HEAT FROM SMALL CYLINDERS IN A STREAM OF FLUID. 
395 
the purpose of determining the small end-correct ions it is sufficient to employ 
approximate expressions of the form 
W = A ( 6 — 6 0 ) and R = R 0 [l ( 0 — 0 O )], .... (46) 
where A = /3V-+y, and a and y are average values of the coefficients over the range 
of temperature considered. 
Under these conditions (43) becomes 
Kw^-A (0-0 o ) = —rR 0 [l +a (0—0 O )], 
or, writing p 2 = (A—t 2 R 0 a)/K&>, the above equation takes the form 
ax 
GO. 
(47) 
Since we may neglect the current in the potential terminals (see equation (35)), the 
temperature O' at a distance x' from the junction is determined from the equation 
K»'gi-A'(9'-e„) = o, 
(48) 
where the accented symbols refer to the potential wire. The solution of (48), which 
makes O' = 0 0 at x' — oo and O' = 0 ' 0 at the junction x' = 0, may be written 
0 ' o -6' = {Q'o-0,) e --Y ( A7M.( 49 ) 
The quantity of heat carried away by the potential lead from the point of junction 
is given by 
H' = IWdO'/dx' = (e^-ffiMlU/A') at x' — 0 .(50) 
Taking the origin at the centre of the anemometer-wire, the solution of (47), which 
makes 0 = 0' 0 at x — / is given by 
0 — [&’ 2 R 0 /K®p 2 — H'/y/(K(o'A')\ . coshp.r/cosh pi. . . (51) 
The flow of heat Hj towards the junction at x — l is given by 
Hj = — Kco dO/clx — Ka>p [? s Pt 0 /Ka)jo 2 —H7v / (Kw'A')] tanhp/. . . (52) 
For the determination of the temperature in the portion of the anemometer-wire 
between the potential terminal F 1 and the terminal C l5 take the origin at the 
junction. The solution of (47), which makes 0 — 0 ' o at x = 0 and 0 = at x — l 0 , is 
given by 
_ i 2 F 0 L sinh px \ [ IF rR 0 | sinh p {1,-x) / 53 \ 
u Kayp 2 \ sinhpZj l v /(Ka) , A / ) K up 2 ) sinh pi, '' ' V ’ 
The flow of heat away from the junction x — 0 is given by 
H 2 = — Kw dO/clx = ( i 2 FJp ). cosech pi, +[H 7 /(KFA')—FRjKwyr] . Ko p coth_p/ 0 . (54) 
3 e 2 
