RESEARCHES IN SOUND, 477 



sure in the boiler witli an increase of the elasticity of the reed, every- 

 thing else being the same, would produce an increase in penetrating 

 power. From the general analogy of mechanical effects produced by 

 motive power, we may denote the effect upon the ear by the expression 

 mv'^, in which m expresses the mass or quantity of air in motion, and v 

 the Telocity of the particles in vibration. 



If this be the expression for the effect upon the ear, it is evident that 

 in case of a very high note the amplitude of the vibration must be so 

 small that the effect would approximate that of a continued pressure 

 rather than that of distinct alternations of pressure, giving a vibrating 

 motion to the drum of the ear. 



4. ]S^ext, exi^erimcnts were made to determine the penetrating power in 

 the case of the siren under different pressures of steam in the boiler. 

 The experiments commenced with a pressure of 100 pounds. The pres- 

 sure at each blast was noted by two observers, and to compare these 

 pressures with the indications of the sand, the time of the blasts was 

 also noted. 



The following are the results : 



Pressure. Relative distances a*" which 



the saucl ceased to inove. 



100 61 



00 60 



80 5S 



70 57 



()0 57 



50 50 



40 55 



30 53 



'20 51 



Fi-om this series of experiments, it appears that a diminution of pres- 

 sure is attended with a comi)aratively small diminution in the pene- 

 trating power of the siren. 



In regard to this unexpected result of greit practical importance, the 

 following appears to be the explanation. It is a well-known ijrincii^le 

 in aerial mechanics that the velocity of the efflux of air from an orifice 

 in a reservoir does not increase with an increase of condensation, when 

 the spouting is into a vacuum. This is evident when we retlect that 

 the weight of density of the air moving out is increased in proi)ortion 

 to the elasticity or pressure; that is, the increase in thepropeUing force 

 is proportional to the increase in the weight to be moved, hence the 

 velocity* must remain the same. 



In the foregoing experiments with high pressures large in proportion 

 to the resistance of the air, the velocity of efllux should therefore be 

 but little increased with the increase of pressure, and inasmuch as the 

 velocity is the most important factor in the expression mv-, which indi- 

 cates the effect on the tympanum, the penetrating power of the sound 

 should be in accordance with the above experimental results. 



