for the bare wire as functions of 7 (a, — yp”) and P/x,. If P/«, is small, both P/x, and 
Q/x, may be replaced by their series expansions ina, and p. From Equations [45] and [10] 
P a? b2 (: n a,” b2 a’ p4 ) 
— = —_ ——+ oO 00 
Ky 2 8 48 
[113] 
2 2 2 42 444 
ie Jt Giese ee) 
K 8 48 
Then A, and D, from Equations [46] and [68] become the following functions ofa, and pn 
ss det (a, a u?) 6? . (a? + Qi) (a,? Ee u2)b4 
ae) 114 
1 8 96 me 
2 
(a,? - p?) 54 
a ee ee ee, 115 
1 192 (115) 
Thus A, and D, are very nearly unity. Asa, >>a, forn 2 2, the corresponding coefficients 
A, and D,, in the infinite sums are negligibly small. Similarly in the expressions for the wire 
response, Equations [42] and [62], only the leading terms need be considered. In terms of 
a, and » these become 
2 2 2 2) p74 
A Pu Leg Ge Se eres 116] 
1 Qa.? 192 eda 
1 
2 
P yw? a, (a,? = pu?) pe 
Dy eee Soe alee eRe [117] 
Qa, (1+F) 3072 
To a very good approximation the response of a bare wire to a change in convective cooling or 
to a change in current input is given by 
Ra 2_2yt 
a tahoe [118] 
b, t)= 94," [1 - 
To this approximation 
1 Ky b2 
nla? - yp?) 27n(P-@) 
{119] 
4 
mB" 91% =) -T, 
Roal?  pa(b)- Ty += 
