426 
PROF. LOUIS VESSOT KING ON THE CONVECTION OF 
Diagram I.—Graph of the Function x j j e x K 0 (x) dx 
The values of the function y 
= x j 
LJ 0 
e x K 0 (x) dx 
are required for the purpose of making a comparison 
between theory and experiment in the convection losses of a cylindrical wire cooled by a stream of air. 
These values may be easily obtained from Table I. or from the graph of the function given in Diagram I. 
We notice that, for small values of the variable x, equation (23) enables us to write approximately 
y = 1/[(1 - y) - log (x/2)] = 1/[1 -11593 + log (l/x)] .(i.) 
(Error < 1 per cent, if x < 0 - 02.) 
When x is sufficiently large (24) gives approximately 
y = 1/(2tt)+ = 0-15915 + 0-39894 Jx .(ii.) 
(Error < 1 per cent, if x >0-3.) 
It is of importance in the application of these approximate equations to know for what values of x they 
may be employed with sufficient accuracy. The following table sets forward this comparison:— 
x. 
fx. 
y ■ 
Formula 
(i.) 
Per 
cent. 
error. 
Formula 
(ii.) 
Per 
cent. 
error. 
X. 
y • 
Formula 
(ii.) 
Per 
cent. 
error. 
•01 
•1 
•1740 
•1748 
+ 0-5 
•1990 
+ 15-0 
4 
2 
•9607 
•9571 
-0-4 
•04 
•2 
•2266 
•2307 
+ 2-0 
•2389 
+ 5-0 
9 
3 
1-3591 
1-3561 
-0-2 
•09 
•3 
•2727 
•2809 
4-3-0 
■2788 
+ 2-2 
16 
4 
1-7575 
1-7551 
-o-i 
1-0 
1-0 
•5616 
— 
— 
•5581 
- 0-6 
100 
10 
4-1500 
4-1490 
-0'02 
From this table we notice that to an accuracy of 1 per cent, we must have a; < 0 - 02 in (i.) and x > O'3 
in (ii.). The values given by formulae (i.) and (ii.) become equal at about x = 0-08, at which point the 
error is somewhat less than 2-5 per cent. This point may in practice enable us to define a limiting air- 
velocity, affording a criterion as to which of the approximate formulae (32) or (33) should be used. 
Remembering that in the case of a circular cylinder of radius d/2 we have x = scrV d/x, and inserting the 
values s = 0-171, <r = P3x 10~ 3 , k = 5-2 x 10 -5 , we find the limiting value of Yd given by 
Yd = 1 • 87 x lO- 2 .(iii.) 
In the case of a 3-mil wire this limiting velocity is about 2-4 cm./sec. representing an accuracy of 
2 • 5 per cent. To an accuracy of 1 per cent, the measurement of velocity by a 3-mil wire can be obtained 
for velocities greater than 9 cm./sec., provided the free convection current due to the heating current is 
less than this amount. 
