MEMORY FAITHFUL TO ITS TRUST. 35 



diate observation. Many of the simple, yet comprehensive 

 formulae, to which your attention has been directed in 

 your mathematical [course, will, upon an analogous 

 principle, facilitate your other researches in an extraor- 

 dinary degree. And you have on former occasions been 

 especially shown how essentially even the simple 

 improvement introduced by Professor T. Simpson, (in 

 1757,) in the designation of trigonometrical functions, 

 sin. a, cos. a, tan. a, &c., have conduced to the sublime 

 discoveries of La Grange and La Place, to which I have 

 already adverted in this Lecture. 



Indeed, mathematics and philosophy abound with 

 evidence of the advantages, as well as the beauty of 

 scientific grouping and arrangement. You trace them, 

 for example, in the connexion of the length of the 

 second's pendulum in any place, with the lineal measure 

 of the force of gravity as marked by the space described 

 uniformly in a second unit of time, with the velocity 

 acquired by a body falling freely during the first unit ; 

 and the rich train of results that are deducible from that 

 connexion : you trace them in the admirable chemical 

 technology introduced by Lavoisier, and in the theory 

 of definite proportions : you trace them again in the 

 reference of the specific gravities of all substances to that 

 of pure rain water; in that of all temperatures to 

 the measure supplied by comparing the temperature of 

 boiling water and that of thawing ice ; and in the inves- 

 tigation of the properties of curves of different orders 

 by means of equations of different degrees; together 

 with the method of co-ordinates, and its easy and elegant 

 application to every department of mathematical physics. 



V. While, however, scientific classification will relieve 

 the memory of much of the burden which it would 



