275 



result should be true about the temperature of spring and 

 autumn. 



When Newton completed this investigation the true 

 velocity of sound was not accurately known. From some 

 rough experiments, conducted by himself, he believed 

 that this result was really near the truth. But subsequent 

 experiments showed that it was erroneous by 163 feet. 

 This was a very serious error, and Xewton tried to explain 

 it away, by saying that no allowance had been made either 

 for the crassitude of the solid particles of the air, or the 

 presence of vapours. He even attempted to show that 

 on taking these into account, the calculated and observed 

 velocities were in close agreement. Such explanations are, 

 however, unsatisfactory, and unless some other explanation 

 had been found, the theory would stand in direct opposition 

 to experiment. The theory of sound continued to advance 

 by the labours of the great mathematicians who followed 

 Xewton ; the motion of sound in a tube was investigated 

 without any assumption as to the nature of the motion, but 

 the discrepancy still remained unexplained. 



This was reserved for Laplace, who remarked that in 

 rapid vibrations, the sudden rarefactions and condensations 

 of the air must affect its temperature, and therefore its 

 elasticity. The amount of this must be determined by 

 experiment, and it was shown that if s represent the 

 condensation, the form to be used must be, not as 

 heretofore 



p = * D (1 + *), 



but 



p = K (I + ft) D . (1 -f 5), 



where ft lies between *3748 and 4. The velocity of sound, 

 therefore, is not \/ x, but V K (I + ft). The agreement 



T 2 



