HALL. — AIR RESISTANCE TO FALLING INCH SPHERES. 381 



of the Laboratory tower and bad a new cloth tube suspended for the 

 balls to drop through. This tube, like the old one, which had wasted 

 away, was about 35 cm. in diameter, and the balls fell along its axis. 



At the bottom of the tower the receiving apparatus was now a hori- 

 zontal plate of brass, fastened at one end but free at the other, so as 

 to be capable of up and down motion. Near the free end of this plate 

 a square hole, about 5 cm. on each side, was cut. Over this hole was 

 placed in some cases a sheet of lead somewhat narrower than the hole 

 but long enough to be clamped fast to the brass plate at each end. 

 Later a thin sheet of wood was placed over the hole before each fall. 

 In either case the ball, after falling from the top of the tower, would 

 strike the cover of the hole and break through it, the first shock of its 

 impact pulling the brass plate down far enough to break the contact 

 which made part of an electrical circuit including a chronograph. At 

 the top of the tower the release of the ball broke the same electrical 

 circuit, which was, however, closed a fraction of a second later. It 

 is hardly necessary to give further details of the apparatus except 

 this, that the chronograph, which was driven by an electric motor at 

 the rate of about 3 cm. per second, was not under the best of control, 

 and it was accordingly necessary to make a greater number of trials 

 than would otherwise have been required in order to determine the 

 time of fall with sufficient accuracy. It should be added that the rate 

 of the clock giving the second signals at the chronograph was not very 

 accurately known, as it varied somewhat from day to day, probably 

 because of changes of temperature. Its error may have been as much 

 as half a minute per day, but was probably less than this. An error 

 of this magnitude is not serious for our present purpose, and the clock 

 was in my calculations assumed to be correct. 



On the 16th of October 17 balls were dropped with such success as 

 to give usable records. The mean time of fall was 2.176 seconds, with 

 a probable error about 0.002 second. 



On the 25th of October I made another series of trials, dispensing 

 with the protecting cloth tube. In this series records were obtained 

 from 15 balls, the mean time of fall being 2.174 seconds, with a prob- 

 able error about 0.004 second. It appears, then, that the presence of 

 the tube has little if any influence on the time of fall. 



The latitude of Cambridge being 42° 22', very nearly, and the eleva- 

 tion above sea level very slight, we find that, according to the general 

 formula for g as a function of A, its value here is, to the first decimal 

 place, 980.4. Accordingly we have as Gauss's /+ 8, the distance a 

 body would fall in vacuum in 2.176 seconds, 



/+ 8 = I X 980.4 X 2.176 2 = 2321 cm. 



