190 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. 
The equation simplified. — To simplify this formula we replace h -. ~T . 
by h 0y or the tension which would be observed if the bulb were placed 
in melting snow. Equation (1) then becomes, after solving for T, 
H-ho + 2 
aho — pH—a2 ' ' ' ■ \** 
where 2 stands for the whole bracket [ ] of equation (1). This equation 
is still rigorous, but it is very inconvenient for calculation. An equally 
rigorous but much more serviceable form is obtained by introducing T 
into the corrective member coefficiented by 2". In this way equation (3) 
results 
H-K ["1,1+ ocT -| 
a form which is still rigorous, but may be conveniently used in practice 
with any desirable degree of approximation, as will presently appear. 
In equation (3) 2 has the form 
v' 
which may be further simplified. Fortunately - is very small, for the 
mean temperature T' is only determinable with rough approximation. 
I will define r' by the equation 
i 
1 + aT' 1 + at' v 1 + ar v ' 
and then use t in a simplified form of 2. In the second term of the 
form (4) T" = t" very nearly. If, finally, H—h and H—h be regarded 
identical, equation (3) reduces finally to the approximate practical form 
1 -ah -pH[_ l + {L+al \vl+aT'+Tl + at?'JJ " { ] 
in which the terms J3r' and fit" may also be neglected, as is obvious a^ 
once. 
Error of the approximation. — It next becomes necessary to determine 
the numerical importance of the approximation just made, viz, the 
approximation in equation (5), and furthermore T"=t"y R—h =H—h, 
l-\-/3r'=l+flt"=l in the correctives. It also is necessary to investi- 
gate the effect of the individual variables of measurement on the result. 
Regarding the quantity H—h it is obvious that its value will be at once 
H—h when the bulb is surrounded by melting snow, as is usual. To 
(844) 
