270 EXTINCTION OF SOUND IN A VISCOUS ATMOSPHERE, ETC. 



The last relation may be written in the form 



1-L 2 ) (7). 



It follows that the ratio of the lost energy to that incident upon the obstacle is 

 given by 



/ IT \ 



7 _4^,4/,,4 i / Q / 'o l/2/>il/2/,, i I / 1 T 2\ /Q\ 



"q~ CT Oj 1C r I O\/ ZiCT V 1C "r O I \ -L -^7 V^ / 



\ caj 



Extending this result to the case of a number of free spherical obstacles we obtain, 



instead of (4), 9 



a = n?ra 2 K 



where K represents the ratio of the lost to the incident energy given in (8). 



It follows from this investigation that the results obtained in this paper are only 

 applicable to fogs if f (p u /pi) X~ 2 ~ 2 is a small fraction. This condition is satisfied for 

 obstacles of radius 10~ 2 cm., and also for obstacles of radius 10~ 3 cm. when the wave- 

 length of the incident sound is not too long. In the case of obstacles of radius 

 10~* cm., however, this condition is no longer satisfied; L approaches close to unity 

 for all wave-lengths, and consequently a and K are very small. Hence, if the 

 diameter of the drops of water in a fog is as small as '002 mm., such a fog does not 

 interfere appreciably with the propagation of sound, and a result is obtained in 

 agreement with TYNDALL'S observations. 



I append a table giving the values of L in a number of different cases. When the 

 wave-length of the sound is very great, or when the obstacle is extremely minute, the 

 obstacle vibrates with the air surrounding it. 



a = 10~ 3 cm. a= 10~ 4 cm. 



\. L. \. L. X. L. 



5 "019 200 '595 5 '877 



10 -037 300 746 10 '961 



20 -074 400 -833 20 "990 



30 -110 500 -877 30 "996 



40 -147 600 '918 100 '9996 



50 -182 700 -935 oo I'OOO 



60 -217 800 '955 



70 -251 900 -961 



80 -284 1000 -971 



90 '316 oo 1-000 



100 '347 



