493 



DEUTOXIDE. 



DEW. 



494 



chap, xxviii. proclaim the blessings promised to the observers of the 

 the law, and the fifty-five following verses recite the curses on the 

 disobedient. The last twelve verses of the xxvii.th chapter contain the 

 twelve curses which serve to compose the Commination of the English 

 Liturgy. The passages in chap. xviiL 15, 18, 19, are considered as 

 prophetical of the Messiah, on the authority of Acts iii. 22, 23 ; and 

 vii. 37. Chap, xxxii. consists of the last song of Moses, the poetry of 

 which, in the opinion of a very competent judge, Bishop Lowth, is 

 singularly magnificent. Dr. Adam Clarke remarks, that "very few 

 parts of the Old Testament Scriptures can be read with greater profit 

 by the genuine Christian than the book of Deuteronomy," which is to 

 be considered as correlative with St. Paul's Epistle to the Hebrews. In 

 Wilson's ' Archaeological Dictionary,' article Law, a valuable tabulated 

 exhibition is given of the whole Mosaic Law, in three classes, moral, 

 ceremonial, and political, with the places of references to Exod., Levit., 

 Numb., and Deut. Dr. Adam Clarke concludes his commentary on the 

 book with six elaborate chronological tables, for which he deserves the 

 thanks of every biblical student. The 'Biblioth. Brit.,' by Watt, 

 contains a numerous list of sermons and commentaries on Deu- 

 teronomy. 



(Eichhorn's Einleitung in das Alte ?%>(., abtheilii ; Poli, Synopsis Cri- 

 ticorum, torn. i. ; Calmet's Diet. ; Home's Introduc., vol. iv. ; Hartf 

 Mtaaica, by Rev. G. Faber ; Lecturet on the Pentateuch, by Dr. Graves; 

 Comment. OH the Mosaic Lam, by Michaelis, trans, by Dr. Smith.) 



DEUTOXIDE. A chemical term applied to compounds of oxygen, 

 containing two equivalents of oxygen to one of some other body. It 

 ia synonymous with binnxicle. [CHEMICAL NOMENCLATURE.] 

 DEVASTAVIT. [EXECUTOR.] 



DEVELOPMENT. (Algebra, &c.) A name given to the process 

 by which any mathematical expression is changed into another of 

 equivalent value or meaning, and of more expanded form. It is not to 

 be understood that development either facilitates the calculation or 

 the explanation of an expression, necessarily; it may sometimes do 

 the one, and sometimes the other, but as often it is the reverse. Never- 

 theless, the mathematical use of an expression is frequently facilitated 

 by employing its development, and this in a great variety of ways. 



The expressions of common algebra will frequently furnish instances 

 of this. Let us take the development of (x + y)\ namely 3? + Sj&y + 

 3.i-7/ s + y 3 . The original expression implies an addition and two mul- 

 tiplications, while the development involves six multiplications as 

 difficult as those of the original, two of a more simple character, 

 and three additions. Nevertheless the BINOMIAL THEOREM, of which 

 the preceding is a particular case, is the foundation of many import- 

 ant branches of algebra. But the usual form of development is into 

 infinite series [SERIES], a subject of peculiar interest, and the higher 

 points of which, as may readily be seen from comparison of mathe- 

 matical writings, are not perfectly well settled. 



The mere word development suggests only one question, namely, 

 what connection exists between the expression itself and its develop- 

 ment. Are they both actual representations of the same arithmetical 

 value ? Or do they merely represent algebraical forms which have the 

 same properties ? There are cases in which the first question must 

 be answered in the affirmative, and others in which the second question 

 must be so answered, while it is palpably the contrary with regard to 

 the first. Without entering into the reasons of such difficulties, it 

 must here suffice to remind the student who seeks for such matter 

 as is immediately connected with the common use of the word, that 

 he must be cautious what he admits upon any point connected with 

 it, since it may frequently happen that he will find himself endeavour- 

 ing to reconcile a very narrow meaning of the term with the forms 

 of expression used by writers who take for granted a knowledge such 

 as can only be acquired by considerable experience and reflection. So 

 wide is the modern use of the term, that the following caution may 

 frequently be useful. When an author speaks of the development of 

 an expression, remember that he may have so extended a signification 

 of the word, that the student should consider him as meaning merely 

 " algebraical substitute," or an expression which may be used for the 

 original without change of algebraical properties. He will hardly 

 understand what we mean, nor is it for our present purpose necessary 

 that he should do so : our intention will be answered, if, in referring 

 to this work for the use of this particular term, he should be dis- 

 tinctly made to understand that in all probability his difficulty arises 

 from an indistinct view of the meaning of equality, or of the sign =, 

 as employed in algebra, such as we conceive a very eminent modern 

 English writer to have had, when he proposed, in order to overcome 

 the difficulties attending the interpretation of a series, to consider 

 one plus one as having a meaning distinct from two. 



There are two points connected with developments which it may be 

 worth while to point out, as illustrative of this (at first sight) apparent 

 want of connection between an expression and its development, which 

 it should seem ought to exist between two forms which are used 

 indifferently each for the other. 



1. An expression may preserve an algebraical identity with its 

 development in cases where arithmetical identity is entirely lost. Le< 

 us consider the series P=\+x + x* + . . , . continued without end, o! 

 which it is an evident property that P= 1 + a; P. And the same is also 

 a property of its well-known equivalent form l-:-(l x), which is in 

 truth nothing more than the value of P derived from the last equation. 



