4382 C. & Hastings—Triple Objectives 
If we tabulate the differences between the observed values 
and those derived by substitution in the formula, we have the 
following expressed in units of the sixth place: 
TaBLeE II. 
n—N. 
eh 84D E F GiA);H 
5614 4548 
a 0| (0 0 0 0 0 0 0 Obs tebe 
B | +26] — 4| —12| —31] ~ 6] + 3} +23] + 4| +12) — 4) —10 
Y +24! —10) —10) —21/ — 4) + 6 +19} + 44 + 44-1) —17 
56 | — 9 — O| + 2] — 1] +16] 416) —14, —| —20) 0) +12 
1s a 8 3} —10/} + 4 +13; + 5) —| —10) — 9) +12 
4 —~ +46—-1) —| 44 -h. -|—4 +3 
2 —i—10 + 4) +16 — — 3 +14 —| —34 —| +16 
8 Ape at + Bl 3B) ee et ep a ae ee 
‘ —|— — 7 —21 _ + 3€ +16 —| —24 —| + 2 
k —| 43) 90 BB) th aot + 8 ae 
a —| — 1) +45) --27) — y y —| +19) —| —36 
# —| 10} 430) 84) cl 5 80 ot | 480] ee 
y |} +23) +19) —23) —42)  —| 44:14) $90) «=~ —} +18) +19 
€ | +21| — 3! —16) —16] —| +16) +11} —| —10| +22 
o | +38} —27) —13} —25) -—|] + 2) +28) —| +15) —19 
© | +64, —16) —a7] —34) —| “— 9} +28! —] +29) +17 
oo 1440) +20) 80) —19] ¢ 1 425} —| +4 l 
o | —60) —47] —26] +25; —| +119) +116] —| —32| —92 
T — 8 +26! —10| —341 —0| +43} —| + 8] —26 
The systematic distribution of the differences in the first 
group shows, not only the short-coming of the formula, but 
also that the extreme accuracy, indicated by the probable errors 
attached to the indices, is not imaginary. 
The accuracy of the second group is also great but much 
inferior to the first. Occasional abrupt changes as in that of 
at. 
The indices of the following groups are only given to five 
places of decimals and are evidently made with much less 
: t values for the curvature sums, but 
uces eight out of the nineteen glasses which are most useful. 
