Mathematical Correfponience. 'tL\ 



CASE ir. x^—a>i = —b. ^"1 



KUhV..— Proceed as before, except that injlead of aiding the tiuo lajl figures ef the quotient to 



ebch divifor, as in the former Cafe, they mufl in this be fubtracled from it, and the remainder will 



be the new divifor for each repetition of the divifion. 



The quotient is the leffer -value of the root, which ,fubtraEied from the original divifor a, will give 



the other value, both of them being ajprmative. If b be greater than the fquare of \a, the folution 



is however impojfthle. 



EXAMPLE. 



Given *- — 19.23456*;. — — 83-57214567. Qusre A-. 



a . . . . =19.23456. 

 — 6 



ift Divifor 



=: 13.23456. ) 83.57214567, ( + 6.630654987. Sec. = *. 



— 66 79.40736. 19.23456. 



2d D = 663456. 



- 63 



3d D z= 600456. 



— 30 



4th D. 



597456. 

 c6 



4164785 +12.603905012. &C. = K. 



1840496 ■ 



3912870. 



328494. 



29796 



5900 



524 



46. 



S 



5'liD = 597396 



It is unneceflary to remark, that the contraftions ordinarily made ufe of in the extraftioE 

 of the fquare root are equally applicable here ; and they are accordingly applied in all the 

 examples except the firft. 



I am inclined to believe that fuch as ufe this procefs will find it attended with fome ad- 

 vantages in point of expedition, efpeclally where a confiderable number of places is re- 

 quired in the root — and being mathematically correct, it may of courfe be extended to any 

 length. 



I am. Sir, your mo(V obedient Servant, 

 l^\\i May 1797. J. F — :— : — : — r. 



SCIENTIFIC NEIVS. 



Account of Memoirs pubtijlicd by the Polytechnic School at Paris. 



[Continue^ from page ^5.] 



AT ha.ilpngheen known, that the fulphurcof potafh attradls die cxygcne in the atmofphere, 



and frparates it from the azote with which it is combined. Attempts were confcquently. 



nadr to conltrufl rudiomcters with this fulphure in imitation ofScliccle ; but none of thefe 



6 gav« 



