398 
PROF. LOUIS VESSOT KING ON THE CONVECTION OF 
of the wire relative to the stream at any instant is given by U = \/(Y 2 + v 2 ). The 
heat-loss at any instant is given by the experimental relation W = /3 (6 — #„)\/U + y, 
so that the average heat-loss, W = I li 2 , is given by 
W = l/T I' W dt = (3 (<9-6> 0 ) T - 1 f (Y'+tffdt + y. 
J 0 J 0 
Writing w wci = 2x«/T and <p — 2-Trt/T, we find 
W = /3 (6—6 0 ) V- 2tt~ 1 [l + {w 2 /Y 2 ) cos 2 <pf d<p + y .(63) 
Jo 
If V be the apparent velocity corresponding to the observed heat-loss W we have, 
writing w = 0, ' 
W = (0—d 0 ) x/Y + y .(^4) 
Comparing (63) and (64) we obtain finally 
(V/V)- = I j [1 + {'iv 2 /Y 2 ) cos 2 tpf dtp | = 7 r \/ld j J 2 j dm- (u, k) cfotj, (65) 
where K is the complete elliptic integral of the first kind with modulus 
k = w 2 /(iv 2 + Y 2 ). When w/Y is small we have approximately, 
{Y/V) lj = 1 -> 2 /Y 2 +... or V/V - 1 -ho 2 /Y 2 .( 66 ) 
As an illustration, take the amplitude a = O'Ol cm., T = l/lOO sec., so that 
w — 6'2 cm./sec. The error due to vibration will remain less than \ of a per cent, 
as long as V is less than 60 cm./sec. An increase of amplitude* to a = O'l cm. will 
introduce an appreciable error for velocities less than 600 cm./sec. It is thus 
important in the design of practical anemometers to construct the apparatus in such 
a way as to eliminate vibration or reduce it to so small an amplitude that the error 
contributed is negligible. In the present series of experiments the method adopted 
of keeping the wire under tension by means of a small weight in the manner shown 
in Diagram II. (c) proved to be effective in preventing the vibrations over the range 
of velocities employed. At very high velocities vibrations of considerable amplitude 
were at times set up in spite of the frictional constraint at the lower end of 
the wire. 
Section 13. On the Reduction and Interpretation of the Observations. 
Sample series of observations are given in Tables III. and IV. showing the method of 
entering the observations in the case of each wire. For each velocity (corrected for 
swirl) the current required to heat the wire to a predetermined series of resistances 
(from which the temperatures were calculated) were measured. The corresponding 
heat-loss in watts per unit length was then calculated and entered as the second entry 
