I N F 



y\r- - ^ a y' y- + 4 "" y'- 



— ~ = o, and thefe again reduced to a com- 



y - a 

 mon denominator will be 

 4j'> — \2ay' -u 12 ^'y' — ^ a'' y"' + Ja^^'j— 2 a' !,'- 



a- b'- {y - a) 

 = O, or M ; the roots of which equations will give thofe 

 values of y, or of B F, that anfwer to fo many different 

 points of contrary flexure. In p;eneral the number of roots 

 in the iinite equation always indicate the number of points 

 of inflexion or retrogreiTion belonging to the curve which 

 is the fubjecl of invelligation ; and confequently, in thofe 

 curves that have but one fuch point, it is determined by a 

 llniplc equation. 



Curves may alfo have another kind of retrogreffion different 

 from that we have been confidering ; which is, when the 

 turve returns backwards towards its origin, turning its ca- 

 vity the fame way that it did before its retrogreflioii, as in 

 the following cafe. 



Let the curve be BAC(/^. 7.), with a contrary 

 flexure at A, and let it be evolved by a thread beginning 

 at any point D, different from the point of contrary flexure 

 A : the evolution of tlie portion D C generates the curve 

 T) G, and that of the portion A 13 generates the curve E F ; 

 lii fuch manner that the evolution of the whole curve B A C 

 will form the entire curve F EDO, which has two retro- 

 grefTions, one at D of the ufual form, becaufe the two 

 branches D E, D G, turn their convexity ; the other at 

 E of the fecond fort, becaufe the branches E D, E F, 

 are concave towards the fame parts. Let now m N, N« m, 

 he any two radii, indelinitely near, of the evolute D A ; 

 and N H, and « H, two perpendiculars to the fame ; the 

 two indefinitely fmall feftors N m M, H N «, will be 

 funilar, and therefore H N : N M : : N n : M w. But 

 in the point of contrary flexure A, the radius H N 

 ought to be either infinite, or nothing ; and the radius 

 N m, which becomes A E, continues finite. Therefore, in 

 the cafe of contrary flexure A, that is, the point of retro- 

 greffion E, of the fecond fort, the ratio of N n, M m, or the 

 ratio of the fluxion of the radius M N, to the element of 

 the curve, ought to be either infinitely great, or infinitely 



T T-1 T>._^ .1 _ f i_ _r *!,« — i:..o AT M \c- V ' .' ' 



V <-v^ 



y + 



o, or CO i 



v/bicli is the formula for points of retrogreffion of the fe- 

 cond order. 



For other methods of finding the points of inflexion and 

 retrogreffion of curves, the reader is referred to Simpfon's 

 a'ld Maclaurin's Fluxions ; Donna Agnefi's Analytical In- 

 Jlitutes ; and to the Traite Elementaire deCalcul Differen- 

 ticl, par La Croix. 



INFLORESCENCE, in Botanical Phrafeology, wjloref 

 rcnt'ia of Linnxns, is ufed to exprefs the particular manner 

 in which flowers are difpofed upon a plant, and which pre- 

 ceding writers denominated the modus Jlorenili, or " manner 

 of flowering." The fcveral kinds of inflorefcencc come 

 under the heads of Feitkillus, Racnnus, Spka, Corymhuh 



1 N F 



Fafaciihu, Cop'itulum, Umhelk, Cyma, Pankuk and Thyrfm, 

 which the reader will find in their proper places. A 

 flight correction of the definition which {lands under our 

 article C.■\^ITlLl;.^I is neceffary, the Slatke Armnui 

 Tlirift, and Gomphrcna globofa or Globe amaranthus, b. : 

 better examples of that kind of inflorefcence than any c 

 pound flower. 



For the reafons againfl taking generic characters fioia 

 the inflorefcence, fee Cyme and Gk.nu.s. 



INFLUENCE, a quality fuppofed to flow from t! - 

 bodies of the liars, either with their heat or light, to wlnu 

 allrologers vainly atU'ibute all the events w^bich happen i i 

 the earth. 



Alchemifts, alfo, who to this afcribe the philofopliei 'o 

 fl.one, tell us tlsat every thing in nature is produceil by tin' 

 influences of the fliars, whicli, in their paffage through ti c 

 atmofphere, imbibe many of its moid parts, the grolll :i 

 whereof they depofit in the fands and earths where they fali ; 

 that thefe, filtrating through the pores of the earth, defec; ,'. 

 even to the centre, whence they are driven, by the ce.i:. 

 fire, back again to the furface ; and in their afcent, ! 

 natural kind of fublimation, as they find earths duly difp> 

 they form natural bodies, as metals, minerals and \ 

 tables, &c. Thus it is pretended, that chemiftry, conlii 

 of an artificial imitation of thefe natural operations, ;: 

 in applying aClive principles to paffive principles, can lej::, 

 natural bodies, make gold, &c. See TuANSMUTATio.^, 

 and Philosopher's Stose. 



INFLUENT, a term ufed where a liquor or juice, by 

 the contrivance of nature, and the laws of circulation, falls 

 into a current or receptacle. 



Thus with refpefl: to the common receptacle, the chyle 

 is its influent juice ; and fo is the bile to the gall-bladder ; 

 the venal blood to the heart in its diaftole ; and the like. 



INFLUENZA, in Medicine, a term generally employed 

 to denote an epidemic catarrh, which has at different times 

 fpread more rapidly and extenfively than any other epidemic 

 diforder. For it has feldom occurred in any one country of 

 Europe without appearing fucceffively in every other part of 

 it ; it has fometimes apparently traverfed the whole of the 

 old world; and, in fome infl;ances, it has been even trans- 

 ferred to America, and has fpread itfelf over that continent 

 likewife. The French give it the name of La Grippe. 



In truth, this extenfive prevalence of the difeafe confti- 

 tiites its moft remarkable peculiarity : for in all the inftances 

 of its occurrence, from the fourteenth century down to the 

 prcfent day, its phenomena have not only been pretty uni- 

 formly the fame, but have differed little, except in fevcrity, 

 from thofe of the common febrile catarrh. ( See C.VTARRH. ) 

 This will appear from the following defcription of the dif- 

 eafe, when epidemic in 1782, which is taken from a compre- 

 henfive view of it, compiled by the late Dr. Gray, of the 

 Britifli Mufeum, from a number of accounts given by phyfi- 

 cians, in various parts of Great Britain, from their own per- 

 fonal obfervation (fee Medical Communications, vol. i. 

 art. I. Lond. 1-S4); and from a fimilar account publifhed by 

 the College of Phyiicians. Med. TranfaCtions, vol. iii. art. 8. 



Very little authentic information was procured refpedting 

 the hiltory of this epidemic, before the time of its appear- 

 ance in London: all that was dated, on good authority, was, 

 that it prevailed at Mofcow in the months of December 

 1781, and January 1782, and at Peterfburgh in February 

 1782 ; and it was traced to Tobolflii, to which place it was 

 fuppofed to have been brought from China. In confirmation 

 of this opinion it was obferved, that feveral accounts from 

 different parts of the Eaft Indies made mention of a dilorder, 

 fimilar in its fymptoms, which prevailed in thofe parts in the 



