VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 151 



tensive and convenient in its application than any method hitherto offered. The 

 general resolution of the given fluxion into a series of fluxions of the same kind, 

 where the index of the unknown quantity without the vinculum keeps decreasing 

 or increasing either by the index under or by half the index, has not, that I know 

 of, before been given ; which furnishes us at once not only with a very easy 

 method of continuing fluents, but also points out a very simple method of in- 

 vestigating the fluent of the given fluxion without continuation. For if /a = p 

 -f U/b + cfc + dfo + &c./b =P' -\-c' /c + d'fi + &c. /c = p" If r/h 

 -|- &c. &c. &c. then if for fsfjc, &c. &c. we substitute their respective values, we 

 shall get a general series for fk without continuation. The extent of any new 

 method is, at first, seldom obvious ; and how far that which is here proposed 

 may be successfully employed in other cases will best appear from its application. 

 Different methods will always be found to have their uses in particular cases ; for 

 where one becomes impracticable, another will often be found to succeed ; and I 

 hope that which is here offered will contribute something towards facilitating the 

 investigation of fluents. 



Here, Mr. V. finds the fluent of -■ , "^ , r- from that of ^ being: sriven. 



(a" + jf")' a" -j_ j;» b to 



x'x 



From the fluent of — — r~ — jr-j he finds that of , 

 From the fluent of -, is found that of — — . 



1 — X Vi — x^ 



From the fluent of -^ — 7, is found that of oCxs/ 



— b' x" — 6* 



All these are determined by very ingenious contrivances, and illustrated by 

 many neat examples of particular cases. A variety of other useful and kindred 

 methods and forms may be profitably consulted in the author's treatise on 

 Fluxions since published in 1 vol. 8vo. 



XXVI. Conjectures relative to the Petrifactions found in St. Peter'' s Mountain, 

 near Maestricht. By Petrus Camper, M. D., F. R. S. p. 443. 



The discovery of a great number of petrified bones about the year 1770, in 

 the mountain of St. Peter at Maestricht, and particularly of large jaw-bones 

 with their teeth, suggested to the late M. Hoffinan, first Surgeon to the Military 

 Hospital at Maestricht, a worthy member of several learned Societies, and a 

 great admirer of natural history, the idea that these maxillae belonged to croco- 

 diles. This notion was spread by himself and his literary correspondents through 

 all Europe. He did me the favour to send me, not only the history of those 

 petrifactions, but also several figures of the jaw-bones in question, and of other 

 bones, which were all entirely new to me, except some fragments of the bones 

 of turtles. I discovered however, at the very first sight, the characteristical 



