140 HYPOTHESIS OF THE DEVELOPMENT OF 



probably elapsed since the origin of the coralline limestone 

 over which the Niagara is precipitated at the Falls. Now, 

 the number of grades of what may be called the first degree 

 (transitions from class to class) passed through by the verte- 

 brata since their origin in the early rocks is, at the utmost, 

 three. Such a leap in organic progress has, therefore, only 

 taken place once in many millions of millions of years. If such 

 be the case, all chance of such grade transitions being wit- 

 nessed within the four thousand years of historical humanity 

 becomes so attenuated as scarcely to have an existence. As 

 to the possible occurrence of such unusual events in the midst 

 of a series which appears fixed and regular, let us call forward 

 an illustration from the Ninth Bridyewater Treatise of Mr. 

 Babbage. The reader is requested to suppose himself seated 

 before the calculating machine, and observing it. It is moved 

 by a weight, and there is a wheel which revolves through a 

 small angle round its axis, at short intervals, presenting to the 

 eye successively a series of numbers engraved on its divided 

 circumference. 



Let the figures thus seen be the series, 1, 2, 3, 4, 5, &c., of 

 natural numbers, each of which exceeds its immediate ante- 

 cedent by unity. 



" Now, reader," says Mr. Babbage, " let me ask you how long 

 you will have counted before you are firmly convinced that the 

 engine has been so adjusted, that it will continue, while its 

 motion is maintained, to produce the same series of natural 

 numbers 1 Some minds are so constituted, that after passing 

 the first hundred terms, they will be satisfied that they are 

 acquainted with the law. After seeing five hundred terms 

 few will doubt, and after the fifty thousandth term the pro- 

 pensity to believe that the succeeding term will be fifty thousand 

 and one, will be almost irresistible. That term will be fifty 

 thousand and one : and the same regular succession will con- 

 tinue ; the five millionth and the fifty millionth term will still 

 appear in their expected order, and one unbroken chain of 

 natural numbers will pass before your eyes, from one up to 

 one hundred million. 



" True to the vast induction which has been made, the next 

 succeeding term will be one hundred million and one ; but the 

 next number presented by the rim of the wheel, instead of 

 being one hundred million and two, is one hundred million 

 ten thousand and two. The whole series from the commence- 

 ment being thus : 



