453 



DEFILE. 



DELIRIUM TREMENS. 



45-1 



imagined to tonch the summit of the eminence in front, to pass above 

 all the intermediate ground, and to meet that in rear of the work ; 

 then the relative heights, with respect to the plane of comparison, of 

 the several points in the plane of site which are vertically above the 

 inequalities before mentioned of the natural ground, must be com- 

 puted, and the differences (which express the heights of the plane of 

 site above the natural ground in such places) being added to the given 

 height which the rampart or parapet is to have above the plane of site, 

 the sums will express the heights to which the works are to be raised 

 above the natural ground at the same places. 



When the work is of small importance, the elevations of the parapets 

 above the ground are generally determined by the eye, thus : Pickets 

 are planted in convenient places, chiefly at the angles of the intended 

 work (the plan of which has been already traced on the ground), and 

 on the summit of the commanding eminence, the picket in this place 

 being about eight feet high. The visual rays being supposed to pro- 

 ceed from the top of this picket to two or more points, which must be 

 also eight feet above the ground, in rear of the work, the intersections 

 of these rays with the pickets planted on the magistal or ground line 

 of the work, will show the heights to which the parapet is to be 

 raised at those places in order that the interior may be effectually 

 protected. 



A similar process is employed when it is required to protect the 

 defenders of any parapet from the fire of the enemy on a commanding 

 eminence in their rear ; in which case it is frequently necessary to 

 raise, in the interior of the work, a mass of earth, which is called a 

 traverse or a parados, according to its situation. 



DEFILE, in military writings, is a name given to any narrow way. 

 Every piece of ground which, in consequence of local impediments, 

 can be passed by a column only on a narrow front, is called a defile. 

 Such are roads along valleys, between walls or hedges, or over dykes 

 raised across marshes. Sometimes also the term is applied to a street 

 in a village, and to the path over a small bridge. 



DEFINITE PROPORTIONS. [ATOMIC THEORY.] 



DEFINITION (dtfinire, to mark out a boundary) is the process of 

 stating the exact meaning of a word, by means of other words. From 

 so boundless a subject, we can only select a very few points, such as 

 have reference to the most common uses of the term. In the first 

 place, it is evident that all definition contains a species of fallacy, if 

 considered as an absolute determination of the meaning of words. 

 Quii custodlet ipsoi castodet f who shall determine the meaning of the 

 words which make up the definition ? The process of definition can 

 never appear satisfactory unless it be considered as a transition from 

 many words to the single term which it is agreed shall stand for 

 their meaning, be that what it may. All attempts at absolute defini- 

 tion must end in confusion of ideas. 



But at least, perhaps it may be said, the mathematical sciences are 

 founded upon exactness of definition. Nothing is more common than 

 this assertion coupled with another, namely, that these sciences depend 

 entirely upon definitions. In a certain sense both are true, but that 

 sense is not the most frequent meaning of them. The exactness of 

 mathematical definition is not of arbiti'ary construction, but a con- 

 sequence of the exactness of the notions which all men have, or may 

 be made to have, upon the things which the words represent. There 

 is no exactness in the fundamental definitions of mathematics, verbally 

 considered, but only much confusion arising from the attempt to intro- 

 duce conventional accuracy. The words "straight line" carry with 

 them their own meaning, and even explain the attempt which is made 

 to explain them ; for no one would easily guess what sort of line it is 

 which " lies evenly between its extreme points/' unless he were 

 aware that it is a "straight" Una which these words attempt ^ 

 describe. 



Definition may either be purely nominal, or it may be such a de- 

 scription of the thing denned as amounts to a statement of some one 

 of it fundamental properties. The first we see in the words " isosceles 

 triangle," the definition of which is a simple announcement that we 

 intend to use a Greek term. The second may be seen in the article 

 CONCAVE AND CONVEX, in which the definition is made by means of 

 an absolute mathematical property of the thing defined : the relative 

 position of the spectator, the curve in question, and a straight line, do 

 not enter into the notion which the words immediately suggest. The 

 method of Euclid is to supply a rough and descriptive definition 

 addressed to the common notion of the word, followed by an assump- 

 tion of a mathematical property under the shape of an axiom. Thus a 

 straight line is " that which lies evenly between its extreme points ;" 

 while the real definition, or distinction between straightness and every 

 thing else is contained in the axiom " two straight lines cannot enclose 

 a space." Every attempt at mathematical definition, which does not 

 rest upon the selection of a substantive property of the thing defined, 

 to be the test of its existence, is either the mere substitution of words 

 for words, or an attempt to make that mere substitution effect some- 

 thing more than lies in it to perform. 



The conditions of a good definition are : 1, perfect axiomatic evidence 

 tha the property which is made the distinguishing test belongs to the 

 object intended to be defined, and to nothing else; 2, entire separation 

 of the part of the property, if any, which admits of being demon- 

 strably connected with the notion defined, from that which contains 

 the assumption ; 3, the introduction of the definition in the proper 



place, namely, when the necessity for a new verbal representation has 

 Degun to appear. 



