J 815.] in the Physical Sciences. 53 



11. Geognosy. 



I ought now to give a sketch of tlie recent improvements in this 

 branch of science, which of late years has become a fashionable 

 object of study in Great Britain ; but I have already extended this 

 article to such an enormous, and I fear improper length, that I 

 must, however reluctantly, stop short here. The great object of 

 geognosts on the Continent at present seems to be to trace to their 

 utmost extent the formations discovered in the neighbourhood of 

 Paris ; and to extend as much as possible the transition formations 

 in those countries hitherto considered as primitive. In this country 

 we have no fewer than three geological societies, the Wernerian, 

 the London, and the Cornwall. The first two have recently pub- 

 lished each a volume of Transactions, I shall give an analysis of 

 each of these books as speedily as possible. They contain almost all 

 the important geological facts that have been lately ascertained ia 

 Great Britain. 



Article II. 



Solution of a Prohlem of Col. Silas Titus. {See JFalUs's Algelra, 

 Chap. 60.) By the Abbe Buee.* 

 SIR, 



Having for many years considered the different algebraical 

 methods for the solution of arithmetical problems by approximation 

 to be deficient in their fundamental principles, I have been led to 

 mistrust tlie whole science of algebra as generally taught, and am 

 convinced that if we place an implicit faith in it we shall be involved 

 in the most revolting absurdities. Pell's problem (see Wallis's 

 Algebra, chap. (JO, 62, &c.), and all those which can only be re- 

 solved by approximation, are examples of this kind. The absurdity 

 belonging to the solution of these sort of problems is to represent 

 numbers of whicli we know not the fundamental unity. In specu- 

 lation this al)surdity is not felt ; but we easily perceive it when we 

 (juit speculation, and are engaged in questions respecting real 

 beings, such as men. In this case the solution gives for units 

 fractions as much smaller as the approximation is farther extended. 

 If, then, the real unit be a man, the solution gives for unit a frac- 

 tion of a man, which goes on always diminishing, and by that 

 means becomes more and more absurd. In general the speculative 



* Tlic following curious tolution of a well-kno\vn ])r(>l)Ii'ni was sent by tli* 

 Ablj(^ l>ii(<e to !i m.'illiomalicul geiitlciniin in IjOikIoii, w Iid iIin-Iiiios cuMiniiinicutiiig 

 his namo to ilic piililic. Tlioii(;li I (In not paitii-ipntc in the Alibi'-'s i>hji'ilions to 

 algebraic appniximation, yet I cnnreivc llic- boiutiDii of Ilic piohlcni iisolf to br so 

 curious as (o Itv well cntillrd lo tlic nKciilitm of ina(licii);iticiuns ; unit on that 

 account 1 a;;riT(l williotil liofilalinn lo invert it in l\\f ylntials of Pliiloncy/iy. The 

 letter whicli mtvcs ris an intiuduclion lo th« prublciii it written by tin* Abbtf 

 Uuiv. — i. 



