The indicated temperature, 7’. , can be made linear by adding a 
temperature correction * Ty to give the true (linear) temperature, 
ieee hus 
SE til (1) 
C t 
Typical values of ** 7 T. ,are shown in table 1. 
(Here the second subscript ee the Jjth point of observation 
and j=0, 1,...,7”.) The approximation of ue by a harmonic se- 
ries, rather than a polynomial, is indicated. The use of the ex- 
pression "harmonic" is not quite proper if the intervals are not 
a (It is difficult to measure the 7’, ;'s for equal intervals of 
7) Also, it is usual to consider both sine as well as cosine 
Baas. If this is done, the highest harmonic, /, in the series 
must satisfy the condition 24+ 1=n. It is clear from the table 
that higher harmonics are present. For this reason, the function 
T., (T;) is continued to the left of the initial value as an even func- 
tion of that point. Then harmonics up to and including the 7th can 
be used; the series is the cosine series: 
n 
Se COS [ia 
C . J i ; : 
4 =@© tn OO 
(2) 
Now the q ; are chosen to minimize the residual equation 
n 
Eee > Seen Pain tae a. cos | jn 
k,=0 Or j y 
where 7’, 7, 18 the 4th indicated temperature. The partial deriva- 
tives with respect to q+; are set equal to zero. When done for each 
aj, the result is a set of (27 + 1) normal equations: 
*Note that 7 5 should be given as a function of 7; 
**These values were obtained before the techniques of Appendix 
B were developed. 
23 