The mere verbal definition is not to be regarded as taking for 

 granted the existence of the thing defined. When Euclid defines 

 parallel lines, he does not require consent to the proposition that 

 parallels exist. All he is to be taken as asking is this : If there be two 

 straight lines which being in one plane never meet, let them be called 

 -parallels. 



DEFLAGRATION is a term employed to denote the sparkling com- 

 bustion of substances without violent explosion : thus when nitre and 

 sulphuret of antimony are mixed and ignited or thrown into a hot 

 crucible, the combustion which occurs is of the kind termed de- 

 flagration. 



DEFLECTION. A term applied to the distance by which a curve 

 departs from another curve, or from a straight line ; and also to any 

 effect either of curvature or of discontinuous change of direction. It 

 is used where any " bending off" takes place, which is in fact the 

 etymological meaning of the word. 

 DEGREE. [ARTS; UNIVERSITIES.] 

 DEGREE OF ANGULAR MEASURE. [ANGLE.] 

 DEGREE OF AN EQUATION. The degree of an algebraical 

 term is the number of letters which enter into it as factors. Thus 

 xPy 3 is absolutely of the fifth degree ; but of the second degree with 

 respect to x, and of the third with respect to y. The degree of an 

 equation is the degree of its highest term. 



DEGREE OF LATITUDE, OF LONGITUDE, OF MERIDIAN, 

 &c. [GEODESY.] 



DEIFICATION. [APOTHEOSIS; CONSECRATION.] 

 DEISM properly means belief in the existence of a God, but is gene- 

 rally applied to all such belief as goes no farther, that is to say, to 

 disbelief of revelation. It is always applied dyslogistically, and fre- 

 quently merely as a term of reproach. But the identical word, in its 

 Greek form, theisl, is not a word of disapprobation, and, consistently 

 with established usage, may be appropriately applied as opposed to 

 atheist, when the latter term is correctly used. For it must be observed 

 that the term atheist has been not unfrequently employed in the sense 

 of an unbeliever in Christianity, though at the same time professing 

 theism. 



DEL CREDERE COMMISSION. [AGENT.] 



DELEGATES, THE COURT OF, was formerly the great court of 

 appeal in ecclesiastical causes, and from the decisions of the Admiralty 

 Court. It was so called because the judges had delegated to them by 

 commission under the great seal the appellate jurisdiction of the 

 crown in these matters. These delegates usually consisted of judges 

 of the courts at Westminster and doctors of the civil law, but lords 

 spiritual and temporal might be joined. This court was first created, 

 in consequence of the statute 25 Henry VIII., c. 19, which transferred 

 to the crown the authority of the pope to entertain appeals from the 

 courts Christian. 



By the constitutions made at Clarendon, 11 Henry II., the practice 

 of appealing to the pope had been condenlned ; but though frequently 

 checked, it was never thoroughly broken off until the final rupture 

 with the court of Rome, in the reign of Henry VIII. After sentence 

 by the delegates, the crown might grant a commission of review ; but 

 the power was rarely exercised, except upon the ground of error in 

 fact or in law, and it was usual to refer the memorial praying for a 

 commission of review to the chancellor, before whom the expediency 

 of granting the prayer was argued. 



By 2 & 3 Wm. IV. c. 92, the Court of Delegates was abolished, and 

 its powers and functions were transferred to the crown in council 

 [PRIVY COUNCIL]. The same statute enacted, that no commission of 

 review should in future be granted. This jurisdiction is now exercised 

 by the Judicial Committee (3 & 4 Wm. IV. c. 41). 

 DELIAN PROBLEM. [DUPLICATION.] 



DELIQUESCENCE, the change of form which certain bodies 

 undergo from solid to fluid by exposure to the air, and absorbing 

 moisture from it. 



There are many substances which partake of this property : among 

 the more remarkable are potash, carbonate of potash, chloride of 

 calcium, and nitrate of copper ; all these will in a short time attract 

 sufficient water from the air to become fluid in it. Other saline 

 bodies are deliquescent only in moist air, such aa chloride of ammo- 

 nium and nitrate of ammonia. 



Certain deliquescent salts, and more especially chloride of calcium, 

 are employed for the purpose of drying gaseous bodies which are the 

 subject of experiment. 



DELI'RIUM TREMENS, a disease of the nervous system, to which 

 persons addicted to alcoholic drinks, though not exclusively, are pecu- 

 liarly liable. As its name indicates, its principal symptoms are delirium 

 and trembling. The delirium is a constant symptom ; but the tremor 

 is not always apparent, or does not exist. The delirium is always 

 attended with sleeplessness : the patient is busy, and constantly talk- 

 ing, but is seldom or ever angry or violent. If he is questioned, he 

 answers rationally, but speaks in an agitated and suspicious manner ; 

 he mostly docs whatever he is told, and is frequently anxious to oblige. 

 His thoughts, however, wander very quickly from objects around him, 

 and he is apparently surrounded by the scenes of his imagination. 

 Here, according to his occupation, he is busily engaged. If he is a 



