494 D'ALEMBERT. 



we have just been describing the nature and the subdivisions. 

 In common with the different branches of Natural Philo- 

 sophy, it possesses all the interest derived from the contem- 

 plation of important truths, the first and the purest of the 

 pleasures derived from any department of science. There is 

 a positive pleasure in that exercise of the mental faculties 

 which the investigation of mathematical and physical truth 

 affords. The contemplation of mathematical and physical 

 truths is, in itself, always pleasing and wholesome to the 

 mind. There is a real pleasure in tracing the relations between 

 figures and between substances, the resemblances unexpect- 

 edly found to exist among those which seem to differ, the 

 precise differences found to exist between one figure and 

 another, or one body and another. Thus, to find that the 

 sum of the angles of all triangles, be their size or their form 

 what it may, is uniformly the same, or that all circles, from 

 the sun down to a watch dial, are to each other in one fixed 

 proportion, as the squares of their diameters, is a matter of 

 pleasing contemplation which we are glad to learn and to re- 

 member from the very constitution of our minds. So there 

 is a great, even an exquisite pleasure in learning the compo- 

 sition of bodies : in knowing, for instance, that water, once 

 believed to be a simple element, is composed of two sub- 

 stances, the more considerable of which makes, when united 

 with heat in a certain form, the air we burn and the air we 

 breathe; that rust is the combination of this last substance 

 with metals; that flame is supported by it; that respiration 

 is performed by means of it; that rusting, breathing, and 

 burning, are all processes of the same kind; that two of the 

 alkaline salts are themselves rusts of metals, one of these 

 metals being lighter than water, burning spontaneously when 

 exposed to the air, without any heat, and forming the salt by 

 its combination. To know these things, and to contemplate 

 such relations between bodies or operations seemingly so 

 unlike, is in a high degree delightful, even if no practical use 

 could be made of such knowledge. So the sublime truths of 

 astronomy afford extreme gratification to the student. To 

 find that the planets and the comets which wheel round the 

 sun with a swiftness immensely greater than that of a cannon- 



