846 PROCEEDINGS OF THE AMERICAN ACADEMY. 



one hanging nearly over the line of sight of telescope No. 1, the other 

 neai'ly over the line of sight of telescope No. 2, the one nearest to the 

 line of fall being, perhaps, 35 cm. distant from it. The question whether 

 one of these lamps could by its heating effect maintain a circulation of 

 air sufficiently brisk to affect the course of the descending balls appre- 

 ciably was often in my mind. I found, however, by trial, that nowhere 

 was the horizontal current caused by the lamp strong enough to show any 

 effect on the most sensitive anemometer at my service, — an instrument 

 made by Hicks, of London, for which the correction for friction is given 

 as 30 feet per minute. For a short distance directly above the lamp the 

 upward current was able to keep the vanes in motion ; but it is evident 

 that the disturbance of ths air by the heat of the lamp is very slight 

 along the line of fall of the balls, altogether too slight to produce in the 

 very little time, perhaps 0.1 second, during which the ball is falling 

 through the free air of the room, a horizontal deviation discernible in 

 this investigation. 



It seemed quite possible, however, that the circulation of air due to 

 the lamp might affect perceptibly the position of the lower end of the 

 plumb-line. The weight of the ivory plumb-ball being about 82 gms. in 

 water, and the length of the suspension being 23 m., the horizontal force 

 which, applied at the lower end of the suspending wire, would have kept 

 it 1 mm. aside from its proper position, is less than 4 milligrams. Care- 

 ful experiment showed, however, that the heat of a 16 c. p. lamp placed 

 about 30 cm. from the wire, not far from its lower end, had so little 

 effect on the position of the wire that I could not make sure of perceiv- 

 ing the deflection. It was, apparently, less than 0.001 cm. 



But the very motion of the falling ball must have produced within 

 the long cloth tube a very considerable disturbance of the air. Could 

 such a disturbance affect the line of fall ? If the tube were exactly 

 cylinilrical and the line of fall strictly along its axis, the symmetry of 

 the conditions would answer this question in the negative. The tube 

 was nearly cylindrical and the line of fall coincided nearly, but not per- 

 fectly, with its axis. How much deflection would be produced by a 

 slight eccentricity of this line of fall? This question I found myself 

 unable to answer without special experiments, which accordingly were 

 undertaken. October 15, 1902, I dropped twelve balls with the spout 

 displaced about 10 cm. toward the south, and twelve balls with the spout 

 displaced about 10 cm. toward the north. The first set were deflected 

 on the average about 0.18 cm. towards the south and the second set 

 about 0.46 cm. toward the north, a mean deflection of 0.32 cm. away from 



