INFLECTION. 



■fcent from it, or towards it ; which is a kind of imperfccl re- 

 flection or rcfraClion. See Diffraction'. 



This property was firft taken notice of by Dr. Hooke ; 

 who ihows th^t it differs botli from refttlhn and refrac- 

 tion ; and focnis to depend on the unequal denfity of tlic con- 

 ftitucHt parts of the ray, whereby the hglit is difperfcd 

 from l!ie place of condenfation, and rarilied or gradually 

 diverged into a quadrant : and this defleiSiion, he fays, is 

 made towards the fuperficies of the opaque body perpendicu- 

 laily. Some writers afcribe the iirft difcovci-j- of it to 

 Griinaldi, the Jefuit. He firft publiflied an account of it, 

 in his treatife «' De Lumine, Coloribus, et Iride," printed 

 in 1666 ; nor did any other perfon lay claim to the dilco- 

 very, except Dr. Hooke, wlio comnuuiicated his obferva- 

 tions on this fubjecl to the Royal Society, in 1672. It 

 appears, however, that Dr. Hooke had not heard of the dif- 

 coveries of Grimaldi ; for he fpeaks of his own as a diftovery 

 of a sievv property of light, not mentioned by any optical 

 writer before him. 



Sir li'aac Newton difcovered alfo, by plain experiment, 

 this inflexion of the rays of ligiit ; and M. de la Hire affures 

 us he found, that the beams of the liars being obferved, in 

 a deep valley, to pafs near the brow of a hill, are always 

 more refracted than if there were no fuch hill, or the obfer- 

 vations were made on the top thereof ; as if the rays of 

 light were bent down into a curve, by pafling near the fur- 

 face of the mountain. 



Sir Ifaac Newton, in his Optics, makes feveral experi- 

 ments and obfervations on the infleiflion of the rays of light ; 

 which fee under Light, and Ravs. 



Although fir I. Newton particularly examined the pheno- 

 mena, relating to this fubject, under a confiderable variety 

 of circumftances, his obfervations were not quite correft ; 

 nor was his hypothetical explanation very plaufible. Sub- 

 fequent experiments and obfervations feem to reduce the 

 phenomena of inflection to a fingle principle, •v'lx. to the at- 

 traction of bodies towards hght ; which attraction becomes 

 confpicuous when the rays of light pafs within a certain 

 diftance of their lurfaces. Befides their being bent, the 

 rays of light are likewife feparated into colours by the vici- 

 nity of bodies, and this produces the fuigular phenomenon 

 of the coloured fringes that accompany the inflection. 

 Various experiments have been made relative to the infleftion 

 of light by Maraldi, Grimaldi, Delifle, Mairan, Du Tour, 

 Mufchenbroek, and others, as well as Newton ; an account 

 of which experiments the reader may fee in Prieftley's 

 Hiftory of Vifion, Light, and Colours, part vi. ^ 6. 



M. de la Hire obferved, that when we look at a candle, 

 or any luminous body, with our eyes nearlv (hut, rays of 

 light are extended from it, in feveral directions, to a con- 

 fiderable diftance, like the tails of comets. The true 

 occafion of this phenomenon, which has exercifed the faga- 

 city of Des Cartes, Rohault, and others, feems to be, that 

 the liglit pafling among the eye-lafties, in this fituation of the 

 eye, is inflefted by its near approach to them, and therefore 

 enters the eye in a great variety of directions. 



Inflection, in Grammar, the variation of nouns and 

 verbs, in their feveral cafes, tcnfes, and declenfions. 



Inflection is a general name, under which are compre- 

 hended both conjugation and declenfion. 



IxFLKCTlON, Point of, of a curve, in Geometry, is a point 

 or place where the curve begins to bend, or turn a contrary 

 way. 



if a curve line, as A F K {Plate X. Analyfis, fg. 2.) be 

 partly concave, and partly convex towards a right fine, as 

 A B, or towards a fixed point, the point F, which divides 

 ihc concave from the convex part, and confequenlly is at the 



beginning of the one and end of the other, is called thc/wKf 

 of infledion, as long as the curve, being continued beyond F, 

 keeps its courfe the fame : when it returns back again towards 

 that part or fide from whence it took its origin, it is 

 called the point nf relro^rejfton. 



To conceive tliis, it is to be confidered, that any quantity, 

 which goes on continually increafing or decreafing, cannot 

 change from a pofitivc to a negative exprefiion, or from a 

 negative to a pofitivc one, without firft becoming equal to an 

 infinite, or nothing. It becomes equal to nothing, if it con- 

 tinually decreafe ; and equal to an infinite if it continually 

 increafe. 



Now, if through the point F be drawn the ordinate E F, 

 and the tangent FL, and from any point, as M, on the 

 fame fide of .A F, be drawn the ordinate M P, and the tan- 

 gent M T ; then in curves which have a point of inflection, 

 the abfcifs A P continually incrcafes, and the part A T of 

 the diameter, intercepted between the vertex of the dia- 

 meter, and the tangent M T, incrcafes alfo, till the point 

 P fall into E ; after which it again begins to dimiuifli : 

 whence the line A T mull become a maximum A L, when 

 the point P falls into the point E. 



In thofe curves which have a point of retrogrei^on, the 

 part A T increafes continually, and the abfcifs incrcafes, till 

 the point T falls into L ; after which it again diminiflics : 

 whence A P muft become a maximum, when the point T 

 falls into L. 



If A E z= .V, E F = y, then will A L = ^ - .v (fee 

 Taxgext), whofe fluxion, which is •^ "^ .. '^ - — x = 



'-^-r. '- =— --^, fuppofing X conftant, 



being divided by a-, the fluxion of A L muft become 



nothing; /". e. — ^ = o: fo that multiplying by, v', and 



dividing by — v, j = o ; which is a general form for find- 

 ing F, the point of infleclion, or retrogreflion, in thofe 

 curves whofe ordinates are parallel to one another. For the 

 nature of the curve A F K being given, put the equation of 

 the curve into fluxions ; from which, or from other pro- 

 perties of the curve, find the value of x or 1", and put this jc- 

 or j and its value into fluxions, making both x and v = o : 

 then by expunging the reft of the fluxional quantities. 



AE. 



EF, at 



fliall determine the value of 

 the point of infledicn fought. 



To diftinguifli the points of inflexion from thofe of retro- 

 greflion, which arife indifcriminately according to the above 

 method, it will be fufficient to attend to the progrefs of the 

 curve, by taking any ordinate very near the point ; which 

 will always ferve to remove any doubt on that head. 



£x. 1. — To find the point of infieftion B in the curve 

 A B Y {Jij. 3.) whofe equation (putting the abfcifs A C 

 = J', ordinate C B = y,anil the perpendicular A E =^ a) hax' 

 = ay + .v'j'. From the fluxion of this equation, viz. 2 ax x 



■J + 2 



deduce v = 



by fubftiluting for_y its value —^ — -, 



(a- + x-y 



and the fluxion of this equation, making both x and_>' = o 

 2 a' a" (a" + x^f — (4 ei^ XX -\- 4 .r' x) 2 a^ x x 



02 



which 



