402 
PROF. LOUIS VESSOT KING ON THE CONVECTION OF 
Section 14. On the Variation of the Convection Constants with Inclination to 
the Di rection of the Stream. 
In order to study the effect of the inclination of the wire on the convection 
constants, a series of observations was taken on Wire No. 1 (diameter 0'0153 cm.), 
mounted in the fork of the rotating arm and set at various angles to the vertical. 
The wire was arranged in such a manner as to eliminate the disturbing effect of the 
fork when set horizontally. For each inclination the relation W = B v V + C was 
found to hold good, and the values of the constants B and C were determined in the 
manner already described. It was further found that the relation B = /3(0 — 6 0 ) held 
good, and that /3 increased slightly with the temperature according to the formula 
/3 = /3 0 [l+6 (6 — 0 O )], h having a value very nearly the same for each inclination and 
agreeing roughly with the value already given. The constant C was also determined 
and was found to vary very little with the inclination. These variations were very 
little greater than errors arising from uncertainties of determination, so that the term 
C was not studied in further detail. In Table VII. are given the variations of B and 
/3 with the inclination of the wire to the vertical. It will be noticed that the current 
required to maintain the wire at a given temperature is markedly greater when the 
wire is perpendicular to, than when its direction coincides with that of, the stream, 
a point which is utilized in the design of practical hot-wire anemometers. Since the 
study of the effect of inclination on convection is much more easily carried out in a 
wind-tunnel, experiments were not carried further than those described under 
Table VII. 
Section 15. Note on the Calculation of the Free Convection of Heat from 
Small Platinum Wires. 
Although the complete investigation of the problem of free convection from a 
heated cylinder is one which at present transcends mathematical representation, it is 
not without interest to examine to what an extent the problem may be dealt with by 
supposing that the wire is cooled by a current of “ effective ” velocity V imposed on 
the wire by the ascent of heated air from the surface of the cylinder. Since the 
velocity will be small, we may employ formula (32) on the supposition that k is the 
value of the conductivity appropriate to the temperature difference 0 — 0 o . From the 
examination of the experimental results of forced convection, described in Section 13, 
it would appear that the variation of the thermal conductivity with the temperature 
could be expressed by the relation 
« = ^„[l + c(0-0 o )].. (74) 
with c — 0'00114 and /c 0 = 5‘66 x 10 -5 calories per cm. 2 per sec. = 2'37 x 10 -4 watts. 