Jut suppose that x2, and there is no imaginable arithmetical con- 

 nection between 1 + 3 + 4 + 8+ .... continued for ever, and 1-^-1(1 2) 

 1. On this point, see INFINITE, DIVERGENT, and SERIES. 

 2. A development may present an intelligible result in cases where 

 .he original expression altogether loses meaning. Thus, let the follow- 

 ng expression be considered : " the product of all whole numbers, 

 jeginning with 1 and ending with x" of which 1.2.3.4.5, or 120, is a 

 >articular case. Considering this as a function of x, it is obvious that 

 we can find meaning and value in all cases in which x is a whole num- 

 ber. But when a; is a fraction, we lose all idea of meaning : what is 

 implied, for instance, by the product of all whole numbers up to 10J ? 

 Nevertheless, when we take the approximate expression for this pro- 

 duct mentioned in COMBINATIONS, or the series of which it is the first 

 term, namely, 



the difficulty has disappeared : this series is as easily intelligible and 

 calculable when a; is a fraction as. when x is a whole number. This 

 paradox namely, an alteration of form, giving more meaning to an 

 expression than it had at first is of a character which cannot be 

 briefly treated. 



The inverse word to development should be invelopment ; so that while 

 we say that 1 +x + a? + . . . is the development of !-=-(! x), we should 

 also say that the latter is the inrelopment of the former. But the latter 

 term is never used, which frequently gives rise to a circumlocutory and 

 sometimes to a defective mode of description. 



DEVICE, an emblem or ensign, formerly borne on shields or em- 

 broidered upon banners as a cognisance, contemporary, in the history 

 of heraldry, with coat-armour itself. As early as the 12th century, 

 King Henry II. caused certain devices to be painted, which had a 

 descriptive reference to his name ; the planta-genista, or broom-sprig, 

 and a jenet passing between two broom plants, the former of which is 

 engraved upon the great seal of hia son, Richard I., on either side of 

 the throne. For many succeeding centuries these devices appear to 

 have been confined to the royal use ; but from the reign of Richard II., 

 various houses of the nobility adopted their use. Thomas Mowbray, 

 duke of Norfolk, appeared against Henry, duke of Hereford, in the 

 celebrated joust at Coventry, upon a horse whose velvet trappings were 

 embroidered with lions and mulberry trees, intended to typify his 

 name. The devices of greatest notoriety were the white and red 

 roses, by which the contending families of the royal stem are still 

 metaphorically described. From the close of the 15th to the middle 

 of the 16th century the friezes, entablatures, and stained windows of 

 the more sumptuous habitations were crowded with devices. The 

 Bourchier and Stafford knots were of this description. Camden, in 

 his Remains, has a section entitled ' Rebus, or Name-Devices ; ' these 

 were probably adopted in imitation of the emblems which, during the 

 Neapolitan wars of the 15th century, were painted by the Italian 

 chiefs upon their shields, accompanied by mottoes or quotations de- 

 scriptive of enterprise, or of the general character of the bearer. Such 

 were called Impresses, from the Italian word ' Impresa.' 



DEVISE. [WILL.] 



DEW is the moisture which, when the surface of the ground is 

 colder than the atmosphere, whether at night or in the day, but prin- 

 cipally, and as usually observed, between sunset and sunrise, is depo- 

 sited from the air, in the form of minute globules, on the surface of 

 bodies in contact with it. When the cold is extremely great, the 

 vapour becomes solid instead of merely condensing into liquid water, 

 forming a dendritic crystallisation of ice, or the globules of water 

 freeze or solidify after deposition ; producing what is called hoarfrost, 

 of two kinds. 



The history of our knowledge of dew, as an object of scientific in- 

 vestigation, is singularly interesting, and the process by which it is 

 formed involves several of the great principles of nature. In some 

 remarkable speculations of Aristotle (' Meteor.' i. 10), it is supposed to 

 be a species of rain formed in the lower atmosphere in consequence of 

 the moisture which had been carried up during the day by evaporation 

 being condensed by the cold of the night into minute drops. In 1784 

 Professor Patrick Wilson, of Glasgow, published a paper on hoar-frost 

 in the Transactions of the Royal Society of Edinburgh, in which he 

 supposes that cold is occasioned by its formation. In the course of the 

 same year, and in 1788, Mr. Six communicated papers to the Royal 

 Society of London in which he imagines that dew proceeds partly from 

 the low temperature of the air through which the dew already formed 

 in the atmosphere had descended, and partly from the evaporation of 

 moisture from the ground, on which his thermometer had been placed. 

 In a subsequent and posthumous work printed in 1794, the cold of 

 the grass is, however, attributed, in agreement with the opinion of Mr. 

 Wilson, altogether to the dew deposited upon it. Mr. Wilson and 

 Mr. Six observed, that the production of (hoar-frost or) dew is accom- 

 panied with cold on the surface of the ground greater than in the 

 atmosphere a few feet above, the differences being frequently 5, 10, or 

 even more degrees of Fahrenheit's scale. This cold, as has just been 

 mentioned, was considered as the effect of the formation of the dew, 

 though this conclusion involved a very considerable difficulty ; for as 

 the transition of a body from the state of vapour to the fluid or solid 

 form is always accompanied with an evolution of heat (which, as will 



