THE VEGETABLE AND ANIMAL KINGDOMS. 123 



time which has probably elapsed since the origin of the coral- 

 line 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 vertebrata since their origin in the Devonian 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 transi- 

 tions being witnessed within the four thousand years of his- 

 torical humanity vanishes. As to the possible occurrence of 

 such unusual events in the midst of a series which appear 

 fixed and regular, let us call forward an illustration from the 

 Ninth Bridgewaier 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 ? 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 

 propensity 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 continue ; 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 



