69 



SOLECISM. 



SOLIDIFICATION. 



670 



fortified with the principles which should have been implanted in his 

 mind by a sound education. The probability of a return to his native 

 land before many years have passed is small, and the diseases to which 

 he is exposed from the unhealthiness of the climate frequently termi- 

 nate fatally : hence he becomes reckless from despair, and the facilities 

 with which wine or spirituous liquors may often be obtained lead him 

 into excesses which, while they accelerate the ruin of his health and 

 render him unfit for duty, cause him to commit offences both against 

 discipline and morals. Thus hi the colonies there arises a necessity for 

 greater restraints on the freedom of the soldier, and for the infliction 

 of heavier punishments than are required at home. (Maj.-Gen. Sir 

 Charles Napier, ' Remarks on Military Law.' ) Lastly, in time of war 

 and on foreign service a vigorous discipline is essentially necessary ; 

 the privations to which soldiers are then exposed strongly induce those 

 who are not thoroughly imbued with moral and religious principles to 

 plunder the country-people, in order to supply their immediate wants, 

 or to drown the sense of their sufferings in liquor. 



SOLECISM (loloeciimui, voKoiKurn&s), a grammatical term which is 

 used by the later Greek and Roman writers, and by modern gram- 

 marians also, though in a somewhat different sense. It is defined by 

 Sinnius Capito (Gell., v. 20) as an unequal and improper arrangement 

 of the parts of speech, that is, as a violation of the rules of syntax. 

 Quinctilian (i. s. 28, &c.) specifies four kinds of solecisms : the first 

 u in the addition of a superfluous word ; the second, in leaving 

 out one that is necessary ; the third, in perverting the order of the 

 words of a sentence ; and the fourth, in using an improper form of 

 a word. The ancients also used the word in a wider sense, under- 

 standing by it any kind of fault, error, or mistake, whether made in 

 speaking, writing, or acting. Modern grammarians designate by 

 solecism any word or expression which does not agree with the 

 established usage of writing or speaking. But, as customs change, 

 I Inch at one time is considered a solecism, may at another be 

 regarded as correct language. A solecism therefore differs from a 

 barbarism, inasmuch as the latter consists in the use of a word or expres- 

 sion which M altogether contrary to the spirit of the language, and 

 can, properly speaking, never become established as correct language. 

 . PA-INO. ISOLMISATIOS.] 

 i.ICITOR. [ATTORNEY; Six CLERKS.] 



ID, SOLIDITY. (Mechanics.) A solid body is one which is 

 c imposed of matter so connected together that the relative positions 

 of its parts cannot be altered without the application of sensible force. 

 The force which resists the alteration of the relative positions is called 

 force of cohesion [ATTRACTION] : the perfect absence of this force 

 <j m-titutes fluidity [FLUID]. 



SOLID ANliLE, a name given to the idea of opening conveyed by 

 three planes which meet at a point. The properties of a solid angle 

 are considered under the head SPHERICAL TRIANGLE. 



SOLID, SURFACE, LINE, POINT. (Geometry.) We have 

 thought it best to bring together the remarks which it is necessary to 

 make upon these fundamental terms of geometry. According to 

 Euclid, a point has no dimensions ; a line, length only ; a surface, 

 length and breadth : a solid, length, breadth, and thickness. No one 

 lias the least doubt about each of these terms representing a clear and 

 distinct notion already in the mind ; in spite of this, however, the 

 propriety of the definitions has been made matter of much discussion. 

 Space being distinctly conceived, parts of space become perfectly 

 intelligible. Hence arises the notion of a boundary separating one 

 part of space from the rest. That a material object, a desk or an ink- 

 stand, occupies a certain portion of space, separated by a boundary 

 from all that is external, needs no explanation : this boundary is called 

 surface, and possesses none of the solidity either of the desk or ink- 

 stand, or of the external space. Surface itself, when distinctly under- 

 stood, \ capable of division into parts, and the boundary which 

 separates two parts of a surface has none of the surface, either on one 

 side or the other : it therefore presents length only to the imagination. 

 Again, length itself is capable of division into parts : the boundaries do 

 not possess any portion of length, either on one side or the other : they 

 are only partition marks or points. Euclid reverses the order of our 

 explanation, requiring first the conception of a point, then of a line, 

 then of a surface, then of a solid. 



That when we think of a point, we deny length, breadth, and 

 thickness ; that when we think of a line, it is length without breadth 

 that we figure to ourselves ; that in the same manner the surface of 

 our thoughts possesses no thickness whatever are, to us at least, real 

 truths. We cannot, for instance, imagine what Dr. Beddoes meant 

 when he said (' Obs. on Demonstrative Evidence,' p. 33), " Draw your 

 lines aa narrow as you conveniently can, your diagrams will be the 

 clearer ; but you cannot, and you need not, conceive length without 

 breadth." Why are diagrams the clearer, the narrower the lines of 

 which they consist T Diagrams have no clearness in themselves ; the 

 comprehension of them is hi the mind of the observer. If diagrams 

 having (so called) lines of one-hundredth of an inch in breadth be 

 clearer than others of five-hundredths of an inch, it is because the 

 former approach nearer than the latter to a true representation of that 

 which is in the mind, or of that which the mind desires to see por- 

 trayed. If the smaller the breadth the better the diagram in the 

 clearness which it gives to the mind, it must be because the mind 

 would have no breadth at all. 



