Mechanical Vibration of Atoms. 659 



halogens, the wave-lengths being given in the last row in 

 terms of /z, = 10~ 4 cm. as unit. 



Li. Na. K. Rb. Cs. F. CI. Br. I. 



10-6M&... 24 35 4-6 60 73 0"9 21 27 3-6 



M/p 2-0 74 18-6 34-4 560 9 19 26 36 



M 7 23 39 855 133 19 354 80 127 



P 350 3-11 2-10 2-485 2*375 2*11 1'86 308 3*53 



X 19-12 70-69 1510 2862 4403 2942 351-6 505-9 6039 



To use these results for comparison with the experimental 

 ones of Rubens and Hollnagel, I shall form the wave-length 

 for NaCl by adding those in the table for Na and CI, thus 

 70*69 + 354-6 =425*3. The next table contains in the first 

 row the wave-lengths thus calculated, in the second the 

 experimental wave-lengths, and in the third the ratio of the 

 calculated to the experimental wave-length. 



NaCl. KOI. KBr. KI. 



X calcul 425-3 505*6 6569 7549 



Xexper 517 63*4 82-3 96"4 



Ratio 8-23 7'97 798 7-83 



The mean value of the ratio is 8*00. It is rather by chance 

 that this ratio comes so exactly to 8, since the separate 

 experimental determinations of these large wave-lengths, and 

 the data and approximations used in the theoretical calcula- 

 tions, do not lead us to expect such exactness at the present. 

 But it is sufficiently remarkable that we have found the 

 calculated mechanical period of vibration and wave-length to 

 be nearly three octaves below the lowest experimental period 

 and length yet measured in each case. The theoretical 

 fundamental wave-length for LiF is 313*3//,, which is only 

 between one and two octaves below the longest wave measured 

 by Rubens and Hollnagel for KI. 



It is necessary to comment on the process of adding the 

 wave-length for combined Na to that for combined CI to 

 obtain the wave-length for NaCl. Let us consider an 

 analogous case in acoustics. Suppose a length of tube ^ is 

 filled with gas 1, say hydrogen, and with both ends open is 

 caused to sound, its period of vibration r 1 is 2li/v^ where v l 

 is the velocity of propagation of sound through gas 1. For 

 a length / 2 filled with gas 2, for instance carbon dioxide, we 

 have t 2 =2/ 3 /i? 2 . If now the two tubes were placed so as 10 

 form a single one of length li + l 2 open at both ends, but the 

 part li still filled with gas 1 and / 2 with 2, and the combined 



2X2 



