THE ATOMIC VIEW OF NATURE. 439 



theory of gases suggests, we begin to realise the enormous 

 numbers of individual elements of matter with which we 

 have to do in any physical or chemical operation or ex- 

 periment. The step which enabled mathematicians to 

 calculate molar and cosmical phenomena by looking upon 

 them as made up of an immeasurably, nay infinitely, large 

 number of elementary parts, be these of space or time, 

 was taken by Newton and Leibniz : its result was the 

 invention, development, and application of the infinitesi- 

 mal calculus. Our fundamental notions applied only to 

 integrals, to a summation of these differential properties. 

 It was the problem of the new calculus to deduce from 

 the simple differential properties, expressed in what is 

 called the differential equation, the results of finite ob- 

 servable quantities. This was done by a process of sum- 

 mation or integration. In this process the elements were, 

 however, all considered to be equal. This was an assump- 

 tion which, for the purposes of simplicity, might be safely 

 made in a first approximation. When, however, the kin- 

 etic theory of gases took seriously into account the motion, 

 velocity, number, and size of the constituent particles of 

 matter contained in any finite measurable volume, or por- 

 tion of matter, two distinct views presented themselves : 

 the one which looks only at the total or average result 

 and aspect of the phenomena, the other which looks at 

 the actual behaviour and properties of the component 

 parts, be these ever so numerous or ever so small. These 

 latter could no longer be regarded as differentials which 

 lose their independent existence in the process of summa- 

 tion : they had individual properties, which were not lost 

 in the aggregate. It is evident that chemists had been 



