PHYSICS: H. S. UHLER 
489 
nitely. The curve also brings out two more properties of function (1) 
which are that the number of lines is finite and infinite respectively in 
the regions of the head and tail of a band. 
A straight line parallel to the axis of n, and at a suitable distance 
therefrom, will intersect the curve in two points, such as D and E. 
Hence, if n and n' denote (the algebraic values of) the abscissae of any 
two points on the curve which have the same value of X, it follows at 
once that c = - i (n + W). [GH = c, HE = n, DH = -n'.] _ In 
the case of any series whose wave-lengths have been accuratelyv de- 
termined there is no inherent difficulty associated with the calculation 
of n and corresponding to a chosen numerical wave-length. It is 
only necessary to evaluate the coefficients of any simple, convenient 
interpolation formula which represents a curve FQ fitting the locus of 
actual wave-lengths sufficiently closely over a limited range of spectral 
lines, such as FL or BM. In 
other words, the value of c 
may be obtained by taking an 
adequate number of terms of 
the power polynomial X = 
4- Gifi 4- a2n^ -f . . . -f- akf!^, 
determining the coefficients 
ao, ai, . . dk from the known 
wave-lengths, substituting for 
X an arbitrary wave-length 
(OH), and solving for n. 
Then using the same value of 
X and repeating the process 
for the negative quadrant, the 
corresponding value of is computed. Knowing n and n\ c follows 
immediately from the relation c = — ^ (n n'). In practice I have 
found that three coefficients (do, ai, are sufiicient for all cases, that 
the method of least squares can be used to great advantage, and 
that certain transformations of coordinates simpHfy the computations 
enormously. 
The accompanying table gives the values of c computed by the above 
method for two of the series of the X 5165 carbon band. This band is 
the one investigated arithmetically by Thiele who obtained mean 
values of c by applying the laborious method of trial and error to formula 
(2). The tabulated values of the phase were calculated from the more 
recent and accurate wave-lengths pubHshed by Leinen in the year 1905. 
The numbers in the fourth column show conclusively that c is not 
