472 THE POPULAR SCIENCE MONTHLY. 



probability, or as a fair guess, that this handful was taken out of that 

 bag. This sort of inference is called making an hypothesis. It is the 

 inference of a case from a rule and result. We have, then 



Deduction. 



Rule. All the beans from this bag are white. 

 Case. These beans are from this bao\ 

 .'. Result. These beans are white. 



Induction. 



Case. These beans are from this bag. 

 Result. These beans are white. 

 .*. Rule. All the beans from this bag are white. 



Hypothesis. 



Rule. All the beans from this bag are white. 

 Result. These beans are white. 

 .'. Case. These beans are from this bajr. 



We, accordingly, classify all inference as follows : 



Inference. 



Deductive or Analytic. Synthetic. 



Induction. Hypothesis. 



Induction is where we generalize from a number of cases of which 

 something is true, and infer that the same thing is true of a whole class. 

 Or, where we find a certain thing to be true of a certain proportion of 

 cases and infer that it is true of the same proportion of the whole class. 

 Hypothesis is where we find some very curious circumstance, which 

 would be explained by the supposition that it was a case of a certain 

 general rule, and thereupon adopt that supposition. Or, where we find 

 that in certain respects two objects have a strong resemblance, and infer 

 that they resemble one another strongly in other respects. 



I once landed at a seaport in a Turkish province ; and, as I was 

 walking up to the house which I was to visit, I met a man upon horse- 

 back, surrounded by four horsemen holding a canopy over his head. 

 As the governor of the province was the only personage I could think 

 of who would be so greatly honored, I inferred that this was he. This 

 was an hypothesis. 



Fossils are found ; say, remains like those of fishes, but far in the 

 interior of the country. To explain the phenomenon, we suppose the 

 sea once washed over this land. This is another hypothesis. 



Numberless documents and monuments refer to a conqueror called 

 Napoleon Bonaparte. Though we have not seen the man, yet we can- 



