Some Cranks and their Crotchets 417 



renown by doing what nobody ever did. Hence 

 the fascination exercised upon them by those ap- 

 parently simple problems which already in ancient 

 times were recognized as " old stickers," the quad- 

 rature of the circle, the trisection of angles, and 

 the duplicature of the cube. The ancients found 

 these geometric problems insolvable, though it was 

 left for modern algebra to point out the reason, 

 namely, that no quantities can be geometrically 

 constructed from given quantities, except such as 

 can be formed from them algebraically by the solu- 

 tion of quadratic equations ; if the algebraic solution 

 comes as the root of a cubic or biquadratic equation, 

 it cannot be constructed by geometry. Against 

 this hopeless wall the crowd of paradoxers will 

 doubtless continue to break their heads until the 

 millennium dawns. 



Sometimes, however, our crank has a practical 

 end in view, as in the numerous attempts to dis- 

 cover " perpetual motion," or, in other words, to 

 invent a machine out of which you can get indefi- 

 nitely more energy than you put in. It is not 

 strange that many thousands of dollars have been 

 wasted in this effort to recover Aladdin's lost lamp. 

 The notorious Keely motor is but one of a host of 

 contrivances born and bred of crass ignorance of 

 the alphabet of dynamics. But perpetual motion 



