The temperature at any point along the strut was originally 
approximated by a harmonic series, just as was 7’, in the analysis 
above. The resultant curve exhibited marked maxima and minima 
and hence was undesirable. A power series approximation was 
tried with even worse results. The difficulty arises from the fact 
that, although the temperature rises monotonically as one goes up 
the strut, part of the strut may be in nearly isothermal water. 
el 
This leads to values of aa that are very high. This high slope is 
reduced by first approximating the temperature dependence on Z 
by the best straight line, i.e., by the line of regression. Thus, 
n 
»S, Th 
1 
coer ) om 
1; i 
GR = 
oaks = 0 (*, 
(0) n By? Sf 
gives the points (Zry T) on the line of regression, where 
n 1A) Nn 
my Sek Tie Ae st oS 8 ae ie, 
i i 
5 ho eis hn be obit snare ‘bliss Te (10) 
A, 0 n n 2 
eee Op 
n >: qT, > si 
k=l k=1 
n n 
> T. > 2, 
K=1 ps = Al 
? n 
=I 
and with the axes rotated by 9=tan b7_.7. (Thus the angle of 
the tangent to the curve is reduced by 0.) The variables (7,7) of 
the new coordinate system in terms of the old coordinates are 
Og 
! 
at Aid _ 1 
"ur toh] nefits die glecan/ oper 
Z-T 
(11A) 
