HYDROSTATICS. 9 



which forbad bloody sacrifices." But, if the story be, 

 as is probable, a mere fiction, it still serves to mark the 

 state of mathematical knowledge, when a proposition 

 which, however fertile in its consequences, is now placed 

 among the lowest elements, should be characterised as 

 the most brilliant discovery of the great man to whom 

 we owe it. 



It does not comport with the nature of an address 

 like the present to contrast these in detail with the 

 modern state of geometry, of algebra, of fluxions, and 

 the differential and integral calculus, of the trigonometri- 

 cal analysis, of logarithms and exponentials, of series, 

 of rectifications, quadratures, cubatures, tangencies, 

 points of contrary flexure ; together with the sublime 

 researches in the theories of partial differences, isoperi- 

 meters, and variations. Much less can I attempt to 

 sketch their diversified applications to mixed mathe- 

 matics, and the contributions which have thus been made 

 to the arts and commodities of civilized life. But on 

 these you will be called to enlarge as suitable opportu- 

 nities occur, in the pursuit of your studies here. 



Leaving then this inexhaustible general topic, let us 

 descant on a few particulars drawn from several depart- 

 ments of science ; taking first, that of the pressure and 

 motion of liquids. Every one who hears me will recol- 

 lect the story of Archimedes's exultation when he 

 discovered the principle by which might be detected the 

 fraud of the goldsmith who made Hiero's crown. An 

 accidental thought, suggested while he was bathing, led 

 to the investigation of a series of propositions, enunciated 

 and demonstrated in his two books, " De Insidentibus 

 in fluido" now extant. The nine propositions demon- 

 strated in the first book relate to the principal laws and 



