AND GEOLOGICAL RELATIONS OF CERTAIN HOT SPRINGS. 
581 
True Temperatures. 
Readings of Scale. 
Errors of Scale. 
o 
0 
° 1 
31-67 
32-0 
+ 0-33 
50-16 
50-65 
+ 0-49 
68-65 
69-1 
+ 0-45 
87-14 
87-25 
+ 0-11 
105-63 
105-8 
+ 0-17 
124-12 
124-2 
+ 0-08 
142-61 
142-6 
- 0-01 
161-10 
160-95 
— 0-15 
179-57 
179-3 
— 0-27 
198-06 
197-7 
— 0-36 
216-55 
216-15 
- 0-40 
The concluding series gives us, 
True temperatures. 
Readings of Scale. 
Errors of Scale. 
o 
o 
o 
31-67 
32-0 
+ 0-33 
53-97 
54-45 
+ 0-48 
76-27 
76-75 
+ 0-48 
98-57 
98-75 
+ 0-18 
120-86 
120-95 
+ 0-09 
143-15 
143-1 
- 0-05 
165-45 
165-3 
— 0-15 
187-75 
187-65 
— 0-10 
210-45 
209-65 
- 0-40 
If we form an interpolating curve, of which the abscissae represent the readings of 
the scale, and the ordinates the errors, we shall be able to deduce the correction ac- 
curately for any part of the scale. The projected errors are shown in Plate XXXIX. 
The agreement between the three series is very satisfactory. It is quite clear that 
the abrupt changes about 90° are owing to inequalities of the tube. The following 
Table exhibits the correction applicable, with the sign affixed, to the readings of the 
scale ; and it is improbable that the uncertainty in these corrections should in any 
case much exceed 0°*]. 
Table of Corrections applicable to Troughton’s Thermometer. 
j Reading. 
Correction. 
Reading. 
Correction. 
Reading. 
Correction. 
o 
o 
o 
o 
o 
O j 
30 
- 0-3 
100 
— 
0-2 
170 
+ 0-2 
40 
— 0-4 
110 
— 
0-1 
180 
+ 0-2 
50 
- 0-5 
120 
— 
0-1 
190 
+ 0-2 
60 
— 0-5 
130 
— 
0-1 
200 
+ 0-3 
70 
- 0-5 
140 
0-0 
210 
+ 0-4 
80 
- 0-4 
150 
+ 
0-2 
90 
— 0-1 
160 
+ 
0-2 
This process is incomparably simpler than that of Bessel; so simple indeed when 
once understood, that I would much rather determine the error of any thermometer 
independently, than attempt to compare it throughout the scale with a standard in- 
strument. After the freezing and boiling points have been fixed, from two to three 
