366 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
frequency curves 1... 14 given above. An estimate of the magnitude of the effect 
to be thus expected is difficult, not only because we have estimated maximum errors 
by Kayser and Runge alone for the arc lines, but because frequently an observed 
difference has to be taken between measurements by two observers whose systematic 
errors may be different. 
The evidence for the reality of the variation in a link is based on the existence of 
long series of the same link. The following are a few examples out of many others. 
In Silver— 
(1) 30514 2460'39 32974 2460'84 35435 2461-00 37896 2457'26 40353. 
(2) 17814 3772-32 21591 3779-86 25371 3778'Ql 29194 3778A6 32928. 
(3) 30959 3776-44 34735 3777’47 38513 3773‘79 42286 2618’00 44904 3767’59 48672. 
In Gold— 
(4) 15293 5634-92 21558 5633'23 27191 5631-12 32822 5635’29 38457 563946 44097 
41320 
3192-47 3197-75. 
(5) 38127 44517 3200-04 47717 
3197-76 3192-46. 
41325 
(6) 33784 3194-86 36979 3197'04 40176 3196'71 43372. 
The first three indicate without any doubt that the links about 2460 and 3778 are 
real effects, and they show that they cannot be explained by errors of observation, for 
if so, the extreme lines would have to be affected with errors beyond any possibility. 
For instance, in (2), the differences refer clearly to one about 3778'4 and individual 
errors of small amount assigned to the lines will make the differences all equal to this. 
But if the link is supposed to be the calculated 3771, the errors in the extreme lines 
would have to be 29'7 distributed between them—a value manifestly too large. The 
existence of these variations is also shown clearly by (5) (see p. 367). The origin of 
these variations is discussed below in more detail. 
The probability curves offer incontestable evidence that the existence of these links 
is not due to chance coincidences. But other evidence is available. The fact that the 
vast majority of the spark lines are thus connected can be explained in no other way. 
A glance at the maps of the linkages given below, and consideration of the way in 
which the links are combined, are convincing that although some of the links shown 
are certainly due to coincidences the linkage effect is a real one. Amongst such 
peculiarities may be mentioned the long sequences of the same link referred to above, 
the existence of numerous meshes and congeries of meshes, of parallel sequences, 
repetitions, &c. A few of these are exhibited in diagrammatic form in Plate 6. 
