( 605 ) 



5 = 0,005 - = 0,01 — = 500 

 c X 



and we then find by (32) the following limits for i} 



550 and 270. 



These results fully verify our assumption that ii would be a 

 large number. 



Finally we can compare the values we have found for r with 

 the period of the vibrations. In this way we see that in the tlame 

 some six or twelve thousand vibrations follow each other in uninter- 

 rupted succession. In the carbonic dioxyd on the contrary no more 

 than a few vibrations can take place between two successive blows. 



^13. After having found (he number ^V of molecules in the 

 sodium flame we can deduce from it the density d of the \apour of 

 sodium. In doing so, I shall suppose the molecules to be single atoms, 

 so that each has a mass equal to 23 times that of a mass of liydrogcn. 

 Taking for this latter 1,3 X i<>"-'* gramme, I find 



^;= 12 X 10-9. 

 This is not very different from the number 7 X^O"^ found by Hai.t.o. 



H\i,L0 has already pointed out that this value is ver^' much smaller 

 than the density of the vapour really present in the flame; at least, 

 this must be concluded if we may apply a statement made by 

 E. Wiedemann, according to which a certain flame with which he 

 has worked contained per cm', about 5X10-' gramme of sodium. 

 Perhaps the difference must be explained by supposing that only 

 those particles that are in some peculiar state, a small portion of the 

 whole number, play a part in the phenomenon of absorption. This 

 would agree with the views to which Lenakd has been led by his 

 investigation of the emission by vapour of sodium. 



It must be noticed that the value of .^V we have calculated for 

 carbonic dioxyd warrants a similar conclusion. In the experiments of 

 Angstrom the pressure was 739 mm. At this pressure and at 15° C. 

 the number of molecules per cm', may be estimated at 3,2X10"- 

 This is 50 times the number we have found in § 10. 



^ 14. An iiHeresting result is obtained if the time r we have 

 calculated for carbonic dioxyd is compared with the mean lapse of 

 time between two successive encounters of a molecule. Under the 

 circumstances mentioned at the end of § 13, the mean length of the 

 free path is about 7 X lO^*" cm. The molecular velocity being 

 4 X 10* cm. per sec, this distance is travelled over in 



