Mr. Goodwyii's Manuscyip/x. 141 



terest and annuities; othei's to the determination of powers 

 and roots; others to the reduction and comparison of weights 

 and measures, whether British or foreign, and to the forma- 

 tion of a general system ; and others he rendered apphcable 

 to the rules of mensuration and to still higher inquiries among 

 mathematicians. 



" In the pursuit of these researches he developed various in- 

 teresting properties indicative of the mutual connexion be- 

 tween circulating decimals and prime numbers, entering either 

 simply or compositely into the denominators of fractions re- 

 spectively equivalent to those decimals ; of which propei'ties 

 some have been long known to mathematicians, while others 

 had almost, if not altogether, escaped their notice. A few of 

 these are explained in the Appendix to the quarto pamphlet 

 to which this paper is attached * ; and in that appendix 07te 

 of Mr. Goodwyn's ingenious improvements in computation is 

 described and applied. 



" The resultsof his persevering and long-continued labours, 

 have, as yet, been only very partially laid before the public 

 in a few detached pamphlets, volumes, &c. ; — copies of all 

 which are herewith transmitted. But his two works of greatest 

 labour, the one denominated " A Table of complete decimal 

 quotients, " and the other " A Tabular series of decimal 

 quotients for all the proper vulgar fractions," of which, when 

 in their lowest terms, neither the numerator nor the denomi- 

 nator is greater than 1000, still remain in manuscript. The 

 former of these is comprised in four folio volumes of manu- 

 script, and lettered " Table of complete quotients." 



" Mr. Goodwyn had finished their computation, and by sub- 

 sequent calculations had nearly', if not entii'ely, verified the 

 correctness of the whole. He had also advanced considerably 

 in the comi)utation of the "Tabular series," the results being 

 entered and duly arrariged in five volumes large quarto ; in 

 the last of which, however, the j^lat/hnn oi' hh labours is alone 

 exhibited. 



"A comparison of the respective manuscripts with the two 

 royal octavo printed volumes entitled " Table of the circles 

 and tabular series," and with tlie quarto jiamphlet to which 

 this is annexed, will enable any competent judge to appreciate 

 the extent of tiiese classes of Mr. Goodwyn's labours, their 

 utility, and the c()m))arative value of those portions which still 

 remain unpublished. 



" Mr. Goodwyn's family, anxious to consign these manu- 



• Kiititlcd " The first Contcnary of a concise anil ii-ofiil Tabic of coni- 

 |ilcte Decimal Quotients," with n specimen of '' A tahuhn- Series," &c. • 



scripts 



