81 



and the " operator" switches off the current, the balls drop simul- 

 taneously and, as they have fallen from equal heights, they reach 

 the tables at the same instant. The two sounds, however, will 

 not be heard simultaneously by the listeners, but that from the 

 more remote ball will lag behind the other by the time required 

 for sound to travel through the distance between the stands. The 

 operator now raises the clamp on the stand nearer to the listeners 

 and the experiment is repeated again and again until the listeners 

 judge that the two sounds reach them at exactly the same instant. 

 The nearer ball has to fall through a greater distance and the 

 excess of time required is equal to the time that sound takes to 

 travel through the distance between the stands. The calculation 

 is simple. Let h^ and h^ be the heights through which the balls 

 have to fall, and let d be the distance between the stands. Then 

 if ii and t 2 be the times of fall, we have 



The accuracy to be expected is not great. It depends upon 

 the listeners' powers of distinguishing between sounds that are 

 and sounds that are not, perfectly simultaneous. With a little 

 practice this, according to my experiments, can be done to about 

 1-lOOth of a second. Thus, if the distance d is about 110ft. the 

 error may amount to about 10 per cent. 



The first experiment with the new apparatus was performed 

 on March 29th, Miss Marcia Penrose and Miss Frances Penrose 

 acting as listeners. The he : ghts from which the balls were 

 dropped were 30.9 and 20.1 inches respectively and the distance 

 between the stands was 75 feet 2 inches. These figures give a 

 velocity of 986 feet per sec, instead of 1,114, the velocity corres- 

 ponding to a temperature of 12°C. The error is about 11 per cent. 



Putting the stands side by side on the same table the 

 apparatus may be used for comparing the degrees of delicacy with 

 which different persons can detect small departures from simul- 

 taneity in the case of two similar sounds. The few experiments 

 hitherto done seem to indicate that this delicacy of discrimination 

 is greater in young than in middle-aged or elderly persons. 



h x =Jgt^ or i,= (Sb)t 



g, as usual, is the acceleration due to gravity. 

 The velocity is then given by the equation 



