II 



8TB1IGHT, STKAU;llT I.I.NE, 1'LANK. 



STRATEGY. 



In nuking such a definition Euclid U well aware that he cannot rest 

 any ooncliunon upon it, and that in the poituUta that two straight 

 linn cannot induce a apace lie* all his power of producing a theorem. 

 Why tlu-n, it may be asked, doe* he introduce a definition at all .' \Vliy 

 not give the reader to understand that a straight line U a notion uni- 

 versally understood and incapable of definition in simpler terms ? To 

 these question* the answer may be twofold. In the first place, he is 

 not answerable for the genius uf any language but his own, and it is 

 rery possible that to a Greek commencing geometry, >v0<ia might be 

 a hard word, and /{ laau nermi a real explanation ; in which caw hi* 

 definition is defensible until it can be shown that he might have chosen 

 a better one. We are not to judge of the force of the last-quoted 

 words from the ex <rquo of the middle Latin, or the tvenly or equally 

 of the English. Secondly, he is evidently, in some of the first defini- 

 tions, recalling, and not instilling, notions : he U proceeding with his 

 reader aa by words to which both attach a conception, and he trie* 

 those words fur use by ascertaining that both parties agree on such 

 circumlocution as can be substituted for them. 



The greatest defect of Euclid's definition, since it applies even to the 

 riew just taken of its intent, is the want of words signifying that /{ 

 Iffou refers equally to all adjoining parts of space : Euclid is thinking 

 too much of a plane before he has defined a plane. Suppose, for in- 

 stance, a sphere, and that lines on a sphere only are contemplated : 

 the line which joins two points t( laov with reference to all adjacent 

 parts of that sphere is not a straight line, but an arc of a great circle. 



Is it possible, taking such allowances as Euclid sanctions in the use 

 of figure, to give what shall be, whether difficult or not difficult, 

 capable of use or not capable, a just definition of a straight lino ? We 

 think it is, as follows : The Greek geometer implicitly allows (i. 4) a 

 THAXSLATIOX of figure without change of form or properties: from 

 this, by first defining the plane, a definition of the straight line may 

 be proposed, which we bring forward, not for any value which it has, 

 but because the stipulations of geometry are better understood by 

 consideration of cases proposed for acceptance or rejection, than by 

 any other method. 



1. Let two points (A and B) be said to be at the same distance from 

 a third (c), when A and c being joined by any line, the line c A can be 

 translated, c remaining fixed, so that A shall be brought to coincide 

 with B. 



2. A plane is a surface any point of which is equally distant from 

 two given points. 



3. A straight line is the intersection of two planes. 



In the debates of the normal school, which were taken down in 

 shorthand, and published in 1800, is a discussion on this subject. 

 Lagrange presiding, Fourier, then one of the pupils, proposed the pre- 

 ceding second and third definitions, but without assigning a definition 

 of equi-distance independently of the straight Hue. He also proposed 

 as the definition of a straight line the locus of a point which is equi- 

 distant from three given points ; which is faulty, inasmuch as the three 

 given points should not be in one straight line, which cannot be sup- 

 posed until the straight line is defined. Lagrange admitted the rigor 

 of the definition, but considered that it failed in presenting a sensible 

 image of the thing defined. Another of the pupils however insisted 

 that the idea of distance involved that of a straight line, which is true 

 of distance as a quantity, though not necessarily so of equi-distance as 

 a relati'tn. 



General Thompson proposes" to define a straight line as one which 

 being turned about its extreme points suffers no change of place. 

 I ._!. !_. in tli. debate abort .illuoVil to. HUL'-. .-tnl the .-.imr notion. 

 This definition, we think, offers the most tangible illustration of that 

 of Kuclid. Let the two extremities of the intended straight line be 

 situated in a solid ; and let them remain fixed in space while the solid 

 takes such motion as, under that condition, it is capable of. The 

 straight line, the line which lies if tffov with regard to the extreme 

 points, then remains fixed. For if any part of it moved, there would 

 be in every position a relation to adjoining parts of space, which would 

 be in a state of continual change. The connexion between this defini- 

 tion by rotation and tliat of Euclid might require more development 

 to render it as clear aa possible : but we think the student's own 

 reflection will lead him to make it satisfactorily. But whatever may 

 be thought of the endeavour to exercise the discrimination of which 

 geometry points out the possibility by framing or arguing on defini- 

 tions, we do not remember to have seen one so well calculate. 1 fur the 

 were beginner as the following : " A straight line is a straight line." 



The postulates relative to a straight line demanded by Kuclid (we 

 do not K|H>ak of his translators) are : 1. That such a line can be drawn 

 from any one point to any other. 2. That when terminated, it can be 

 lengthened indefinitely. 3. That two such line^ cannot inclose (w>i 

 wipitXtui) a space. It is also tacitly assumed that every part of a 

 straight line is a straight line : that every straight line, infinitely pro- 

 duced, divides a plane in which it lies into two parU, and will be cut 

 by any line drawn from a point on one side of it to a point on the 

 other. It might also have been assumed that two straight lines which 

 coincide in two | point*, coincide when produced beyond those points; 

 but here Euclid lias preferred to assume that all right aneles are equal. 

 [RloilT Asp.ii.:.] 



