THE STUDY OF SOCIOLOGY. 265 



eider an instance. What is meant by the ratio of A to B may be ex- 

 plained to a boy, by drawing a short line A and a long line B, telling 

 him that A is said to bear a small ratio to B; and then, after lengthen- 

 ing the line A, telling him that A is now said to bear a larger ratio to 

 B. But suppose I have to explain what is meant by saying that the 

 ratio of A to B is equal to the ratio of C to D. This conception is 

 much more complex : instead of two different quantities and one rela- 

 tion, there are four different quantities and three relations. To under- 

 stand the proposition, the boy has to think of A and B and their dif- 

 ference, and, without losing his intellectual grasp of these, he has to 

 think of C and D and their difference, and, without losing his intellect- 

 ual grasp of these, he has to think of the two differences as each hav- 

 ing a like relation to its pair of quantities. Thus the number of terms 

 and relations to be kept before the mind is such as to imply the co- 

 operation of many more agents of thought, any of which being absent, 

 the proposition cannot be understood : the boy must be older before he 

 will understand it, and, if uncultured, will probably never understand 

 it at all. Pass now to a conception of still greater complexity say 

 that the ratio of A to B varies as the ratio of C to D. Far more 

 numerous things have now to be represented in consciousness with ap- 

 proximate simultaneity. A and B have to be thought of as not constant 

 in their lengths, but as one or both of them changing in their lengths, 

 so that their difference is indefinitely variable. Similarly with C and 

 D. And then the variability of the ratio in each case being duly con- 

 ceived in terms of lines that lengthen and shorten, the thing to be un- 

 derstood is, that whatever difference any change brings about between 

 A and B, the relation it bears to one or other of them is always like 

 that which the difference simultaneously arising between O and D 

 bears to one or other of them. The greater multiplicity of ideas re- 

 quired for mentally framing this proposition evidently puts it further 

 beyond the reach of faculties not developed by appropriate culture, or 

 not capable of being so developed. And as the type of proposition 

 becomes still more involved, as it does when two such groups of depend- 

 ent variables are compared and conclusions drawn, it begins to require 

 a grasp that is easy only to the disciplined mathematician. 



One who does not possess that complexity of faculty which, as we 

 here see, is requisite for the grasping of a complex conception, may, in 

 cases like these, become conscious of his incapacity ; not from perceiving 

 what it is that he lacks, but from perceiving that, by another person, 

 results can be achieved which he cannot achieve. But, where no such 

 thing as the verifying of exact predictions comes in to prove to one of 

 inferior faculty that his faculty is inferior, he is usually unaware of the 

 inferiority. To imagine a higher mode of consciousness is in some de- 

 gree to have it ; sc that, until he has it in some degree, he cannot really 

 conceive of its existence. An illustration or two will make this 

 clear. 



