EXAMINATION. 



EXCHANGE. 



EXAMINATION. [EVIDENCE.] 



EXANTHEMATA (Exanthematotu disease*), ^dySrifa, an efflores- 

 cence ; a term under which are comprehended the eruptive fevers, or 

 the diseases commonly termed rashes. Rashes are superficial red 

 patches, variously figured, and diffused irregularly over the body, 

 leaving interstices of a natural colour, and terminating in cuticular 

 exfoliations. Fever is an essential element in the definition of an 

 exanthematous disease, as this term is usually employed by nosologists ; 

 but the writers on cutaneous diseases give to it a modified significa- 

 tion, and comprehend under it only those diseases which are properly 

 termed rashes, whether those rashes are attended with fever, and 

 whether they are contagious or not. Thus Dr. Bateman comprehends 

 under the order Exanthemata measles, scarlet fever, nettle-rash, 

 roseola or the rose, purpura, and erythema. 



EXARCH was the title of the governor of Italy under the Byzantine 

 Emperors, established by Justinian after the reconquest of Italy from 

 the Goths in the sixth century. The first exarch was Narses, who 

 was also the greatest, about A.D. 568, ' and who held the exarchate for 

 fifteen years. The residence of the exarch was at Ravenna, then a 

 sea-port town, and the great entrepot between Greece and Italy; 

 and Italy was nearly equally divided between the kingdom of the 

 Longobards and the exarchate of Ravenna, which included the Romagna, 

 the Adriatic coast, Venice, and Naples ; while the more inland portions 

 were held by the Longobards. The exarchs, who were generally chosen 

 among the officers and favourites of the Byzantine court, were of 

 course removable at the pleasure of the Emperor, but several of them 

 remained in their office to the end of their lives. Their administra- 

 tion was often marked by acts of oppression and treachery, the results 

 of Byzantine corruption as well as of the peculiar difficulties of their 

 situation. They were engaged in frequent hostilities against the 

 Longobards who had invaded the greater part of Italy, and were also 

 not unfrequently at variance with the popes, and their authority was 

 often confined within the walls of Ravenna. At last, in the year 752, 

 Ravenna being taken by Astulf or Astolphus, king of the Longobards, 

 the exarchate, as well as all 'dominion of the Byzantines over North 

 Italy, was at an end ; but the Greek emperors still retained possession 

 of partu of Apulia and Calabria, where Bari became the residence of the 

 catapan or Byzantine governor. (See ' Chronological Series of the 

 Exarchs,' in Petau, ' Rationarium Temporum.') 

 KXi.'ENTRIC. [PTOLEMAIC SYSTEM.] 



KXCENTRIC, or ECCENTRIC, in machinery, a kind of wheel, or 

 revolving cam, in which the axis or centre of motion does not coincide 

 with the geometrical centre, or in which the periphery is not circular. 

 A general notice of such contrivances, and a representation of the kind 

 of excentric employed for working the valves of a steam-engine, will 

 be given under WHEELS. 



Excentrics of various kinds form an important class of mechanical 

 expedients for converting one kind of motion into another. They 

 afford means for converting continuous circular motion, in various 

 ways, into alternating or intermitting rectilinear motion, or into 

 curvilinear, though not rotatory motion. They also furnish means for 

 I IP 1 1 icing, from the uniform speed of one revolving shaft, rotatory 

 in-.ti-.n of continually varying speed in shafts placed in connexion with 

 it. As an illustration of such an application, Professor Willis, in his 

 ' Principle* of Mechanism,' refers to an excentric crown-wheel contrived 

 by Huyghens to produce some of the complex movements of a plane- 

 tarium. The subjoined diagram will illustrate the action of this 



apparatus, a representing the crown-wheel, which is mounted excentri- 



cally upon a shaft which revolves with a uniform speed, and ft r a 



pinion driven l.y it, and made so long that it may be acted upon either 



by that portion of the periphery of the crown-wheel which is nearest 



to its axis, and which describes in its revolution a path indicated by 



..ill dotted circle, coming in contact with the pinion at b, or by 



pposite portion of the periphery, which describes the path 



iled by the large dotted circle, and engages the pinion at c, where 



it i.< intersected by that circle. As the distance from the axis of the 



crown-wheel to the point ft is little more than one- third of the distance 



from the axis to c, and as the velocity of the axis or shaft is uniform, 



it follows that the pinion will be driven nearly three times as fast when 



in contact with that part of the periphery of the crown-wheel which 



lies farthest from the axis as when in contact with the part which 



intersects it .it h, while every intermediate portion of the periphery of 



the crown-wheel will impart a different, but intermediate velocity. 



i combiaition of wheels might be driven by the pinion, in which 



case, supposing the pinion to have a uniform velocity, that of tlie 

 crown-wheel, or rather of its axis, will vary. Further variations might 

 introduced by making the periphery of the crown-wheel of other 

 ,han a circular form. 



