There is another class of cases where induction is naturally and necessarily limited to a definite number of alternatives. Of the regular solids we can say without the least doubt that no one has more than twenty faces, thirty edges, and twenty corners; for by the principles of geometry we learn that there cannot exist more than five regular solids, of each of which we easily observe that the above statements are true. In the theory of numbers, an endless variety of perfect inductions might be made; we can show that no number less than sixty possesses so many divisors, and the like is true of 360; for it does not require a great amount of labour to ascertain and count all the divisors 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the syllogism; that none of the other kings of England reigned so long as George III.; that Magna Charta has not been repealed by any subsequent statute; that the price of corn in England has never been so high since 1847 as it was in that year; that the price of the English funds has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 47-1/4.