210 W. Gibbs on the wave lengths 
A?A A*/ A‘A A‘ 
-+0°02 +0°48 — 046 — 1°04 
+005 +034 013 — 0°24 
—002 —019 —O12 +025 
+-1°06 +0°69 ++0°57 +0°19 
+034 +004 —O17 —0°39 
+o18 +004 ~—021 —013 
— 0°20 —0°25 —0°47 —0°27 
—0°66 —0°48 —0'51 —0°12 
—046 +038 $158 +127 
=—=O17.  —O85 . +241 +41°46 
These differences are sufficient to show that a straight line 
gives, upon the whole, the best representation of the observa- 
tions, but that in all probability the form of the function to be 
assumed for the purpose of interpolation is not parabolic. The 
same remark applies, though in a much less degree, t0 the § 
sag group. In this case the successive differences are as fo “= 
lows :— : 
A?” AMA A‘), APA 
—0°03 +004 +013 0°25 
+0°06 +0°08 +0°07 0-00 
+0°32 +0°25 +0°17 +0°12 
—0°16 —0'27 —0°36 —0°29 
+)°23 +0°09 +0°08 +0°25 
—0°03 — 0°16 —O15 seb OT 
—0°19 —0*32 —0°30 —0°17 
—0'18 —0°27 —0°19 — 0°27 
+009 -+0°06 +0-14 — 0°09 
—0°38 —O0°15 —0°38 +0°20 
In computing the wave lengths of the lines on Kirchhoffs — 
scale between the scale numbers 20671 and 2250°0, a parabola 
of the 5th order was employed, because this distributes the — 
rors rather more evenly than the straight line the constants 
for which are given for group 9 in table VIII. The probable 
error is about the same in both cases : 
extent the wave lengths calculated by the two wholly in 
uggins’s scales, respectively ; columns KA ant 
Hi the corresponding wave lengths, ao aa a, their dine 
ences, An impartial examination of this table—which =! 
includes table V—will show, I think, as close an agreement 
can be reasonably expected. The differences between the wa¥? 
