RADIATION IN ABSOLUTE MEASURE AT VERY LOW TEMPERATURES. 
363 
The quantity n is now assumed to be of the parabolic form 
71 — cl -|- ftt T y t“. 
The justification for this assumption will be made clear presently from a comparison 
between observed and calculated values of n. 
30. Returning, now, to the original forms, we have 
dv 0 n , cl dv 
— c — — ehv and hence e= — 7 -. —. . 
dt S v dt 
But we have also 
log i’o— log v, 
known by experiment, and equal to K t + n ; and we have, moreover, 
log e v 0 —log, v = M (log v 0 — log v), 
where M is the modulus of the common logarithms. 
Hence by differentiation, and comparison, 
— - ~ — M (log Vq —log v ) 
v dt dt Xh b ’ 
= M^{K t + n} = M {(K+ft)+‘2yt}, 
and, by substitution, we find 
e = 2M{(K+/3) + 2y(}; 
t 1 (= 300) being introduced since K, a, /3, y, are in terms of 5 minutes as the unit of 
time. 
Thus e is the emissivity when t — 0 , plus or minus a quantity which, for want of a 
better name, we have been in the habit of calling “ the time correction.” 
31. It now only remains to explain how n is dealt with, and how the values of 
oc, /3, and y, are found. Referring again to the specimen page, 011 p. 364, and to 
Column 5, which contains the values of log i \—log v ; the next column, Column 6 , 
contains the values of K/, K being chosen by inspection to be 25, so that when 
the values of Kd are subtracted from the corresponding numbers in the preceding 
Column 5, the remainders, shown in Column 7, shall be small and convenient for the 
process which is to follow. The numbers in Column 7 are sometimes even negative ; 
experience directs the choosing of K. It is to be observed, also, that the factor 10 -4 
has been taken out of the numbers in Column 6 . This must be kept in mind, and the 
factor inserted at the proper time, at the end of the calculations. 
32. The next process is to form three simultaneous equations for the determination 
of a, ft. and y in the equation a + ftt + yt 2 = n'. There are different ways in which 
this might be done, but perhaps the simplest way is to divide Column 7, containing n> 
into three equal parts, and construct columns containing the corresponding values of t 