It matters nothing that the point, line, and surface are mechanical 

 impossibilities ; that no point or line, if they actually existed, could 

 reflect light to show them ; and that no surface could continue to exist 

 for any perceptible time, even supposing it to have one moment of 

 existence. Neither does it signify whether the ideas be necessary, or 

 acquired from the senses ; the question in geometry is, Have you got 

 them ? not, How did they come ? There may be danger that some 

 students should need at first to be frequently reminded of the abstract 

 limits of which the conceptions must be made permanent, lest they 

 should accustom themselves to rest in the imperfect approaches to these 

 conceptions which are realised in their diagrams; but it is always 

 found that a moment's recollection will produce a satisfactory answer 

 to any question upon this point. 



There is, it is true, one circumstance in which the pupil may acquire 

 a permanently false notion of the object of geometry. If an instructor 

 should require what is called a very well-drawn figure in every case, 

 with very thin lines and very small points, he may perhaps succeed in 

 giving the learner some idea that geometry consists in that approach 

 to accuracy which constitutes practical excellence in the applications 

 of the science. No idea can be more false : let the good line be ex- 

 amined under a microscope, and it is seen to be a solid mound of black 

 lead or ink, as the case may be. Hence it is perhaps desirable that the 

 demonstrations should be frequently conducted with what are called 

 ill-drawn figures, in order that no reliance may be placed on the 

 diagram, further than as serving to remind the student of the ideal con- 

 ception which is the real object of his demonstration. This of course 

 is recommended without prejudice to his learning the accurate use ef 

 the ruler and compasses for another distinct purpose, namely, the 

 intention of producing avowedly approximate practical results. 



It is to be noted that these definitions, so called, are in Euclid more 

 than definitions. They appeal to conceptions supposed to exist, in 

 words which are considered sufficient not to give, but to recall, the neces- 

 sary ideas. This they actually do, to the satisfaction of the learner, 

 who would never dream of their containing anything dubious, if it 

 were not for the ill-advised interference of the psychologist. Whatever 

 of pleasure or profit there may be in the subsequent union of the 

 sciences, there is, we think, no doubt that the young geometer should 

 not be required to examine the foundations of his notions of space : 

 he cannot do this with effect until he has seen what these notions are 

 by the light of their geometrical consequences. 



SOLID, SUPERFICIAL, AND LINEAR DIMENSIONS. A solid, 

 a surface, and a line, when they come to be the objects of arithmetic, 

 are things as distinct as a weight and a time. That a surface is 

 included by lines, or a solid by surfaces, makes no more of necessary 

 connection between them than exists between weight and time, because 

 the former can never be made sensible without the latter. Length 

 only can measure length, a surface only a surface, a solid only a solid. 

 Reasons of arithmetical convenience, not of necessity, make it advisable 

 that whatever length may be chosen to measure length, the SQUAKE 

 on that length should be the surface by which surface is measured, 

 and the CUBE en that length the solid by which solidity is measured. 

 Unfortunately, if a foot be the measure of length, the square on a foot 

 and the cube on a foot have no other names than square foot and cubic 

 foot. The farmer with his acres, and the distiller with his gallons, 

 have an advantage which is denied to the young mathematician. Ask 

 the first how many acres make a gallon, and the second how many 

 gallons make an acre, and both would laugh at the question ; the third 

 is allowed an indistinct conception of measuring surfaces and solids in 

 feet or inches, as if they were lilies, from the occurrence of the same 

 word in all his measures. 



Length is said to be a quantity of one dimension, surface of two, 

 and solidity of three. The right line, the right surface or RECTANGLE, 

 and the right solid or rectangular PAHALLELOPIPED (the figure of a 

 box, a die, a plank, a beam, &c.), are the implements of mensuration. 

 Every surface must be reduced to the second form, and every solid to 

 the third, before it can be measured. The rules (which tacitly contain 

 these reductions) for measuring different superficial or solid figures 

 will be found under the several heads : the two fundamental theorems 

 by which measurement becomes practicable are as follows : 



1. The numbers of linear units in the two sides of a rectangle being 

 multiplied together, give the number of superficial units, square units, 

 or squares on the linear unit, which the rectangle contains. Thus a 



5 13 C5 

 rectangle of '2[ by 4J feet contains ^ * "3", or "g"' or 10 S }'' feet. 



2. The numbers of linear units in the length, breadth, and thick- 

 ness of a right solid, being multiplied together, give the number of 

 solid units, cubic units, or cubes on the linear unit, which the right 

 solid contains. Thus a plank of 2j inches broad, 14 inch thick, and 



9 3 31 279 

 10J inches long, contains j x j x -g-j or ~g~t or 34J cubic inches. ' 



SOLIDIFICATION. If heat be abstracted in sufficient quantity 

 from a body in the liquid state, it will become solid. This change in 

 the case of water is termed congelation. During solidification, the heat 

 of liquefaction becomes apparent, as explained under LATENT HI:AT. 

 Certain liquids, however, have not been solidified at so low a tempe- 

 rature as 166 Fahr., such as alcohol, ether, and some others, noticed 



