Appendix 361 



pole in ever-narrowing and scarcely perceptible 

 circles. There is not, of course, absolute mathe- 

 matical accuracy, but a very close approxima- 

 tion to that accuracy. The Epeira winds nearer 

 and nearer round her pole, so far as her equip- 

 ment, which, like our own, is defective, will 

 allow her. One would believe her to be 

 thoroughly versed in the laws of the spiral. 



I will continue to set forth, without explana- 

 tions, some of the properties of this curious 

 curve. Picture a flexible thread wound round 

 a logarithmic spiral. If we then unwind it, 

 keeping it taut the while, its free extremity 

 will describe a spiral similar at all points to the 

 original. The curve will merely have changed 

 places. 



Jacques Bernouilli,^ to whom geometry owes 

 this magnificent theorem, had engraved on his 

 tomb, as one of his proudest titles to fame, 

 the generating spiral and its double, begotten 

 of the unwinding of the thread. An inscrip- 



* Jacques Bernouilli (1654-1705), professor of mathematics at 

 the University of Basel from 1687 to the year of his death. He 

 improved the differential calculus, solved the isoperimetrical 

 problem and discovered the properties of the logarithmic spiral. — 

 Translator's Note. 



