440 Mr. M. Ponton on the Law of the Wave-lengths 
yantage possessed by it over the second, which makes the value 
of E1945. 
Another advantage presented by the first series will be brought 
to light by the following arrangement :—Let the whole of the 
wave-lengths be formed into an equicentral series of fractions, 
BCDBCD EEE 
thus, 3, => ae OT a , in which each greater is di- 
vided by each less, regarding E as the centre of the system. 
Arranging the quotients in the order of their magnitudes, call 
B C E B C E 
HM Te.G re Bin? ie Be egies 
and pay: the following are the values of these quantities 
according to the two sets of observations, adopting in both the 
above adjusted values of B and D, and in the case of the first 
series, the above adjusted value of E. 
Ist set. 2nd set. Differences. 
o =1:'751099 1:735549 0:015550 
qm == 1:529968 1°526150 0:003818 
P= 1°338832 1°328562 0:010270 
o = 1:307930 1:306347 0:001583 
Tr = 1:248298 1°245244 0:008054: 
v = 1:225643 1:2255838 0-000060 
o'= 1:215826 1:212437 0:008389 
x= 1°119665 1:118310 0:001355 
y= 1:085883 1:084169 0:001714: 
Tn this series we have p= 5 pa =, and y = e so that only 
5 
six of the nine members are primary. 
Now if in both series the differences between the terms 0, 7, 
o, and yf be taken, they will stand thus :— 
Nos. Diff. Nos. Diff. 
Ist Ser. 0 =1°751099 0°221131 2nd Ser. o =1°735549 0:209399 
m =1°529968 0°222038 mw =1'526150 0:219803 
o =1°307930 0:222047 o =1°306347 0:222178 
W=1:085883 W=1:084169 
The near approach to a common difference of 0°222! is here 
too striking to be overlooked, and too important to be thrown 
aside,—the more especially as, in the case of the first series, the 
alterations required to make this progression perfect are very 
slight—a second advantage which it enjoys over its rival. Further, 
if in each case we take the sum of the first and middle terms, or 
o+7, they will stand as under :— 
