HEAT FROM SMALL CYLINDERS IN A STREAM OF FLUID. 
403 
It follows from (32) that the heat-loss by convection can be obtained from a formula 
of the form 
H = 2t -k 0 ( 6-e 0 ) [1 +c (0-9 0 )]/[log b/a], .(75) 
to which must be added the radiation loss given by 
E = 2tt«x (T514 (0/1OOO) 5-2 , . ..(76) 
E being expressed in watts per cm. 2 Formula (75) is tested in the light of Langmuir’s 
observations on free convection( 44 ) which were carried out over a much wider range 
of temperature than those of the writer. The analysis of these observations is 
discussed under Table VIII., from which it appears that to a fair degree of accuracy 
the denominator log b/a is independent of the temperature, but depends on the radius 
of the wire in the manner shown in fig. 9, the use of which affords a simple method 
of calculating the actual convection loss in any actual case. 
It is interesting from the relation (28), b = Ke 1 ~ y /(saY) to determine the effective 
velocity V of the convection current by means of which the wire is cooled. The 
variation of the term v, kSct with the temperature is small, and from the results of 
Section 13 may be expressed by means of the relation 
ks<t = \/ ic 0 s 0 <t 0 [l +b (0— $,,)],.(77) 
where b — (F000080. Thus making use of (74) and writing 
Vo = K {) e'~ y /(s 0 cr 0 b), .(78) 
we have 
V ^ V 0 [l +c (0 —9 0 )] 2 /[l + b (0-9 0 )] 2 .(79) 
Values of the effective velocities V 0 and V are given in Table VIII. It is probable 
that the values of V present velocities of the same order as the actual average 
velocity of the convection current generated by the heated wire, estimates of which 
are useful in determining the limits of temperature and velocity within which a hot¬ 
wire anemometer can be employed with accuracy. 
( 44 ) Langmuir, ‘ Phys. Rev.,’ 34, p. 415, 1912. 
