G R A 



G R ^ 



<Jivifion 54*, or -^,^3 of the whole circle ; tliere will therefore aid to the introduftion of ufelefs innovatioiu, by entering 



be 54' — 53^ = i' by approximation within the required niore minutely into the fubjeft. 



dejrree of accuracy. L. Mafcheroni is the Italian geometrician, we are in- 



Soliition 2— Let the arc B Z be taken = 10' 30', (by formed, who taught Bonaparte feme problems, when in 



the divifions exilling) from the centre a, and with the one of his campaigns in Italy, with one of wLicli he puz- 



diftance i Z as radius, crofs the circumference in the faid zled the Frencli mathematicians, and gained the reputation 



point Z' = 2(f 29' iHI> or 29' 3°' without an error of of being an adept in mathematics. 



halfafecond; then look for 28^ 30' in the exilling divifions, Gkadvatiok, in Mir^alogy. When a mineral is dif- 



-«- of the circle, and the difference will be very nearly covered wliich is intermediate between other known fpecie., 



f^ than fli/. . _ J ■ T/r . <- *- . ^ - *. 



as before 

 former 



r "7 ' '• J*"'', ^°'"''°," ■■' l^'■^„='«"■•»t<^ 'han the and in different fpccimen., or parts of the fame fpeEmien,' 

 by about 4'" i the error being 29 ". approaches very near to fuch known minerals, it is faid to 



Problem II. 



Tajind an arc of 15' <wUhout an error of l'". 



Se/uJion. — Take the arc B s == 1 2' below B,lhe diftance 

 f z will be the chord of 87 ' 15' ; with a radius of this ex- 

 tent, and from B, as a centre, cut the arc B F above, in 

 the point Z', and the arc B Z' will be 87' 15' ; but among 

 the exilling divilions of the arc is 87^ or ■?4'^th of the cir- 

 cumference ; therefore, the difference of the two arcs is 



Problem III. 

 Tof.nd an arc cf 10' without an error of l o'". 

 So'ution. — Take the arc B s downward = 49" 30' 



the diftance b % will be tlie chord of 38 

 error of 10'"; then, the divifion 39^ or 



and 

 50', without an 



, being found 

 already, their difference on the circumference taken from B 

 upwards, will bean arc of 10'. 



Problem IV. 



To find an arc of 6' •whliin 1 3 '". 



Solution. — Take the chord of 45° from B to G above, 

 and from the point b cut the circumference at =, which will 

 be at 40 6', downwards from B, without an error of 13'', 

 but 40" counted downwards already exifts, therefore the 

 fmall arc between is 6'. 



Problem V. 



To find an arc of l' ivithin 22'". 



Solution. — Let B 2 downwards be ^ 27' ; from the point 

 c as a centre with radius b 2, cut the circumference above at 

 Z ; and the arc B Z will be 29" 59', with an excefs of 22"' ; 

 tlierefore, the arc B N being 30 , the arc ZN will be l' 

 within 22'". 



By fuch means as thefe an arc of 9' uathin 7'" is deter- 

 mined ; alfo, an arc of 20" within 1'"; as arc of 15" within 

 10"; an arc of 12'' within 1'"; an arc of 10" within i"; 

 a!id an arc of 5" within 2'" ; but thefe lafl arcs arc fo minute 

 in all ordinary circles, that «e omit the folutions, as being 

 of no utility. 



We have hitherto fuppofed the circle divided into 360^ 

 with their liib-diviiions, but the French have propoicd a 

 fiintefimal divil'ion of the circle to be fublUtutcd, wlierc 

 eacli quadrant has ico~ inflcad of 9c', making 400' in the 

 vhole circU-. with each degree fub-divided bv lumdreds, &c. 

 Tins mode of dividing has been exemplified by L. Mafcheroni, 



graduate, pafs into, pafs over to, or make tranfitions to, 

 fuch minerals. Frequently, the ftrata of the earth graduate 

 thus into each other, fo that it is extremely difficult to de- 

 fine where one ftratum ends and another of vcr)- different 

 properties begins : thefe graduations arc not uncommon be- 

 tween fome lime-done flrata and the chert beds in thtm. 

 More frequently, each flratum is fcparated by a tliin byer 

 or way -board of pulverulent matter, which occalions the Arata 

 to part freely ; and often, in fuch cafes, the parts of the 

 ftrata in contact with thefe way-boards ditTcr notliing from 

 the general mafs of each flratum, or there is no graduation 

 between one flratum and the next in fuccefTion. 



Graduation of faltne Liquon, in Chswiflry, is a method 

 of concentrating weak faline folutions, by pouring them 

 through a heap of faggots, and expofing them in tliis di- 

 vided ilate to a free current of air. Sec Muriate of 



Soda. 



GRADUS Gemoxic. See Gemoni;?:. 

 GRjEA, Tfaisr, a name ufed by the old Greek writers 

 for the wrinkled pellicle which arifes upon milk in the 

 boiling. 



It was alio ufed in a figurative fenfe for the wrinkles Li 

 the (Ivin of old people. 



GRiECIA, Greece, \n Ancient Geo^aphy, a country of 

 confiderable extent, forming, as it were, the boundary or 

 frontier between Europe and Afia, and comprehending a 

 great number of different Hates and kingdoms. We have 

 various opinions as to the etymology of the appellations 

 Graci and Grscia. The mofl prevalent opinion traces the 

 origin of thefe terms to Graicus or Gricus, the father, as 

 fome fay, but, according to others, the fon of Thelfalus, 

 who gave its name to Theffaly. Salmallus fuppofes llie 

 name Graecus to be derived from Ragau or Rau, the fon of 

 Peleg, the fourth in dcfcent from Shem, the fon of Noah, 

 by the tranfpolition of a letter in order to foften the found. 

 Pezron deduces it from Graia, fignifying in Celtic ancient, 

 and appUcable to the Grecians by way of contradiftinction 

 to more modern people. But it has been objected to this 

 etymology, that the Pelafgi and Hellenes were a more an- 

 cient people than the Greeks. M. de Gebclin fuppofes the 

 origin of the appellation to have been the word rha, or rbe, 

 denoting vail or immeiife, in reference to tlic fca which ter- 

 minated the Adriatic gulf, on the borders of which tlie 

 Greeks migrated iouthwards, whence he forms Rmcus, fig- 

 nifying this fea, and br prefixing the guttural G to the lin- 

 gual R, Gniicus. The Greeks were alfo called Achians, 

 Hellenes and Pelafgi. The lirft of tlufe apptlblions is 



in his Geometry of the Compafs ; and Mr. Troughton has fuppofed to have been derived from Achius, the fon of 



i fcribi-d the mVthod of graduating a circle in this way by Xutluis, the fon of Hellen, and father cf Ion; the fc- 



, : method, if it fhould ever prevail in England; but, as cond from Hellen, jull mentioned, the fon of Deucalion, 



there appears to be no advantage to the divider in afloiding and father of Dorus, from whom fprung the Dorians ; 



lufeclions lower than 25°, and as our tables of logarithms, and the third, from a pretended founder Pelalgus, who, 



.Ts well as aflronomical tables, are adapted to the exiftiug taking poffelTion of the Peloponnefus,_ occafioned its being 



,'n(,de of dividing the circle, we are unwilling to lend our denominated Pelafgia. Grotius, Salmalius, .nnd Stillingfleet, 



4 A 2 jiaii:e& 



