DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 365 



f) as D,, (intensity 10) goes 4241'25 as D.,, (intensity 9). D,,-112'15 should 

 give D It s 4261 '58. This lias not been observed, but it is D,,(l)( 13<5). In fact, 

 the error Ix-tween this calculated value and that deduced from 1).,, is only 

 dX = '02, and a satellite difference of 13(5 is more in accordance with that of 

 other elements than the small one of 14(5, in the accepted series. Amongst the other 

 linns are the collaterals 4280'4 (intensity 9) = (A) (4260) with O-C = -'04, and 

 436.V7 (intensity 2) = (5A) (4260) with O-C = '1. 



In. 



As in the case of Al, so In shows an increase of satellite differences with the order. 

 The first three, 58, 26(5, 26(5 may be considered as certain, but the next, 32(5, although 

 it is close to the observation, may, as in the case of aluminium, be the same as the 

 others (268) within error limits, owing to the large error in D,,. K.R. gives the 

 iliU'erence in wave-lengths as 1'04 A.U., whilst HARTLEY and ADENEY in the spark 

 give it as '4, i.e., closer. In the table it is entered as 32(5 as being closer to the 

 olwervations, but if it really is 26(5, the O C is +'20 against O = '50. It is possible 

 that many cases of diffuseness may be due to the simultaneous existence of several 

 collaterals based on differences of S t , which for lines where m is large or for small 

 wave-lengths give differences in X too small to resolve. In this case, for instance, 

 with m = 5 a displacement by (5, produces collaterals differing by about '006 A.U., 

 and several would give the impression of a nebulous line, broadened on one side or 

 the other. For m = 6 there is clearly some collateral change different in D n and D ai . 

 For if Dj 2 be calculated from D.^ it gives a position for D 12 of longer wave-length 

 than D n , or the inverse of the typical order. No conclusions therefore can be drawn 

 as to the satellite differences for m = 6, except that D 21 is probably of the form 

 (zJ) Dj,,. Beyond this it is curious that the D 2 lines persist while the D, lines do not, 

 which may l)e accounted for by their being also like m = 6 additive collaterals. 



Again, also, the order differences show themselves as close multiples of S. The 

 table is based on = 0, but it may be brought into still closer agreement by taking 

 a small negative number, about '2 to "4. The difference between 5 and 6 

 becoming suddenly so large (59463 order 124(5) and the entrance of the peculiarity 

 mentioned above, suggest that some collateral influence comes in. Further, if we 

 regard the denominators of D.,, or of D,, calculated from D.,, v, after a small 

 difference of 8824, the differences begin again to increase. This has always in the 

 previous cases pointed to a collateral displacement in D(oo). The first object is to 

 see by what displacement the denominators may be brought to a limiting uniform 

 value. If be put - 13, the denominators for m > 5 become 715818,71 4394, 7 1 6 1 98, 

 715743, 7222, 7319. Omitting the values for m = 10 and 11, in which the probable 

 errors are very large, it is clear that, allowing for quite reasonable observation errors, 

 the denominators are in the neighbourhood of a limiting value. Now, a collateral of 

 ( + 2(5,) in D(oo) produces a displacement of 13'48, and this makes the denominator 



