DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
363 
number of lines available for pairs is p-n (p-l)l(N 2 -'N 1 ) = {l-n/(N a -N,)}jp, since 
p is a very large number. Hence the probable number of coincidences will be 
/, n \ 2 px 
v CTEn.-n, ' 
This is the number if we know that the distribution is a wholly chance one. If, 
however, the frequencies are known to be based on certain constant differences the 
numbers found with differences which-are not sums or differences of multiples of these 
constants will not occur. Hence, in this case, the above calculated probable number 
will be too large. It therefore must be regarded as a maximum value, and that the 
chance coincidences will be fewer than the value given by it. 
The first difference to be tested was naturally that of the ordinary doublet 
separation v=p( — A)—p. In the case of Cu a very frequent difference found was 
about 1000. This is rather larger than 4v and it suggests that as v is formed by the 
displacement — A on p, the new difference is formed by the displacement —4 A. But 
the calculated value ofjp( — 4A) — p is too great. The value of p ( — 3A) — p (A), 
however, comes to 99975, which is practically exact. This is the difference of the two 
displacements — 2 A and 2 A on p 2 , that is of symmetrical displacements on either side 
of p 2 , which latter is probably more fundamental than p v The corresponding values 
for Ag and Au were also found to occur in large numbers in their respective spectra. 
This large difference naturally suggested a search for the intermediate ones p—p( A), 
p ( — 2 A )—p ( — A ),p ( — 3 A )—p ( — 2 A), which Avere duly found as well as others given 
by s — s (A), s( — A) — s. 
There are also certain others depending on the d sequence and the satellite 
separations, but these latter are not considered in the present paper. 
It is to be noted that if, for instance, the wave-number of a line is given by 
n = p — X, the addition p( — A)—p simply displaces the line to ( — A )n. If, howe\ T er, 
it be subtracted, the new wave-number is 2 p—p ( — A) —X and a normal displacement 
does not occur. As will be seen later there are numerous instances of displacements 
of the first kind. 
The method adopted in attacking the spectrum of a given element Avas first to make 
a list of the wave-numbers in a vertical column of ascending values downwards. In 
order to test a given difference each number in succession was tested, and when a 
coincidence was found pencil lines were drawn down and up with the actual difference 
found entered. As a rule A T alues were entered when different from that being tested 
by two or three units or more. The result was a maze of pencil lines, many of the 
wave-numbers having as many as fHe or six attached to them. The next step Avas to 
start from some particular Avave-number and make a new list following up the pencil 
lines from one to another. In this way a set would be isolated from the general list, 
all connected together in parallel and series groupings with one another but showing 
no connection with the other waA 7 e-numbers. In most cases the number of individuals 
3 E 2 
