46 UNIVERSITY OF MISSOURI BULLETIN 



you that he really reaches him, though this is a consummation 

 not always recognized by a certain type of scholastic mind. 



These problems of approach, the so-called limit processes 

 form a chapter by themselves in mathematics. They also 

 relate mathematics to science in an exceedingly intimate way. 

 Thus, the velocity of any moving point is best considered as 

 the limit which is approached by the ratio of the distance 

 to the time. The rate of change of anything falls directly 

 under this scheme. Without venturing into further detail, I 

 will simply mention that this topic, the rates of change of 

 varying things, is what we call the Differential Calculus. Now 

 everywhere in science we encounter things which are in 

 states of change ; bodies in motion ; currents of heat, of 

 electricity, sweeping through objects; liquids in process of 

 evaporation; solids in process of melting, in process of solu- 

 tion; materials in process of decay, and so forth, in a variety 

 without end. The rate of change of all of these is absolutely 

 of the type considered in the calculus, which is thus really 

 essential to the intimate study of all things which are not 

 absolutely dead, inert and changeless. In many of these 

 scientific considerations the calculus is not used, that is, it 

 is not consciously used; for, before a conscious use of the 

 calculus in possible, science itself must formulate its concep- 

 tions in such a definite way that they can be expressed by 

 the symbolism of mathematics. This has been done in many 

 a science. In physics, in mechanics, and in engineering, an3 

 also in astronomy, in life insurance, and in a minor degree 

 in other sciences, such formulation has taken place; and in 

 the first group of sciences mentioned we have reached a stage 

 in which further progress is impossible without the processes 

 of the calculus 



Another case of approach which is commonly understood 

 is that which is intended when we say that the length of the 

 circumference of a circle is the limit of the length of the 

 perimeter of an inscribed polygon as the number of sides 



