INDUCTION IN SCIENCE. 701 



barren results. The quantitative is the true scientific method of dealing with 

 facts, and it is by its aid that real advance is made. 



Qualitative induction is that which, starting from a knowledge of a connec- 

 tion between two events, or of the fact that a certain phenomenon is consequent 

 upon a certain combination of circumstances, produces from this knowledge a 

 generalization of a higher order, but of less exactness. There is no estimate of the 

 amount of action either in the facts on which the hypothesis is based or in the 

 hypothesis itself. The kind of action is the only consideration. It is not un- 

 common to find that the natural results of the supposed action have been over- 

 looked, for had they been considered it would have been seen that they be di- 

 rectly contrary to known facts. Sometimes considerations that are connected 

 with the subject are entirely neglected and when brought to bear on the point, 

 even in their qualitative aspect, are found to nullify the whole argument. Taken 

 at its best, qualitative induction is unsatisfactory, and frequently proves mislead- 

 ing and baneful. The operation requires a well trained scientific imagination, 

 and it is too often true that the scientific part is less developed than the imagina- 

 tion. 



Quantitative induction is that method of procedure in which accurately 

 known facts, known both in kind and in amount, are taken as the basis from 

 which the advance is to be made. On these facts is built a generalization which 

 conforms to the knowledge already possessed and awaits the development of new 

 facts with a considerable degree of confidence. For it is one of the sure founda- 

 tions of science that nature is ever consistent with herself j although her laws are 

 contingent truths, they are ever constant. If, after the best endeavors, the gen- 

 eralization can only give an explanation of the kind of action, and is unable to 

 determine the amount, it is a theory, and reaches its highest limit when it can pre- 

 dict a true result from a given combination of matter and force. Should it attain 

 the perfection of being stated in a definite mathematical form, it becomes the ex- 

 pression of a law, and as such is accepted as truth. A generalization thus formed 

 has in it the elements of exactness. It knows its grounds and stands on its own 

 merits. Founded on facts it is as near the truth as the efforts of faUible man can 

 place it. The offspring of labor, rather than the child of fancy, it has come to 

 stay and to make its presence felt in thinking minds. It is the result of a slow 

 growth. The accumulation of facts may have occupied years \ some people col- 

 lecting them with the definite object of reaching an explanation, others gathering 

 information either by accident or for the mere satisfaction of learning " some 

 new thing." It is never given to one person to gather all the facts and develop 

 the result even in one line of research. Life is too short. Seldom indeed that 

 one person formulates a theory in all its completeness. Usually, the final result 

 is the outcome of the labors of many men. It is not so much the work of man 

 as it is the answer which nature has given to patient questioning and persevering 

 scrutiny. 



In physics and astronomy — the sciences which deal with the very small and 

 the very great — we find example of both kinds of induction. The minuteness and 



