196 
MEASUREMENT OF HIGH TEMPERATURES. 
[HULL. 
order that the effect on Tmay not exceed 1 : 1000 follows easily from th< 
equation of errors 
dx T 
S.r= 
(IT 1000 
(1- 
From this the following six special equatums result, equations whic 
are approximate and put in such forms as may best facilitate the co 
putation : 
a— ft 1000 
6h _ /. [«-/?(l+«T)]» T 
^■"^ (^S)(i+«T) 1000 
1000 . « 
(14 
1000 a. (1+aT) 
v' \ 
vVy 1000 . K l+aT, 
l +'ajT 1 •___ 
+fi£T 1000 .{1+aT) 
(15 
(16 
(17 
(18 
If into these equations we introduce // =16 cm , the value which obtains 
in most of the examples below ; if, moreover, ^==0.00367 and //=0.000017 
^ // =L > 0°, then formulae (13) to (18) lead to the following tabular compar 
ison. In the table both the absolute values of the errors o7i , SR, 6/3 
V 
S ( — J, 6( —- ), which give rise to an error of T/1000 in the result 
/ v' \ lv' / 'V 1 ' \ l'V n 
as well as the relative errors dfi//3, 3 ( )/ , and 6 ( — - )/ 
computed for a series of values of T. 
are fall 
Table 47. — Comparison of divers errors which effect, the result by 1 : 1000. 
r 
T 
iho 
SH 
<5j3xl0 6 
«(v)xl0- 
<)*io« 
/3 
v' 
V 
«- i 
V 
v" 
V 

cm. 
cm. 
100 
-0. 004 
0.006 
2.6L 
860 
780 
0.150 
2.2 
0.184 
500 
-0.010 
0.028 
1.27 
680' 
380 
0.074 
1.7 
0.089 
1,000 
-0.012 
0.056 
0.75 
610 
230 
0.044 
1.6 
0.054 
1,500 
-0.013 
0.083 
0.53 
580 
170 
0.031 
1.5 
0.039 
Inasmuch as h () must be measured to 0.01"" it is quite obvious that 
corroborative readings before and after heating are essential, and tha 
(850) 
