during the movement, is con- 

 stantly appearing in one or other of the parts, 

 either complete or modified. In elaborate and 

 long compositions there are also secondary motifs. 



Motion, LAWS OF. In developing the subject 

 of Dynamics (q.v.) it is convenient to lay down in 

 the form of postulates axioms or the fundamental 

 principles on which the science is based. These 

 axioms are generally referred to as the laws of 

 motion. They rest ultimately, as do the axioms 

 of geometry, upon our e.\]>erlence ; and once the 

 terms in which they are expressed are sufficiently 

 understood, the laws themselves are admitted with- 

 out further question. We owe to Newton what 

 still remains the most serviceable, because the 

 most concise and at the same time complete, 

 expression of these dynamical axioms. Newton's 

 predecessors, particularly Galileo, had already 

 formulated some of the fundamental principles of 

 abstract dynamics ; but in the Three Laws of 

 Motion, which form the basis of the Principia, we 

 have for the first time all the necessary and suffi- 

 cient principles laid down in a manner easy to 

 understand and easy to apply. These three laws 

 are given both under DYNAMICS and under FoECE, 

 and need not be reproduced here. 



Newton's method of presenting his definitions 

 and axioms has l>een made the subject of much 

 criticism. And doubtless a logician, confining 

 his attention to the eight definitions of mass, 

 momentum, inertia, force, acceleration, &c., and 

 the three laws of motion, could easily discover 

 faults of logical arrangement. Nevertheless, tak- 

 ing this preliminary section of the Prim-i/tia, with 

 its masterly scholia, at a whole, and bearing in 

 mind that the aim is to establish a theory of 

 dynamics that shall harmonise with the facts of 

 experience, we shall find no difficulty in admitting 

 the soundness of Newton's principles. There is 

 absolutely no confusion of thought. The demands 

 on our intellectual faith, whether explicitly stated 

 or implicitly involved in other statements, are 

 i-scntially rational. The treatment is luminous 

 :i- it is profound. Attempts have been made to 

 substitute a more logical procedure ; but all such 

 attempts lead to intricate phraseology and a 

 corresponding intricacy of dynamic conception 

 quite beyond the powers of apprehension of the 

 tyro. And even when all is done it is doubtful if 

 the strict canons of logic are quite satisfied. It 

 may b: safely said that, as an introduction to the 

 study of dynamics, Newton's laws of motion, along 

 with the definitions of the physical quantities 

 involved, have not as yet l>een surpassed. 



The train of thought running through Newton's 

 method may be thus described. Everything dyna- 

 mical that happens in nature consists of changes 

 of [Nisition and motion of the parts of a material 

 system. Fixing our attention on one body or 

 particle in the system, we soon perceive by experi- 

 ence that its changes of motion or ( more strictly ) 

 momentum relatively to the other parts of the 

 system must dejieml on the mechanism connecting 

 it with these parts. With this mechanism, how- 



ever, we do not at first explicitly concern ourselves. 

 For it we substitute the conception of force, or its 

 time-accumulation, impulse, which we regard as 

 the external something causing the observed 

 change in momentum and measured by that 

 change. This force may be constant or variable 

 in space, or it may depend on the velocity of the 

 body. On these conceptions and definitions we 

 base the simplest department of abstract dynamics 

 that known as the dynamics of a particle. Many 

 of its theorems are found to be very approximately 

 realised in the falling of bodies, in tne flight o"f 

 projectiles, in the motions of planets and comets 

 round the sun. But before we can pass to the 

 dynamics of material systems we must restore the 

 bonds we severed when we introduced the idea of 

 force acting on a single particle. This Newton 

 completely effected by his third law, in which 

 every force is recognised as being only the half of 

 a whole, the other half bein< the equal but 

 oppositely directed reaction. This means that 

 whatever change of momentum may be observed 

 to lie taking place in one particle must be balanced 

 by an equal and opposite change of momentum 

 occurring elsewhere. Thus, the momentum of a 

 material system as a whole can never change, how- 

 ever much its configuration may alter, in virtue of 

 the mutual actions of its parts. And in this state- 

 ment we may readily recognise the generalisation 

 of the first law of motion commonly called the 

 Law of Inertia in its application to any complex 

 material system, dynamically isolated, and con- 

 sidered as a unity. Newton's very remarkable 

 second interpretation of the third law, given at the 

 end of the scholium attached, implicitly contains, 

 as was first pointed out by Thomson and Tait, 

 nearly the whole of the modern doctrine of energy. 

 It is discussed under that heading. See also FORCE 

 for the discussion of the Second Law. For Motion 

 in Plants, see IRRITABILITY, PLANTS, SENSITIVE 

 PLANTS, SPORE; for animal locomotion, see FLY- 

 ING, HORSE, &c. 



Motley, JOHN LOTHROP, historian and diplo- 

 matist, was born in Dorchester, Massachusetts, 

 April 15, 1814. He had an in- co W ri h, in h, u.s. 

 heritance of wit and literary taste <>r J- B. Lippiocoit 

 as well as of fortune, and had all 

 timely advantages of education and travel to 

 make him the 'picked man of countries' which 

 he became. He attended the school at North- 

 ampton, Massachusetts, kept by Dr Cogswell and 

 Bancroft the historian, and at the age of thirteen 

 entered Harvard College, graduating in 1831. 

 He next studied in German universities, and at 

 Gottingen was the intimate friend of Bismarck. 

 HU reading was various and enormous, especially 

 in poetry and fiction, and in modern languages. 

 He ' toiled terribly ' afterwards, when he made the 

 studies for his history, but his early assiduity was 

 like that of a bee in a flower-garden. He was 

 naturally a favourite in society, as lie was tall and 

 exceedingly handsome, with a captivating manner. 

 His reseniblance to Lord Byron was striking. 

 He was married in 1837 to Miss Benjamin, a lady 

 of beauty and accomplishments. In 1839 he pub- 

 lished his first work, an historical novel, entitled 

 Morton's Hope. Its brilliant pictures were ad- 

 mired, but it was not successful. His second 

 novel, Merrymount, was partly a protest against 

 the gloom of Puritanism, and was more favourably 

 received ; yet it was evident that the genius of the 

 author was not to be displayed in fiction. When, 

 afterwards, the splendour of Motley's style lighted 

 up the great scenes of history, as, tor instance, the 

 abdication of Charles V. in the town-hall of 

 Brussels, it was seen that his ardent and im- 

 aginative nature had found its predestined place. 

 Hia studies early turned in this direction, but 



