362 NEWTON S PRINCIPIA. 



8. Motion of the air next the pendulum. &quot; On attaching 

 a piece of gold leaf to the bottom of a pendulum, so as to 

 stick out in a direction perpendicular to the surface, and 

 then setting the pendulum in motion, Sir James South 

 found that the gold leaf retained its perpendicular position, 

 just as if the pendulum had been at rest, and it was not 

 until the gold leaf carried by the pendulum had been re 

 moved to some distance from the surface that it began to 

 lag behind.&quot; Stokes s Cam. Trans., vol. ix. 



9. When the air is reduced to half its usual density, the 

 value of x was found to be nearly the same ; so that only 

 half as much air was dragged. One experiment of Sa- 

 bine. 



10. When hydrogen was substituted for air, the effects 

 on the time was not proportional to the density. Air is 

 thirteen times as dense as hydrogen, but the retardations 

 measured by the number of vibrations were as 5^ to 1. 

 Sabine. 



11. A pendulum vibrating within glasses makes nearly 

 the same number of vibrations as if the glasses were ab 

 sent. The mean difference of three experiments of Sa 

 bine was *007 per diem. 



12. The resistance to small velocities varies partly as the 

 velocity and partly as the square of the velocity. Cou 

 lomb. 



Poisson has calculated from theory the exact effect of 

 the resistance of the air on the motion of the pendulum. 

 His memoir will be found in the third volume of Mem. 

 de rinstitut, 1831. He supposes the oscillations of the 

 pendulum very small, and as a consequence, those also of 

 the fluid are very small. The equations of motion of the 

 air, therefore, reduce themselves to the usual equations 

 for the propagation of sound. But the arbitrary func 

 tions are to be determined by the condition that the velo 

 cities of the molecules of air in contact with the pen 

 dulum are always the same, when resolved along the 

 normal to the surface, as the velocity of that part of 

 pendulum resolved in the same direction. The motion of 



