1 38 Mat}>ematical CorrffpMidetice. 



or '■ = , and confequently F = ^ k/h-x — a= = — — / ^'"'' ~ ^ 



But when the body, in revolving, comes to D, * then becomes = r j in which cafe, 

 p = — , or F is as -^, or as the fquare of the velocity divided by the radius. 



NEIV MATHEMATICAL QUESTIONS. 



Question V. By IF. Simpsox. 



A BOTTLE which held exaiflly 5 oz. 106 gr. of diftilled water, was capable of contain- 

 ing 5^ oz. and 170 gr. of a folution of common fait in diftilled water : Required the weight 

 of the fait held in folution, its fpecific gravity being 2,8 ? 



Question VI. By J. B. 

 THE mean annual temperature of any two latitudes, in the fame hemifphere, being 

 given, to determine the mean annual temperature of any other latitude in that hemifphere ? 



Ti Mr. N/CNOLSOX, Etlitof of " The Journal of Natural Philofophy, Chcmiflry, and the Arts." 



1 DO not know whether you will confider the following as of fufticient importance to merit 

 a place in your valuable publication ; — if fo, I (hall perhaps occafionally, in future, trouble 

 you with other attempts of a fimilar nature. 



Being about four years ago engaged in fome mathematical fpeculations, in the courfe of 

 which the rcfolution of pretty high equations became frequently neceflary, I was induced to 

 fet about the inveftigation of an eafy arithmetical rule for the folution of an adfe£tcd qua- 

 dratic, in order to ftiorten the bufinefs of approximation. — It is, indeed, you know, on ac- 

 count of the prolixity of the ordinary methods by completing the fquare or exterminating the 

 fecond term, that Dr. Hallcy's method of obtaining the approximate value of the root, by 

 taking fuch terms of the affiimed equation as involve the fquare of the converging quantity, 

 is now feldom ufed ; fuch only as contain its firil power being ufually admitted into the cal- 

 culation. The moiie which 1 adopted for this purpofe will be bed underilood by a llate- 

 nient of the principles from whicli it is deduced. 



Let x~ + ax be = b. Then will the affirmative value of at be = \ [y a~- -t- 4^ — a.) — 



1 V ■ i^ _ ^-^ + ^_^'±. _ Io■5■4^i^ 'o -.?-7-4'-^^- . 



2 _ ■ 2.a 2.4./.'. "^ 2.4.6.0'. 2.4.6.8. «'. "^ 2.4.6.8. I0.n9. 



i-jl'liK 2.i>. K.by 14.**. „ „ . , , . ,. , ^ . 



=r •t^' —r- -1 4- — - — &c. But in order to obtam (his latter fcncs, 



a a ■ ai. aT. n'. 



we have pa)^ to divide i by a, adding to the original divifor a, every time of repeating the 



divific I, do-iWe the quotient already found, together with the term which fucli new divifton 



ihall produce, as in the common operation for extracting the fquare root, as follows : 



