264 THE PRINCIPLES OF SCIENCE. 



ties of these six numbers, to infer the properties of the 

 next number ending in five. If we proceed to test their 

 properties by the process of perfect induction, we soon 

 perceive that they have another common property, namely 

 that of being divisible ~by five without remainder. May 

 we then assert that the next number ending in five is also 

 divisible by five, and, if so, upon what grounds 1 Or 

 extending the question, Is every number ending in five 

 divisible by five ? Does it follow that because six num- 

 bers obey a supposed law, therefore 376,685,975 or any 

 other number, however large, obeys the law ? I answer 

 certainly not. The law in question is undoubtedly true ; 

 but its truth is not proved by any finite number of exam- 

 ples. All that these six numbers can do, is to suggest to 

 my mind the possible existence of such a law ; and I then 

 ascertain its truth, by proving deductively from the rules 

 of decimal numeration, that any number ending in five 

 must be made upi of multiples of five, and must therefore 

 be itself a multiple. 



To make this more plain, let the reader now examine 

 the numbers 



7, i7> 37> 47> 6 7> 97- 



They all obviously end in 7 instead of 5, and though not 

 at equal intervals, the intervals are exactly the same as in 

 the previous case. After a little consideration, the reader 

 will perceive that these numbers all agree in being prime 

 numbers, or multiples of unity only. May we then infer 

 that the next, or any other number ending in 7, is a 

 prime number ? Clearly not, for on trial we find that 

 27, 57, 117 are not primes. Six instances, then, treated 

 empirically, lead us to a true and universal law in one 

 case, and mislead us in another case. We ought, in fact 

 to have no confidence in any law until we have treated it 

 deductively, and have shown that from the conditions 

 supposed the results expected must ensue. From the 



