HEAT FROM SMALL CYLINDERS IN A STREAM OF FLUID. 
397 
various diameters in cases where the end corrections are liable to be large, i.e., 
0—0„ = 1165° C., V = 81 cm./sec. for R 0 /R — l/4. It will be noticed that p is 
always fairly large, and since in all the experimental arrangements we had pl> 10 
and_p/ 0 > 2 , the expression (57) may be written approximately in the form 
Q sinh pi = (l +P sinh pl 0 )/{e pl(l + P sinh pl 0 ) 
— (P + cosech pl 0 )/{ P + 1 + coth pl 0 ). 
We have, finally, from (59) the convenient formula 
R = R (l —e), 
where _ 
e = (l —R 0 /R) (P + 2 e _p?0 )/ {pi (P + 2 ) }.(62) 
The values of e are tabulated under the description of Diagram IV., from which it 
will be seen that the calculation of temperature from the resistance between the 
potential leads may be taken to refer to an infinitely long wire to an accuracy 
represented by these values of e; in the case of the larger wires the experiment was 
carried out so that l > 10 cm. and l 0 > 2 cm., while the potential leads were of 1 -mil 
wire. In this case the error introduced by the terminal conditions is well within the 
limits of accuracy imposed by the other measurements. In the case of the finest 
wires it was necessary to employ short specimens so that the possible error in the 
calculation of temperature due to terminal conditions is of the order of 2 or 3 
per cent. 
The preceding calculations are important in the design of hot-wire anemometers 
when the constant of the instrument is determined from the convection constants of 
platinum wire as determined in the present paper. Terminal errors do not need to 
be calculated if the anemometer is directly calibrated as long as the conditions of air 
velocity in the neighbourhood of the terminals are the same during actual service as 
during calibration. 
(iii.) On the Error due to the Vibration of the Anemometer Wire. 
A wire placed in a strong current of air tends to vibrate at right angles to the 
direction of the stream with a frequency depending both on the tension of the wire 
and the velocity of the air current. ( 3a ) Although the amplitude of vibration of the 
wire may be small, the high frequency may lead to an appreciable source of error the 
magnitude of which we now propose to investigate. We suppose the wire to perform 
simple harmonic vibrations of amplitude a and period T at right angles to the stream 
of velocity V. Representing the displacement from the equilibrium position by 
x — a sin wt , the velocity at right angles to the stream is v = aw cos wt. The velocity 
( 3a ) See Rayleigh, ‘Sound,’ vol. II., p. 412 (1896). 
