270 PHYSICAL EXPRESSION. 



ing, and speaking." These latter statements con- 

 cern kinetic action. 



Further to analyze the statements, (1) here we 

 have examples of equal proportional development ; 

 (2) here we have examples of similarity in walking 

 and speaking. Both walking and speaking consist 

 of a series of movements. If Arthur and John 

 have a similar manner of walking, that can be 

 described and demonstrated in terms of a series of 

 movements ; it is a series of kinetic actions that is 

 said to be alike in Arthur and John. 



It remains to explain the terms " equal propor- 

 tional growth" and "a similar series of kinetic 

 actions." When we speak of proportional growth 

 we really refer to two subjects, and we compare 

 in each the function growth as to its quantity. 



We will first inquire what is meant by "pro- 

 portional growth," and then consider some of its 

 variations. 



Proportional groivth. This term, as it concerns 

 a proportion, must imply something about the 

 quantity of the growth ; it is only as to quantities 

 that we can make a proportion or ratio. It con- 

 cerns, at least, two subjects, and implies the condi- 

 tion that the ratio of growth of two or more parts 

 or members of one subject, is equal to the ratio of 

 growth of the corresponding parts or members of 

 the other subject. 



When we speak of proportional growth in John, 

 we really consider two subjects, not one; we are 

 using in reality a condensed phrase. Statement (1) 

 speaks of equal ratios of the head and body in 