Excentrics may be driven by bands or straps ; but unless the bands 

 >e very highly elastic, it is necessary to apply a stretching pulley or 

 roller, which may be pressed against the strap by the action of a weight, 

 <o maintain a uniform degree of tension. 

 EXCENTRIC WHEELS. [WHEELS.] 



EXCENTRICITY, a term applied to the ratio which the distance 

 Between the centre and focus of an ellipse or hyperbola bears to the 

 whole semiaxis. [ELLIPSE; HYPERBOLA.] With regard to this word, 

 it should be noted that in the older writings on conic sections it was 

 not the ratio of these two lines, but the former of them, namely, the 

 distance between the centre and focus, which was called the eccen- 

 tricity. 



Let a, be the semimajor axis of an ellipse or hyperbola, b the semi- 

 minor axis, and e the eccentricity ; then 



i 2 

 in the ellipse e 2 = 1 -5 



I' 

 in the hyperbola e j = 1 + :, 



EXCESS. For a peculiar mathematical use of this term, namely, 

 the ipherical excess, see SPHERICAL TRIANGLE. 



EXCHANGE. The rules by which operations of exchange are 

 conducted must be either the simple rule of three or the chain rule. 



In the simple and direct operation nothing but the rule of three can 

 be required. Thus, the exchange between London and Paris being 2.1 

 Francs 55 centimes to the pound sterling, 6732 francs are converted 

 into English money by finding the fourth term of the following : 



25-55 : 1 : : 6732 : the answer. 

 and 139?. 14. Gd. can be converted into French money by 

 1 : 25-55 : : 139/. 14. 6rf. : the answer. 



But in the case of the indirect operation of passing money from one 

 country into another through a third, a double operation of the rule 

 of three is requisite, which may be facilitated by the use of the chain 

 rule. Suppose, for instance, that the exchange between London and 

 Paris is 25*55 francs to the pound sterling, and that the exchange 

 between Paris and Hamburg is 100 marks to 189 francs. Then, to 

 find out the arbitrated value (as it is called) of 139J. 14s. 6(1., remitted 

 to Hamburg through Paris, we have 



100 marks are worth 189 francs 

 25'55 francs 1 pound 



139/. 14. 6rf. How many marks ? 



It is however more common, first to establish an arbitrated rate of 

 exchange, by putting I/, in the place of 1392. 14s. 6rf., and then 

 deducing the value of the latter sum. This is more convenient, 

 because it establishes a rate once for all until the exchanges vary. 



But the student must not content himself with the simple expo- 

 sition above given. There are many little matters of business which 

 cannot be explained here, but which may be found in such works as 

 Tate's ' Commercial Arithmetic,' and the ' Counting-House Guide ' of 

 the same author. 



EXCHANGE. The term exchange is commonly employed by mer- 

 chants to designate first, the operation of the written instrument, 

 by which the debts of persons residing in different countries, or in 

 different parts of the same country, are brought to a condition for 

 final liquidations ; and, second, the varying price of such negociable 

 instruments in the market, which price is determined by the course of 

 mercantile transactions, by means of which the obligations of debtors 

 residing at a distance from their creditors, are discharged without the 

 transmission of corned money. 



The first division of the subject is discussed under the title BILL OP 

 EXCHANGE ; the following article will comprise the second, and will 

 include an investigation of the principles on which exchange transactions 

 are based. 



International, or, as it is commonly called, foreign trade, arises out 

 of the unequal or exclusive capacity of different countries to produce 

 the various objects of desire. One country, for instance, has abun- 

 dance of coal and iron ; another enjoys a climate especially adapted to 

 the culture of the vine ; whilst a third possesses some peculiar advan- 

 tages for the growth of wheat. If interchange were not restricted by 

 legislative enactments, if trade were perfectly free, the first country 

 would supply the other two with iron wares, taking from the second 

 wines, and from the third wheat; whilst the two last would, in like 

 manner, exchange their respective productions with each other. 



Peculiarities of soil and climate, abundance and cheapness of land or 

 of labour, the exclusive presence of certain animals, vegetables, or 

 minerals, high excellence in particular arts and manufactures, all give 

 rise to interchange between nation and nation. Every country lias 

 some peculiarity which gives it an advantage, with respect to that 

 peculiarity, over all other countries : it is by means of interchange 

 that such advantages are shared equally among all. 



In the article BILL OP EXCHANGE, already referred to, we have 

 explained how this mode of settling accounts, between parties in, 



