5 44 THE POPULAR SCIENCE MONTHLY. 



potheses. Unfortunately, Mill's induction and the ascertainment of 

 cause by eliminating the non-essential conditions will no longer suffice 

 when the natural phenomena to be examined are too complex, or when 

 several important conditions can not be subjected to observation ; this 

 may be owing to various reasons, such as excessive distance, extreme 

 minuteness, insufficient acquaintance with the matter, etc. One has 

 not far to seek for instances of this kind, for a great number of natural 

 phenomena belong wholly or in part to this division. We may here 

 refer to the complex processes which take place in the human system, 

 to many phases of animal and plant life, to the evolution of the crust 

 of our globe, to the problems presented by the starry heavens. 



When observation and direct investigation do not suffice for the 

 finding out of the cause, the investigator turns for aid to theory or 

 hypothesis. These differ only in degree, and we will consider them 

 both as theory in a wider sense. Our main interest here centers in the 

 predictions of a theory ; these afford the standard by which the value 

 of a theory may be determined its merits correctly judged. The 

 larger the number of successful predictions under varying conditions, 

 made by means of a theory, the higher will such a theory deservedly 

 rank in our estimation. 



In chemistry, the modern theory of the science well serves to illus- 

 trate this point ; in physical geography, the tides furnish a striking 

 example. It seems remarkable that Pythias already divined a certain 

 relation between the phenomena presented by the tides and the moon. 

 In the middle ages, however, this view of the case was again obscured 

 by wrong hypotheses. The basis for a clearer understanding of the 

 periodical changes of the sea's surface was presented by Kepler in 

 his statement that, if the earth should suddenly cease to attract the 

 waters upon it, these would immediately strive toward the moon. 

 Why the sea should also rise on that side of the globe not facing the 

 moon was satisfactorily explained by Newton. When the dependence 

 of the tides on the combined force of attraction of all the celestial 

 bodies concerned had been established, much still remained to be done 

 in the last century in the way of accounting for and settling fine 

 points and details. In 1740 the Paris Academy presented as subject 

 for a prize essay the problem of a mathematical theory of the tide phe- 

 nomena ; in consequence, such a theory was partly developed by sev- 

 eral competitors. But it remained for Laplace to bring mathematical 

 calculation into harmony with the theory, by applying it to the pre- 

 diction of the actual movements of the waters. Nowadays many 

 calendars, especially those of seaports, state the exact time of the set- 

 ting in of ebb and flood tide, calculated a year in advance. 



The most striking proofs of the coming true of predictions based 

 on theoretical speculation are undoubtedly furnished by astronomy. 

 The views of Ptolemy already permitted a limited series of predic- 

 tions, but the faults of his system became more and more apparent in 



