202 PHILOSOPHICAL TRANSACTIONS. [aNNO IOQ'J . 



count gives go, the lowest 50, the middle 70 ; the blacks do not understand 

 arithmetic, so the numbers they give in all cases are very uncertain. 



The shore lies almost east and west, exposed to the sea wholly on the south. 

 The country is hilly ; the hills not very high, but thick, clustering together; 

 the valleys between extremely narrow ; the whole in a manner covered with 

 certain low but very thick shrubs. Not the tenth part of the ground is tilled : 

 and where they do till, within half a year the ground is overgrown as before ; 

 for they do not root up the shrubs, but only cut, or sometimes burn them 

 somewhat close to the earth ; so they spring again in a very little time ; this is 

 sufficient for planting their corn, which they do by making small holes in the 

 earth, at a competent distance, and putting seeds into them. 



The water, which they have in pits, rain water for the most part, has a 

 mixed taste of sweet and subacid. At Whiddah, which is one of the most un- 

 healthy places in Guinea, he that opens the ground, though it be but to dig a 

 grave, runs the hazard of his life ; so noxious are the steams arising from it. 



The age of the inhabitants is very uncertain, because none of them keep an 

 account of it ; there are some of them very grey, but if the country be to them 

 unhealthy, grey hairs may come early. Much of the mortality among strangers 

 is the effect of their irregular diet, and drinking to excess very hot and spiritu- 

 ous liquors ; and if any chuse the cold rather, his stomach is chilled, and he is 

 in danger of an immediate flux. 



The Quadrature of Figures Geometrically-Irrational. By John Craig. N° 232, 

 p. 708. Translated from the Latin. 



Let ACF, fig. 1, plate 5, be a semicircle, and ade a curve geometrically irra- 

 tional, whose ordinate bd cuts the semicircle in c. Also let the quantities be 

 thus represented, viz. the diameter af = la, the absciss ab = y, the arc 

 AC = V, the ordinate bd =: z. And let z = rvy" be a general equation, ex- 

 pressing the natures of the geometrically-irrational curves ade, in which r de- 

 notes any given and determinate quantity, and n the indefinite exponent of the 

 indeterminate quantity y. Then I say the area of the curve will be, abd = 



rvyn + 1 , . ra n , 2nra- + ra- n ~ I , OA X 2n — ln-8 



^+T - 9" + ^'^^y-l/I/ >"to =^y + ^^^-^^^ + „-i 1/ 

 1^ n — <Z ^ ?i-3-' ' n — 4, ^ 



be observed, 1. That the capitals, a, b, c, d, &c. denote the coefficients of the 



,. , , ,. . ra- X 2h + 1 OA X 2n — 1 



terms immediately preceding; \\z. a = ^ , , b = — — , c = 



