THE FOUCAULT PENDULUM 



451 



axis of this ellipse turns with the true Foucault motion. For such amplitudes 



as we employ in this paper, Binet's formula - = — ^ shows that with 



a pendulum 500 cm. long and with an entire swing of 17 cm. the semi 



minor axis b of the ellipse = ^— mm. It is plainly of theoretical interest 



only in our experiment. 



Sir John Herschel had pointed out that the path of the pendulum would 

 really be a spiral passing in all its motions to and fro through a point o 

 vertically under the centre of suspension (fig. 5). Binet teaches us that 



Fig. 5 



it is a spiral described by a point executing elliptical harmonic motion in a 

 horizontal ellipse moving imiformly about its centre with an angular 

 speed = CO sin <p (fig. 6). 



The Foucault result remains unmodified. 



Note by L. G. Hoxton. 



This note has been appended to Professor Smith's article as a result 

 of the suggestion on p. 450 which he has been so kind as to make. The 

 improvements there alluded to are for the most part mattery of conven- 



