396 Intelligence and Miscellaneous Articles. 



constant. The other case is to a certain degree of approximation 

 realized when the solid body vibrates in a liquid the surface of which 

 is in part free (that is, bounded by an elastic fluid). As in the 

 other case the variations of the entropy were negligible, so in this 

 are the changes of temperature, and, indeed, for three reasons. In 

 the first place, the condensations are very slight ; therefore no mo- 

 lecular energy is generated. Secondly, the specific heat of water is 

 very great; consequently the temperature is disproportionately 

 little altered. And, thirdly, the conductivity of water for heat is 

 not so inconsiderable that a considerable part of the changes of 

 temperature which might by chance take place would not be again 

 eliminated by equalization. 



The two values of the coefficient of elasticity in these two cases 

 are in the same proportion to each other as the two values possessed 

 by the specific heat, according as the pressure or the volume remains 

 constant. This ratio does not materially differ from 1*4. 



From these cousiderations the nature and quantity of the change 

 of tone can be deduced which took place in the experiment men- 

 tioned at the commencement. The tone must become deeper ; for 

 with the temperature constant the elasticity is less than with a 

 constant entropy ; and the tones in air and in water must be pro- 

 portional to one another as Vl*4 : 1, i. e. as 1*18 : 1, or about as 

 7:6. The interval must therefore be greater than an entire tone, 

 and less than a minor third. 



Indeed experiments show that the interval approximates to this 

 value required by theory as a maximum. That on the average it is 

 somewhat less (viz. for the middle notes exactly a complete tone) 

 is not surprising when it is remembered that the above considera- 

 tions hold for two ideal extreme cases, between which lie those 

 of vibrations in air and in water. For a few tones I have deter- 

 mined the deepening by making use of the beats which are heard 

 when simultaneously with the fork immersed in water another fork, 

 the tone of which is a complete interval deeper than the tone in air 

 of the experiment-fork, is set vibrating in air. In this way I 

 found for the ratio of vibration with the following tones the values 

 placed under them. 



c (132 vibr.). 



Cl (264 vibr.). 



g r (396 vibr.). e 2 (528 vibr.). 



1-11 (<9 : 8) 



1-12 (9 : 8) 



1-13 (<8: 7) 1*15 (>8:7) 



The result derived from these numbers, namely that the ideal 

 extreme value of the interval is the more closely approximated to 

 the higher the tone (i. e. the shorter the period of vibration), agrees, 

 according to the foregoing, with the theory. 



In conclusion, I have instituted some control-experiments with 

 other liquids. From these it follows that the influence of the re- 

 sistance of the liquids, which depends on their density and viscosity, 

 and which is very important for the amplitude and the logarithmic 



