ADVANCEMENT OE SCIENCE. 133 



front than at an equal distance behind. Many experiments have been made on 

 this point, and I may mention those repeated in the open space in front of the 

 Smithsonian Institution. In a circle one hundred feet in diameter, the speaker in 

 the centre and the hearers in succession at different points of the circumference, the 

 voice was heard distinctly directly in front, gradually less so on either side, until in 

 the rear it was scarcely audible. The rates of distance for distinct hearing direct- 

 ly in front, on the sides, and in the rear, were about as 100, 75 and 30. 



Those numbers may serve to determine the form in which an audience should 

 be arranged in an open field, in order that those on the periphery of the space may 

 all have a like favorable opportunity of hearing, though it should not be recommend- 

 ed as the interior form of an apartment, in which a reflecting wall would be behind 

 the speaker. 



The impulse producing souud requires time for its propagation, and thus depends 

 upon the intensity of repulsion among the atoms ; and, secondly, on the specific 

 purity of the matter itself. If the medium were entirely rigid, sound would be 

 propagated instantaneously. The weaker the repulsion between the atoms, the 

 greater will be the time required to transmit the motion from one to the other ; 

 and the heavier the atoms the greater will be the time required for the action of a 

 given force to produce in them a given amount of the motion. Sound, also, in 

 meeting an obstacle, is reflected in accordance with the law of light, making the 

 angle of incidence equal to the angle of reflection. The tendency, however, to a 

 divergency in a single beam of sound, appears to be much greater than that in the 

 case of light. The law, however, appears to be definitely observed in the case of 

 all beams that are reflected in a direction near the perpendicular. It is on the 

 law of the propagation and reflection of sound, that the philosophy of echo depends 

 Knowing the velocity of sound, it is an easy matter to calculate the interval of 

 time which elapses between the original impulse and the return of the echo. 

 Sound moves at the rate of 1,125 feet in a second at the temperature of 60 degrees. 

 If, therefore, we stand at half this distance before a wall, the echo will return to 

 us in one second. It is, however, a fact known from universal experience, that no 

 echo is perceptible from a near wall, though one in all cases must be sent back to 

 the ear ; the reason of this is that the ear cannot distinguish the difference between 

 the similar sounds, as, for example, that from the original impulse and its reflec- 

 tion, if they follow each other at less than a given interval, which can only be de- 

 termined by actual experiment ; and as this is an important element in the con- 

 struction of buildings, the attempt was made to determine it, with some considerable 

 degree of accuracy. For this purpose the observer was placed immediately in front 

 of the wall of the west end of the Smithsonian building, at the distance of 100 

 feet; the hands were then clapped together; a distant echo was perceived, the 

 elapsed time of the passage of the impulse from hand to ear, and that from the 

 hand to the wall and back to the ear was sufficiently great to produce two entirely 

 distinct impressions. The observer then gradually approached the building until 

 no echo or perceptible prolongation of the sound was observed. By accurately 

 measuring this distance, and doubling it, we find the interval of space within 

 wbich two sounds may follow each other without appearing separately. But if 

 two rays of sound reach the ear, without having passed through distances differing 

 from each other greater than this, they produce the effect of separate sounds. This 

 distance we have called the limit of perceptibility in terms of space, If we 



