Rot/al Society. 71 



Locke, and stored with an extent of reading and of acquired know- 

 ledge almost beyond example, there can be found few subjects which 

 he has not illustrated j and in respect to conclusions which seem to 

 differ from the deductions of his great predecessors, his arguments 

 are so fairly stated on either side, that every intelligent reader is 

 placed in a situation to form his own opinion on those profound and 

 abstruse points. Mr. Stewart has somewhere quoted — Mei^ov so-ri ro 

 ivva^iv ava.\vriKr)V Ktrjo-aa-Qat rov -TtoXXa; txiro^si^st; rcuv eiri it-spovs 

 eyjiv. And, " Mathematica multi sciunt, Mathesin pauci. Aliud est 

 enim n6sse propositiones aliquot, et nonnuUas ex iis elicere, casu 

 potiiis quam certa aliqua discursandi norma, aliud scientise ipsius na- 

 turam ac indolem prospectam habere, in ejus se adita penetrare, et 

 ab universalibus instructum esse prseceptis quibus theoremata ac pro- 

 blemata innumeraexcogitandi, eademque demonstrandi facilitas com- 

 paretur. Ut enim pictorum vulgus, prototypon ssepe saepius experi- 

 mendo, quendam pingendi usum, nuUam vero pictoriee artis, quam 

 optica suggerit, scientiam adquirit ; ita multi, lectis Euclidis et alio- 

 rum geometrarum libris, eorum imitatione, fingere propositiones ali- 

 quas ac demonstrare solent, ipsam tamen secretissimam difficiliorum 

 theorematum ac problematum solvendi methodum prorsus ignorent." 

 By reverting to the long-neglected controversies of the Nominalists 

 and the Realists, and by adopting the theories of a most acute and 

 subtile reasoiier, who for centuries past has been remembered (such 

 is the caprice of Fame) by a reference only to the frailties and to the 

 misfortunes of his youth, this able metaphysician has either fully ex- 

 plained, or has pointed out the method of explaining, every difficulty 

 which seemed to obstruct the use of imaginary quantities. And by 

 pursuing the same track — if ancient prejudices, derived from far dif- 

 ferent speculations, could once be banished from our minds — it would 

 soon be found that all circumlocution for avoiding the terms infinitely 

 small, infinitely great, and even orders of infinites, might be dismissed 

 from mathematical language, without producing uncertainty, mystery, 

 or confusion. I consider, therefore, Mr. Dugald Stewart as a distin- 

 guished writer in the higher departments of mathematics, and eo no- 

 mine entitled to our respect and our regard. 



On the foreign list we find the name but of one individual whose 

 loss we have to regret in the past year, M. Thunberg of Upsal. 



M. Thunberg, a jjupil of the great Linnaeus, "one of the few remain- 

 ing companions of the prophet," has continued throughout a long life 

 to cultivate a science which Sweden must consider as her peculiar 

 glory. His labours are perhaps little known in this country at present; 

 but at a period when botany stood more pre-eminently forwards, — 

 about forty years ago, — M. Thunberg was chosen on our foreign list. 



On delivering titc Medals. 

 Of the duties devolved on those Fellows of the Society whom in 

 any particular year you may honour by naming on your (.'ouncil, 

 none are equally arduous with the distribution of your medals. If 

 the requisite inquiries were limited to discovering able men, ingeni- 

 ously contrived experiments, or valuable communications, the task 



would 



