DR. W. M. HICKS: A CRITICAL STUDY OP SPECTRAL SERIES. 
3S1 
been taken as normal, although its amount is v ( — 5)+ '21, on account of the large 
errors required in 5, 6 caused by neglect of the apparent displacement 1'5 in the fourth 
link. The e link between Nos. 18, 19 might be the usual modified e( —25), but the 
arrangement adopted to change from the satellite d 2 to the main d l would seem 
preferable. A change from d 2 to d 1 also comes in Nos. 24, 27. It is curious to note that 
all the chains terminate with changes near the end from d 2 to d u with the exception of 
those ending at 32062, 35044, and the doubtfully linked 32936. 
From No. 38 begins the chain which runs into the P map through some false link. 
The formulae are written down as far as the strong line 38234, and so far all the links 
fall in very naturally and give small dX values. The false link is probably, therefore, 
beyond 38234. This last may be written wholly without displacement, those in u,v 
disappearing in it. The list is then continued to embrace the other lines belonging 
to this chain. It is interesting to see how the links fall in naturally, with the 
possible exception of No. 50, which may be a coincidence. 
AgD (5). The only D (5) line observed is D n (5) = 2758673, but with the large 
possible error of 3'8. It differs, however, from the value as calculated from the series 
formula by P67. If it be taken as about correct with a small satellite difference the 
values of D 12 and D 21 would be about 27585‘33 and 2850577. From these 
approximate values it will be seen that linkages extend as shown in the map. The 
table of formulae for the lines are practically all normal links with small errors. It will 
be noticed that No. 7 continues the succession of D 32 , ( — A) D 12 , by (-2A) D 12 . The 
case of 29514, No. 3, as connected with the S (3) linkage, has been there considered, 
and it was suggested that the false link was at 87872. The table gives the formulae 
for a few lines placed in the S (3) linkage on the supposition that it is a real link. It 
is seen how simply the formulae come in, but it is only possible owing to the large 
error which had been attached to 29514, and this again has been caused by the 
adopted value for D 21 (5). The formulae in S (3) appear more complicated because of 
the abnormal e links ; the changes in each table from line to line are of course 
the same. 
II. Gold. 
In the case of gold the series lines in the arc are few, and even these are not certain, 
with the possible exception of the two P(l) lines, They are considered in 
[III., p. 404], and the way in which the constants there determined reproduce the 
links found in the spark spectrum affords very strong confirmation ot the methods 
there employed. The methods are based on an identification of the D 12 (2), I) u (2), 
D 21 (2) lines. These, therefore, will be taken for granted now. I suggest, but with no 
feeling of certainty, two lines for Sj (3), S 2 (3). Their position and their calculated 
denominators show that they range well with those ot Cu and Ag, but there is no 
further evidence beyond their doublet separation. They, however, form starting points 
for long linkages which provisionally may be called by their names. The gold linkages 
