376 T. Russell—Calibration of Thermometers. 
TABLE IV. 
Values of 6; — 6, and residuals in 0°°01 F. 
52 62 72 82 92 102 112 
32 00 —02 —02 —Ol —02 +04 00 +08 
42 00 —07 —09 —09 —04 —12 —10 
52 +02 00 —02 +03 +06 —OL +04 
—1 
62 +02 +07 00 +01 00 —03 +02 
— 8 1 
72 +01 +09 +02 00 +04 —02 +03 
0 — 2 
82 +02 +09 —03 —Ol 00 —07 +04 
= a +1 +41 
92 —04 +04 —06 00 —04 00 +05 
2 —2 
102 00 +12 +01 +03 +02 +07 00 
+ 2 + — 8 
112 —08 +10 —04 —02 —03 —04 —05 00 
+8' —8 —~2 ~2 — 2 41 48 
Sums —05 +51 —12 —09 —17 —04 +405 -—25 +16 
The sum of the numbers in the last horizontal line must be 
zero. This gives a check on the summing of the columns and 
the copying with signs changed. Another check on the wiks 
is this: that the differences of any two quantities in the sa 
horizontal line should be the same, within the limits of the 
errors of observation. 
Analyzing by a process similar to that used for table II, the 
following equations will be found, in which 9,, is the correc- 
tion of the interval 32° to 42°; d,,, that of 42° to 52° and 
Approximations. 
: L ond Third 
8 dgy =Ajgg—Aga—O49 —05 ds. = —*003 —013 —'013 
7 O49 =Ajoa—Age—Jdy Ose 1 .6yq = +°077. .+°080:. +7082 
7 bs2 =Ajna—Ago—y2 —Jo2 —12 so = — “0 —*024 
7 Oga =Aj99—Age—J59 LOye ---09 Ors = -—°009 — 004 — 003 
7 bzg =Ajgga—Ago—Jo2 —Osg —17  J7g = —'020 019 —*019 
q © Aioa—Asge—O72 One —04 Oso = —'001 —'001 
% Goes Ayen—Aaa—-Ooo —Osee £00 Ooo == +011. 4+:°016.. +-OLT 
7 Oy99 = Aja Ase O92 waar 6109== —°03] =*037 — "038 
8 b:19=Ajo2—Age—di9 Oi1e= +°024 4°031 + 032 
The values of 0, are dia dea from these equations by ap- 
proximation. As seven times be correction of any interval 
may be reasonably assumed to_be large as compare with the 
values can be derived from these equations by neglecting the 
6 on the right hand side. J4,,, is known from the first part of 
the work to be +0°-03, and J4,, is zero. When the first ap- 
proximation is made, the values found can be substituted on 
the right hand side of the equations and another set of values 
derived more accurate than the first. A few such processes 
will give the values of 3 with sufficient accuracy. From these 
