PRELUDE TO THE SOLUTION OF PROBLEMS. 327 



by Vitruvius, in the following passage, is even now 

 one of the best we can offer 3 . "Voice is breath, 

 flowing, and made sensible to the hearing by strik- 

 ing the air. It moves in infinite circumferences of 

 circles, as when, by throwing a stone into still 

 water, you produce innumerable circles of waves, 

 increasing from the center and spreading outwards, 

 till the boundary of the space, or some obstacle, 

 prevents their outlines from going further. In the 

 same manner the voice makes its motions in circles. 

 But in water the circle moves breadthways upon a 

 level plane ; the voice proceeds in breadth, and also 

 successively ascends in height." 



Both the comparison, and the notice of the dif- 

 ference of the two cases, prove the architect to 

 have had very clear notions on the subject; which 

 he further shows by comparing the resonance of 

 the walls of a building to the disturbance of the 

 outline of the waves of water when they meet with 

 a boundary, and are thrown back. " Therefore, as 

 in the outlines of waves in water, so in the voice, if 

 no obstacle interrupt the foremost, it does not dis- 

 turb the second and the following ones, so that all 

 come to the ears of persons, whether high up or low 

 down, without resonance. But when they strike 

 against obstacles, the foremost, being thrown back, 

 disturb the lines of those which follow." Similar 

 analogies were employed by the ancients in order 

 to explain the occurrence of echoes. Aristotle 



3 De Arch. v. 3. 



