148 THE PRINCIPLES OP SCIENCE. [CHAP. 



of numbers up to sixty or 360. I can assert that between 

 60,041 and 60,077 no prime number occurs, because the 

 exhaustive examination of those who have constructed 

 tables of prime numbers proves it to be so. 



In matters of human appointment or history, we can 

 frequently have a complete limitation of the number of 

 instances to be included in an induction. We might show 

 that the propositions of the third book of Euclid treat only 

 of circles ; that no part of the works of Galen mentions the 

 fourth figure of the syllogism ; that none of the other kings 

 of England reigned so long as George III.; that Magna 

 Charta has not been repealed by any subsequent statute ; 

 that the price of corn in England has never been so high 

 since 1847 as it was in that year; that the price of the 

 English funds has never been lower than it was on the 

 23rd of January, 1798, when it fell to 47 \. 



It has been urged against this process of Perfect Induc- 

 tion that it gives no new information, and is merely a 

 summing up in a brief form of a multitude of particulars. 

 But mere abbreviation of mental labour is one of the most 

 important aids we can enjoy in the acquisition of knowledge. 

 The powers of the human mind are so limited that multi- 

 plicity of detail is alonp. sufficient to prevent its progress 

 in many directions. Thought would be practically impos- 

 sible if every separate fact had to be separately thought 

 and treated. Economy of mental power may be considered 

 one of the main conditions on which our elevated intellectual 

 position depends. Mathematical processes are for the most 

 part but abbreviations of the simpler acts of addition and 

 subtraction. The invention of logarithms was one of the 

 most striking additions ever made to human power : yet it 

 was a mere abbreviation of operations which could have 

 been done before had a sufficient amount of labour been 

 available. Similar additions to our power will, it is hoped, 

 be made from time to time ; for the number of mathematical 

 problems hitherto solved is but an indefinitely small 

 traction of those which await solution, because the labour 

 they have hitherto demanded renders them impracticable. 

 So it is throughout all regions of thought. The amount 

 of our knowledge depends upon our power of bringing it 

 within practicable compass. Unless we arrange and 

 classify facts and condense them into general truths, they 