The definition which Euclid gives of a plane, ia that of a surface 

 which lies evenly between its bounding straight lines. To this defini- 



tion there is the serious objection that though a plane may be a.- 

 conoeived as a straight line, yet it is actually cajul/lr of delinitipm by ;i 

 straight line. For a plane U the surface any two points of which can 

 be joined by a straight Hue which lies wholly on the surface. Neither 

 this definition (nor Euclid's) precludes the necessity of a postulate 

 demanding the possibility of drawing a plane through any ~ 

 line. Objections might be made to the first part of Km-lid's eleventh 

 book, which would require for their answer tliat another postulate 

 should be granted, similar to that required for a straight line, mum ly, 

 that if two planes coincide in any portion of surface, they coincide 

 altogether. Euclid does in fact assume a postulate which is not ex- 

 pressly hud down, namely, that a finite straight line con be produced 

 in every plane in which it lies, but we think it may be fairly doubted 

 whether the first three propositions of the book in question are aa 

 perfect as they might be made. 



STRAIN. [SIM.AIX.] 



STRAIN AND STKESS. [MATERIALS, STRENGTH OF.] 



STRAMON1N. A crystalline body contained in stramonium seeds. 



STRAMONIUM,} boUnically the Datura Stramonium, or Tlwrn. 

 Apple, an introduced but now fluently self-sown and consequently 

 wild plant, found particularly wherever a garden once has been. The 

 leaves and seeds are officinal. The leaves during drying diffuse a 

 stupifying odour, and become deep grayish green, and then scarcely 

 possess any odour : the taste is disagreeable, saline, and strongly bitter. 

 The seeds are kidney-shaped, flat, about the size of linseed, uneven, 

 nearly black : when bruised the smell is disagreeable and repulsive ; 

 taste bitterish and oily ; by expression sixteen ounces of fresh seeds 

 yield two ounces of clear fat oil, which has neither taste nor odour. 

 The seeds of the other species of datura are often substituted, JK-I Icqi- 

 without any great disadvantage. They are also confounded with the 

 seeds of Nigtlla Satira, which, though black, are smaller, nearly three- 

 cornered, and have an acrid aromatic taste, and in considerable quantity 

 are poisonous like those of stramonium. 



The seeds are used to form the extract ; they, as well as the unripe 

 capsules, yield the alkaloid called datura, which crystallises from its 

 solution in alcohol or water in colourless shining aggregated prisms ; 

 without odour when pure, but when impure possessing a strongly 

 narcotic odour ; taste at first bitter, then very acrid, and like tobacco. 

 This is extremely poisonous : one-eighth of a grain can kill a sparrow 

 in less than three hours ; and the smallest quantity applied to the eye 

 causes very lasting dilatation of the pupil. 



Stramonium in small doses causes slight convulsive action about the 

 throat, with dryness of the tongue, disposition to vomit, and general 

 diminution of sensibiHty, with alight increase of secretion of the skin, 

 mucous membranes, and kidneys ; but if the dose be larger, the bruin 

 becomes affected, and vertigo, indistinctness of vision, with dilatation 

 of the pupil, disposition to sleep, or coma, but more frequently 

 delirium, are added. The delirium is always peculiar, and the indi- 

 vidual manifests a disposition to perform ridiculous actions, or assume 

 absurd positions. If the dose be still larger, .and produce fatal effects, 

 the brain is usually found to be much congested, the vessels being 

 gorged with blood. Large bleedings generally save the patient ; 

 emetics can rarely be made to act, as is observed when other narcotic 

 poisons have been taken. Stramonium is most useful in cases of 

 increased sensibility, particularly in local affections of the nerves ; it is 

 decidedly useful in allaying paiu of the sciatic nerve, particularly when 

 combined with ipecacuan. It has been recommended in mania, 

 especially when accompanied with lucid intervals, in epilepsy, and 

 hysteria ; but with very variable success, probably to be accounted for 

 by the careless preparation of the medicine. It is popularly used for 

 smoking, to allay paroxysms of asthma, but its employment in this 

 way is quite empirical, and regulated by no clear principle. By the 

 action of heat during smoking, an empyreumatic oil is found, similar in 

 properties to that of hyoscyamus. 



STRATEGY (from the Greek ffrpar-nyta, which may be translated 

 " generalship ") is, properly, the science of combining and employing 

 the means which the different branches of the art of war afford for the 

 purpose of forming projects of operations and of directing great 

 military movements: it was formerly distinguished from the art of 

 making dispositions, and of manoeuvring, when in the presence of the 

 enemy; but military writers now, in general, comprehend all these 

 subjects under the terms of grand and elementary tactics. [TACTICS.] 



The general principles of strategy and tactics have been ami must IIP 

 the same in all ages. To overcome the enemy, it is necessary to be 

 superior to him at the point of collision, not necessarily numerically, 

 for number only does not always represent the strength or relative 

 strength of an army, but superior when due allowance is madr for 

 other advantages or disadvantages. The object then of all str.r 

 combinations should be to bring the mass of the forces in collision with 

 fractions of the enemy ; and secondly, to act as much as possible on 

 his communications or lines of operutioiiH without exposing one's own. 

 The roads on which an army, or portion of an army, marches, are 

 termed strategical lines, and the belt of ground containing two or more 

 strategical lines, if lying close together, is termed a line of operations. 

 In order then to bring, and always to have the power of bringing, the 

 mass of the forces in collision with fractions of the enemy, it is neces- 

 sary to choose such lines of operations aa are interior ; interior, that is, 

 with respect to those on which the enemy acts. That is to say, that 



