362 



DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



Hg. 



The D series of Mercury shows a marked divergence from those of the other 

 elements so far considered in that (l) the separations of the satellites increase as tli.-y 

 go from the chief line, (2) the satellites do not seern to correspond in the different 

 orders, and (3) there are a larger number. The increased tendency which this element 

 has shown to break up into collaterals appears also here. One is led to infer that 

 with varying conditions of the production of the light different collaterals appear. 



The dependence on the oun is, however, here clearly shown, and the evidence is all 

 the stronger because the magnitude of <*, itself is large (.363) and because all the 

 apparently unconnected differences come within close multiples of <V This is clearly 

 seen in the following table where the denominator differences are exhibited 

 together : 



3980 = 11^-11 6909 = 19^-15 346= ^-17 



6201 = m, + 32 6530 = 18^+ 2 5398 = 15^-45 

 5782 = 16^-20 6262 = 17^ + 93 9750 = 27^-48 

 7989 = 22<S,+ 6 18516 = 51^-10. 



It is still possible within errors that the differences for the first satellites shall be 

 the same as for the second and succeeding, viz., 17<5 1( but it is very unlikely. For the 

 second satellites this cannot hold. It is clear that the regular law is not contradicted, 

 but is upset by the formation of new configurations or aggregations in the oscillators. 



The table is drawn on = '8. This brings in the best agreement and, moreover, 

 brings S ( ) supposing it and D ( ) are the same closer to the value found from 

 the first three lines. The value given in [II.] being one modified slightly to bring all 

 calculated (even for m = l) within limits. The agreement is seen to be remarkably 

 close. It is to be expected that the differences for the satellites of the same lines 

 will be more accurate than the differences between the chief lines themselves, and 

 this is exemplified in the table. The observation errors after m = 6 are too con- 

 siderable to draw certain conclusions from. Apparently the denominators increase 

 by small multiples of S to about m = 8 and then remain constant. 



Al. 



In Al, the satellite differences deviate from the ordinary rule in that they increase 



with increasing order for m = 2, 3, 4. They are 94, 800 and 1380, and by no 



stretching to the extreme possible errors can the two last be made equal. The 



inequality is certain. Moreover, the observed differences are very close to multiples 



If the first satellite position be calculated from D 21 , its difference is 110, the 



observed is 94 and 4<S = 106, 94 can be 106 within limits. D 21 gives in the same way 



= 3, the same as observed and 1468 for m = 4 instead of 1380. The last 



may be the same as the observed within limits, but as 52^ = 1381 '6 and 553 = 1462, 



