. OHGBBM, 



CONIC SECTIONS. 



140 



. integrant et perfectam eoclesUm, ex suis partibui coniUn- 

 tan immediate et ind<*p*odciatr sub ipw Christo/ It it said that 

 they adopted the name of congregational brethren, and congregational 

 churchw, to aroid the odium of .edition and anarchy which wu 

 charged upon them M the Puritan regicidos of Charlea I. Cromwell 

 made use of them a* a political check on the Prebyterian party. (See 

 ' Declaration of the Faith and Order owned and practised by tho ( ' n 

 gregatkroal rhuirh.-, in KngUnd.' 158.) In the x New England 

 states of North America, which were oolonUed by the EnglUh Puritan*, 

 the Congregational i*t are very numerous ; and in several other parts 

 of the Union their number* are much larger than tho*e of other sects. 

 Their creed and the rule* of their democratic government are givon 

 fully in th.-ir ' Platform* of Discipline.' They beliere in Tlio 

 Trinity ; Predestination ; Total Depravity ; Particular Redemption ; 

 Effectual Grace and Final Perseverance,;" and maintain that 

 congregation of visible saints, furniahed with a pastor, is und, r n- 

 other ecclesiastical jurisdiction whatever." 



(Moaheim, cent. 17, it part ii. ; Neat's Jlitt. Pur!tat; Bumet's 

 Hi*. Om Timtt; Adam's Dirt, of Krligiun.) 



CONGRESS, an assembly of envoy* delegated by different courts 

 with powers to concert measures for their common good or to adjust 

 their mutual concerns. The term is given also to a meeting of sove- 

 reign princes which is held for the like purpose. The delegates from 

 the Assemblies of the British colonies who met at New York, 7th 

 October, 1705, to consider their grievances, called their assemblage a 

 Congress. A second congress, which assembled in June, 1774, and sat 

 for eight week*, published a Declaration of Rights. Another congress' 

 met in May 1775, which proceeded to organise the military and 

 financial resources of the colonies ; and thus these assemblies of dele- 

 gates exercised the functions of a supreme government, and under their 

 authority the war of independence was brought to a successful termi- 

 nation. In 1 789 the constitution was re-organised, and a congress of 

 two bonus was formed. [UNITED STATES or NORTH AIIERICA, in 

 OEOO. Drv.] The meeting of envoys or plenipotentiaries which pre- 

 cedes a treaty of peace is sometimes called a Congress ; but the termjs 

 more generally applied to such meetings when they have to settle, 

 either before or after the peace, an extensive plan of political arrange- 

 ments and re-organisation. This was the business of the Congress of 

 Vienna in 1815. Sometimes a meeting of sovereign princes or pleni- 

 potentiaries takes place to concert a certain line of political action, 

 and this is also commonly termed a Congress. Examples of these 

 are furnished by the Congress of Carlsbad, 1819; of Troppau and 

 Laybach, 1820, and of Verona, in 1822. 



CONIA. The active principle of hemlock appears to be an alkaloid 

 termed conia, which, unlike most vegetable alkaloids previously known, 

 is not fixed and crystalline, but volatile and oleaginous. It has been 

 obtained both from the leaves, and fully developed but still green 

 fruits. Its activity is increased by union with acids, both mineral and 

 vegetable; a circumstance which shows the impropriety of giving 

 vinegar as an antidote in cases of poisoning by hemlock, when any of 

 the substances is yet present in the stomach. Conia is sparingly 

 soluble in water, to which it imparts its odour and taste. It also 

 combines with about a fourth of its weight of water to form a hydrate 

 of eonia. The salts of con in are very soluble in water, but rapidly 

 undergo decomposition, so as to become innocuous ; water is therefore 

 on improper vehicle for their exhibition. When exposed to the air it 

 quickly contracts a dark brown colour, and is slowly resolved into a 

 resinous matter, with the disengagement of ammonia. This change 

 takes place more promptly tinder the co-operation of heat ; but even at 

 common temperatures it is so apt to enshe, that unless the alkaloid 

 be kept very carefully excluded from the air, discoloration will take 

 place in a few hours. Though conia exists in the plant in combi- 

 nation with coniic acid, which may render it less alterable, yet its 

 proneness to decomposition is so great, that either by time or the 

 application of a considerable degree of heat, it may be entirely dis- 

 Rrpated ; which accounts for the inertness of old leaves, and of most 

 extracts which have not been prepared with the greatest care. Qeiger 

 says that the dried leaves do not contain conia ; a statement which, 

 if correct, leads to the conclusion that conia, though the most powerful, 

 is not the only efficient agent in hemlock. 



