394 
PROF. LOUIS YESSOT KING ON THE CONVECTION OF 
(ii.) On the Error Introduced by the Cooling Effect of the Leads and Potential 
Terminals. 
c, 
r, c z 
rh' 
Fig. 3. 
— zl- 
Cooling effect of leads 
and potential terminals. 
It is of importance in the practical design of anemometers to determine the limits 
of error introduced by the leads and potential terminals. Practically all cases are 
covered by that illustrated in fig. 3, where the end- 
leads Off 2 may be considered so heavy that the heated 
wire is maintained at its extremities very nearly at 
air-temperature; in addition it is necessary to allow 
for the heat conducted away by the potential leads 
fused to the anemometer-wire at If It.. The problem 
presents itself in the following way :—A wire whose constants have been determined 
from a very long specimen in which end-corrections are negligible is placed between 
two heavy terminals CfGb at a distance 2 (/ + /„) apart; a current i is passed through 
the wire until the resistance of length 2/ between potential terminals PjP 2 is 2R/; 
it is required to determine to what an extent the determination of air-velocity from 
the measurement of current and resistance is affected by the cooling effect of the 
leads and potential terminals. Let w represent the cross-section of the anemometer- 
wire, <*)' that of the potential leads, and let K be the heat-conductivity of platinum ; 
further, let. W and W' represent the heat-losses per unit length of the two wires 
respectively when*the air-velocity is V. .The temperature 0 at any point of the 
anemometer-wire is determined from the equation 
»h( K A)+W = r>B, 
ox \ ox I ■ 
(43) 
where W and R are known functions of the temperature 6. 
The complete expression for W is shown by the present experiment to be of the 
form 
W =[/3V»+y„{l+c(0-e o )}](0-9„).(44) 
In the case of platinum the variation of resistance with temperature can be 
represented by a formula of the type 
R = R o [l+a(0-0 o )+6(d-0 o ) 2 ].(45) 
It will be noticed that, according to the experimental results expressed in (44) and 
(45), a solution of (43) can be completely determined in terms of elliptic integrals if 
we neglect the variation of the heat conductivity Iv with the temperature. ( 35 ) For 
( 35 ) Little seems to be known with regard to the variation of the heat conductivity of metals at high 
temperatures. The existence of definite experimental relations of the form (44) and (45) seems to 
indicate the possibility through an exact solution of (43) of carrying out an experiment for the deter¬ 
mination of Iv at high temperatures along the lines of Straneo’s method (CARSLAW, ‘ Fourier Series and 
Integrals, 7 Macmillan and Co., 1906, p. 282). 
