TYPICAL FORMS AND SPECIAL ENDS. 15 



of swiftest descent, — then the argument runs in a vicious circle ; — the de- 

 scent in a cycloid is inferred from the wisdom of the Creator, and the 

 wisdom of the Creator is inferred from the descent in the cycloid. That 

 such actually is the process is obvious ; for who is able to tell the way of 

 an eagle in the air ? How often has it happened that any person acquainted 

 with the definition and properties, or even with the name, of a cycloid, has 

 seen an eagle pounce upon its prey ; or who could pretend to trace with any 

 degree of accuracy the curve that she described in that rapid swoop. More- 

 over, even granting the fact, still the argument is unsound mathematically, 

 for the cycloid is the line of swiftest descent only under conditions which 

 never do attend the eagle's swoop, viz., that the motion should be through 

 an unresisting medium, and that the accelerating force should be uniform, 

 when resolved, in the same parallel direction. 



We wish the section on typical numbers had been omitted ; for the au- 

 thors appear to have fallen into the very extravagancies against which they 

 caution their readers, indulging in language incapable of any interpretation 

 consistent with sober reason. After reproving the tendency of some com- 

 mentators to suppose a magical power, or a mystical meaning, in numbers, 

 they goon to say — p. 519, "The existence of this mystical tendency, in 

 premature scientific speculations, should not lead us by an extreme reac- 

 tion to affirm that numbers have no significancy in nature ; it should 

 merely guard us from adopting them too readily — that is, it should pre- 

 vent us from receiving them without inductive evidence, which is now, 

 however, superabundant." And again, p. 520, — " Physical science shows 

 that numbers have a significancy in every department in nature." They 

 then give some examples, of which we shall reproduce a few, — " Six is the 

 proportional number of carbon in chemistry, and 3 X 2 is a common 

 number in the floral organs of monocotyledonous plants, such as the lilies 

 of the field, which we are exhorted to consider." "Eight is the definite 

 number in chemical composition for oxygen, the most universal element 

 in nature, and is very common in the organs of sea-jellies." " In natural 

 philosophy, the highest law, that of forces acting from a centre, proceeds ac- 

 cording to the squares of numbers." Now, as regards this last assertion, 

 it is not true that the law of gravity has any connexion with numbers, ex- 

 cept so far as it is true that every possible proportion is capable of being at 

 least approximately expressed by means of numbers ; and as to the coin- 

 cidences, some of them almost ludicrous, which are adduced, what more do 

 they amount to than this, that among a great multitude of phenomena, in- 

 volving such small numbers, frequent repetitions of the same numbers occur 