Conia appears, from the experiments of Oeiger and Christison, to 

 be a deadly poison to all animals. It acts with the most extraordinary 

 rapidity ; but if it fail to kill, its injurious action passes quickly away, 

 and perfect recovery follows. It acts through every texture of the 

 body where absorption is readily carried on. It acts as a local irritant ; 

 but its ultimate and fatal energy is chiefly exerted on the spinal chord, 

 to which its influence is conveyed by entering the blood and pro- 

 ducing on the inner membrane of the blood-vessels a peculiar nervous 

 impression, which is instantly conveyed by sympathy along the nerves 

 to the organ remotely and ultimately affected. " It exhausts the 

 nervous energy of the spinal chord, producing general muscular 

 paralysis and asphyxia from -relaxation." The heart, how. 

 exempt from this general paralysis, contracting vigorously for a long 

 time after all motion and respiration and other signs of life are ex- 

 tinct. It is, therefore, extremely probable, as suggested by Dr. Chris- 

 that where a dose is not so large as to produce immediate death, 

 the carrying on of artificial respiration and administering vital stimu- 

 lants, might save the life of the patient, especially as the action of 



the poison is so transient, and incapable of producing a permanently 

 injurious impression. 



Infusion of galls, or strong black tea, if speedily administered, might 

 prove an ant 



l< SKCT1ONS, the curves formed by the intersection of ft 

 circular cone and a plane, either oblique or right 



Though the name of conic Motions still remains, yet the interest 

 which attaches to those curves, and the method of treating them, has 

 no longer any reference to the accident from which they derive their 

 name. The Qreek geometers, in pure speculation, occupied themselves 

 with the different method* in which a cone may be out, simply because 

 the conical surface (with the cylindrical and spherical) came within the 

 restrictive definitions under which they had placed geometry. [GEO- 

 METRY.] The works of APOI.LOXII-S and ARCHIMEDCS [Bioo. Div.] are 

 the first in which these lection* were treated ; and their mil-sequent 

 history is nothing but that of the addition of a few remarkable pro- 

 perties, until the discovery that the path of a projected body in an 

 unresisting space is a parabola, and that of a planet round the sun an 

 ellipse. [UAULEO, and KEPLKR, in !!]<><;. Div.] Since that ti 

 might as well attempt to write the history of mathematics and physics 

 as that of conic sections in their results and consequences ; and from 

 that time we have nothing to say of them merely as conic teclioni. 



Some sections of a cone are considered in elementary geometr 

 a plane may meet a cone in a point, or in a single straight line, or in 

 two intersecting straight lines, or in a circle. But the curves which 

 ore peculiarly conic sections are, the oval made by a pUne which cuts 

 the cone entirely on one side of the vertex, culled the ELUPSK ; the 

 indefinitely extended modification of this when the plane becomes 

 ]>arallel to any one slant side of the cone, called the PARABOLA ; and 

 the curve which ie partly on one side and partly on the other of tho 

 vertex, formed by a plane which cuts both surfaces of the cone, called 

 the HYPERBOLA. To these names we refer for the specific properties 

 of the sections. 



Algebraically considered, the conic teetimi are the curvet of the ttfnul 

 degree, meaning the curves belonging to such equations between co- 

 ordinates are of the second degree. Thus, x and y being co-ordinates, 

 oblique or rectangular, the general equation 



a a? + b xy + c j? + d y + c x+f=0, 



may, by properly assuming a, o, r, Ac., be made the equation of every 

 possible section of a cone by the plane in which the co-ordinates are 

 measured. As very many elementry works do not fully discuss the 

 conditions under which the preceding equation represents the different 

 sections, we subjoin the following from the ' Comb. Phil. Trans., 

 vol. v., p. 89. In the following list, 8 means the angle mode by the 

 co-ordinates : 



Let v, 



9 v,=4oc- 



'-i d e . 



6-- 4 a c 



and in the case where v, and c (P + a e*b d e, are both= 0, let 



4 a 



4 c 



In the following table, p means either sign, + or , but in the same 

 line, n means the other sign ; a dotted line means that the sign of the 

 expression at the head of the column need not be considered. The 

 word line by itself means straight line. 



Thus if w' and v, both have the same sign, and v, be positive, the 

 equation cannot be satisfied at all ; but if w' and v, be of different 

 signs, and if T, be positive, the equation is that of an ellipse. \\ V 

 may add that v, = 0, indicates an equilateral hyperbola. [Hvrnii- 

 BOLA.] 



The general properties of the sections are numerous and interesting, 

 but we shall only mention one, because it is the most convenient as a 

 general definition of the curves, combining them at once with each 

 cither, in a manner to which algebra is easily applied. If a point move 

 in such a way that its distance from a given point (called the/nni*) 

 always is the same fraction of its perpendicular distance from a given 

 right line (called the Hirtctri.r), then the curve traced out is an ellipse, 

 parabola, or hyperbola, according as the given fraction is lew than, 

 equal to, or greater than. unit}'. We arc 

 deducing the properties of these curves can be very successfully n i 



