212 MEASUREMENT OF HIGH TEMPERATURES. Ibull.5- 
an abbreviating expression, reduces to 
aM-p ( ° 
This is the form required. It is nearly rigorous, the approximation 
having been inserted in the corrective member . It is perhaps inter 
m 
esting to annotate that the rigorous form (2), under the simplifying 
condition H—h reduces to the unique expression 
l+-^/(21)-/(*)+iSf • p 
(«-/fl-«(i+^/(T0--/W+fl) ^~ aF 
A few remarks on the practical method of using equation (5) are novi 
in place. Equation (4) shows that t, the lower temperature at whicll 
measurement is made, furnishes the fiducial or fixed point of the as 
thermometer, t is obviously the temperature at which V 1 =0 under thk 
given barometric pressure Z>, of the day on which the measurements an 
made. Now, if at the barometric height B and at the temperature 
one observes Vi = r, then 
^=!0+:^)>> « 
where 2(v) is the total volume of the bulb and capillary stems as fai 
as the zero mark of graduation on the tube B G. Equation (G) follow 
at once from equation (1) in the genera) form given on page 189, if w 
impose T—T' — T"— . . . 1\ and t=V = t" . . . , the conditions given m 
the experiment. Equation (6) is therefore generally true. Usually 
and jB, t and r differ but slightly and v is nearly zero. Hence, bavin: 
measured r, B, v, it is easy to find the value of t, which corresponds t 
the barometric height 6 of the day; and it is also easy to make allow 
ance for any variation of barometric height occurring during the cours 
of the experiment. These operations are simple and the correction! 
can mostly be made mentally. 
Mere inspection of equations (4) (5) (G) shows that it is expedient t; 
calculate a table for the function /(fl= L , ^ both for glass and fo 
v 1 + at 
porcelain, once for all. Such a table in which t varies from 0° to 30 c 
in single degrees, will usually suffice. In this table, however, the dat 
l°g/(*)> which is more frequently in demand, must also be inserted foi 
the same range of /. 
If the re-entrant bulb be used, the mercury thermometer is cor 
veniently inserted into the central tube while the bulb is in place i j 
the revolving muffle. The stem of the mercury thermometer should b' 
(S66) 
