A FORM OF ATWOOD'S MACHINE 105 



reduced to the smallest possible value by initial adjustment of 

 the level of the release magnet, but one has no control over its 

 value in the a! determinations. As a rule, however, it is not 

 necessary to evaluate x, the incomplete part of a revolution, in 

 the determination of a and a' ; it is sufficient to plot squares 

 of times from beginning and end respectively against number 

 of complete revolutions, and the products of the slopes of the 

 resulting straight lines into twice the effective distance of one 

 revolution at once give the acceleration and retardation 

 required. This was the procedure adopted in obtaining the 

 results communicated in this paper : the experimental points, 

 as long as the speed did not become excessive, lay exactly on 

 a straight line, whose slope could easily be found to 1 in 1000. 

 The weight of the two pans and string used in the following 

 experiments was 87-5 g, while additional loads of 50, 100, 150, 

 and 200 g were added to each side. In each case two driving 

 weights were tried, viz. 10 g and 20 g. The chronograph clock 

 was carefully calibrated, giving a mean nominal second 

 equivalent to 0-995 true seconds. 



The maximum fall available was about 700 cm., but 

 although records were obtained for the complete fall in every 

 case, the s t z curves showed some curvature for the last feAv 

 metres of fall, and in the case of large acceleration this curva- 

 ture was quite pronounced, the acceleration in every case 

 diminishing as the speed increased. This is obviously due to 

 the resistance of the pans to motion through the air, and, in 

 fact, the apparatus is used chiefly for the determination of 

 these resistances with larger surfaces. The resistance was 

 allowed for in the present experiments by using for the deter- 

 mination of a only the first part of the fall, where the speed was 

 low and the graph was accurately straight ; should it be 

 desired to use it over greater distances, it would be well to 

 dispense entirely with pans, and to use weights made in the 

 form of rods, so that the area presented normally to the 

 direction of motion would be a minimum. 



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