244 



CIRCLE CIRCULATING MEDIUM. 



him no injury, and deliver his companions. Ulyssei 

 remained with her a whole year, and had by her 

 two sons Adrius, or Agrius, and Latinus. Before 

 his departure, she told him that, in order to secure a 

 safe return to his country, he must visit the infernal 

 regions, and ask advice of Tiresias. 



CIRCLE (Latin circulus) ; a plane figure compre- 

 hended under a single line which returns into itself, 

 having a point in the middle, from which all the lines 

 drawn to its circumference are equal. This point is 

 called the centre, and these lines the radii. Al- 

 though, properly speaking, it is the space included 

 within the periphery or circumference, yet, hi the po- 

 pular use of the word circle is frequently used for the 

 periphery alone. From the geometrical definition 

 of the circle, it appears that its magnitude is 

 dependent upon the magnitude of its radius or 

 its diameter, i. e., a line which touches two points 

 of the circumference, and passes at the same time, 

 through the centre, or, which is the same thing, a 

 line equal to twice the length of the radius. The 

 surface of the circle is equal to the product of the 

 circumference and half the radius. If there existed 

 a rational proportion, tliat is, a proportion to be ex- 

 pressed in whole numbers, of the surface of the cir- 

 cle to a square surface, there would be, at the same 

 time, a rational proportion between the diameter and 

 the circumference. But, from geometrical reasons, 

 no rational proportion of the diameter to the circum- 

 ference is possible ; it can be expressed only by ap- 

 proximation. However, the proportion thus obtained 

 is quite as accurate as is necessary for any purpose 

 in the applied mathematics. Yet there have always 

 been instances, and some of a very late date, of men 

 labouring long and intensely in searching for the 

 square equal to the surface of the circle, and who of- 

 ten believed that they had actually solved the pro- 

 blem. Very recently, the newspapers were full of such 

 a solution by a boy in England. In the approximate 

 proportion, if the diameter is called 1, the circumfer- 

 ence will be equal to 3-1415926535. .. . Francis 

 Vieta obtained the proportion to this number of fi- 

 gures. Afterwards it was further determined by 

 Adrianus Romanus to 15, by Ludolphus of Cologne 

 (often improperly called von Keulen) to 35 (from 

 him it is often called the Ludolpliic number), by 

 Sharp to 72, by Machin to 100, by Lagny to 126, 

 and lastly, in an Oxford manuscript, it was obtained 

 up to 156 decimals. Archimedes first estimated the 

 proportion of the diameter to the circumference to be 

 as 7 to 22, or as 1 to 3-142 ....; after him, Metius, 

 as 113 or 355, or as 1 to 3-1415929, which is correct 

 to 6 decimals, and sufficiently accurate for most pur- 

 poses. Every circle is divided into 360 degrees, and 

 by its arcs all angles are measured. The circle, there- 

 fore, is one of the most important geometrical figures, 

 and an accurate division of it is requisite for measur- 

 ing the angles under which distant objects appear 

 (upon which surveying, astronomical observations.&c. 

 rest) a very desirable object, for which many prizes 

 have been offered by learned societies. See Degree. 



Circle, in logic ; the fault of an argument that 

 supposes the principle it should prove, arid after- 

 wards proves the principle by the thing which it 

 seemed to have proved. The same fault takes place 

 in definitions, when an idea is defined by others 

 which suppose the knowledge of the first. Arguing 

 in a circle is a fault into which men are very liable 

 to fall, particularly in theological discussions. 



CIRCUITS ; in England, divisions of the king- 

 dom appointed for the judges to pass through twice 

 in the course of a year for the purpose of administer- 

 ing justice to the several counties. The counties of 

 England are divided into six circuits, and two judges 

 Jfo on each circuit. In America, the same name is 



given to the divisions of the country traversed an- 

 nually by the judges of the supreme court of the 

 United States, for the purpose of trying causes 

 which fall within the jurisdiction of the national 

 courts. 



CIRCULAR INSTRUMENT. See Ke/bctiu* 

 Circle. 



CIRCULAR MOTION. A body in motion, 

 which is continually impelled by some power towards 

 a fixed point out of its original direction, is oblig- 

 ed to describe a curvilinear path round tliis 

 point. A stone, slung round by a string moves in a 

 circle, because it is drawn toward the hand in 

 every point of its path. The moon moves in a circle 

 round the earth, because, it gravitates towards the 

 earth, and is thus drawn from the rectilinear direction, 

 which it would otherwise pursue. In such cases, the 

 point to which the body constantly tends, is called 

 the centre of the forces, the force itself, by which it 

 is impelled, is called the centripetal force ; that by 

 which it strives to fly from the centre is called the 

 centrifugal force, and the motion which is produced 

 by these two forces, the circular motion. All the pla- 

 nets in the solar system are carried round the sun, 

 and the satellites round their planets, by these forces. 

 (See Central Forces.) The theory of circular motion 

 is a subject of celestial mechanics, on which Newton 

 composed his Principia Mathematica Phitosoph. Na- 

 tural., and Laplace lu's Mecanique Celeste, &c. As 

 the model of a concise and beautiful exposition, we 

 recommend the article under this head in Gehler's 

 Physiqalischns JVorterbuch (Dictionary of Natural 

 Philosophy). 



CIRCULAR PARTS (NAPIER'S RULE FOR). A rule 

 invented by Baron Napier of Merchiston near Edin- 

 burgh, for the solution of all cases of right-angled 

 spherical triangles, eminent for its comprehensiveness 

 and utility in extensive surveys, navigation, and prac- 

 tical astronomy. See Trigonometry. 



CIRCULAR SAILING. See Navigation. 

 CIRCULAR SAWS. See Saw Mill. 

 CIRCULATING MEDIUM. The expression cir- 

 culating medium is now much more frequently used 

 than formerly. It means the medium of exchanges, 

 or purchases and sales, whether tliis medium be gold 

 or silver coin, paper, or any other article, as oxen, 

 tobacco, iron, slaves, usually employed in any place 

 as the measure of the values of other articles, and is 

 thus of a more comprehensive signification than the 

 term money, which, though it applies to gold and sil- 

 ver coin, paper currency, and some other of the vari- 

 ous articles used for the above purpose, does not 

 :omprehend them all, since oxen, which have, by 

 some nations, at some periods, been adopted as the 

 measure of the comparative values of articles of com- 

 merce, would hardly be considered as coming under 

 the denomination of money. It is hardly possible to 

 magine a people to be without a circulating medium 

 of some description ; and, accordingly, we find all the 

 tribes of savages hitherto discovered referring to 

 some article in estimating the value of the various 

 commodities which compose their capital. Captain 

 Franklin says, the Krees Indians use beaver skins as 

 their medium, and estimate the value of thing.* by a 

 :ertain number of their skins. The people of Vir- 

 ginia, in the earlier periods of their colonial history, 

 estimated value by pounds of tobacco. In some 

 Darts of Africa, a species of small shells, cowries, are 

 jie medium of exclianges. But from the earliest 

 times, the precious metals, where they could be 

 had, have been preferred for this purpose, because 

 their weight, fineness, and, consequently, value, 

 could be more accurately ascertained than those of 

 any other article, and thus comprise a sufficient value 

 n a small compass and weight to be a convenient 



