20 SCIENCE AND METHOD. 



is the science with the greatest number of methods 

 and the least results. 



It is with regular facts, therefore, that we ought to 

 begin ; but as soon as the rule is well established, as 

 soon as it is no longer in doubt, the facts which are in 

 complete conformity with it lose their interest, since 

 they can teach us nothing new. Then it is the excep- 

 tion which becomes important. We cease to look for 

 resemblances, and apply ourselves before all else to 

 differences, and of these differences we select first 

 those that are most accentuated, not only because 

 they are the most striking, but because they will be 

 the most instructive. This will be best explained by a 

 simple example. Suppose we are seeking to determine 

 a curve by observing some of the points on it. The 

 practical man who looked only to immediate utility 

 would merely observe the points he required for some 

 special object ; these points would be badly distributed 

 on the curve, they would be crowded together in cer- 

 tain parts and scarce in others, so that it would be 

 impossible to connect them by a continuous line, and 

 they would be useless for any other application. The 

 scientist would proceed in a different manner. Since 

 he wishes to study the curve for itself, he will distribute 

 the points to be observed regularly, and as soon as he 

 knows some of them, he will join them by a regular 

 line, and he will then have the complete curve. But 

 how is he to accomplish this? If he has determined 

 one extreme point on the curve, he will not remain 

 close to this extremity, but will move to the other end. 

 After the two extremities, the central point is the most 

 instructive, and so on. 



Thus when a rule has been established, we have first 



