794 
DR. T. R. ROBINSON ON THE DETERMINATION OE 
fixed on the shaft and read by an index on the arm. I hoped the tension of this 
spring would be so nearly as the angle of its torsion that mere reading of the circle 
woidcl give it ; but this was not quite the case, and I had to form a scale for it. The 
instrument was turned through a quadrant, and held while weights were hung on the 
outer edge of the cup till they balanced the spring. As the friction caused some 
uncertainty, the cup was a little raised and allowed to descend gently, and its 
point of rest read ; it was then depressed and allowed to rise, the mean of the two 
readings being considered the true point of equilibrium. This was repeated for the 
second quadrant, and so on for three complete revolutions. The numbers so obtained 
were reduced to the centres of the cups, and corrected for the angular deviation from 
the horizontal position. The same spring was used for No. II. and No. III. with 
separate scales ; but for No. I. it was necessary to combine two springs. As the 
equilibrium points were scarcely ever at the quadrants, they were reduced to them 
by interpolation, and tables formed with first and second differences, which easily 
gave T the tension in grains corresponding to a given 6* 
(27.) Now things being thus arranged, if the whirling machine be put in action the 
anemometer will turn and tend the spring till its elastic force balances the pressure 
aV' 3 ; when this has occurred I place on the brake a weight of 6 lb., which produces 
a friction far surpassing the tension ; the chronograph is then made to record N, 
generally for three minutes. The machine is then stopped, the brake holds the 
anemometer immovable, and 6 is read off on the circle to a tenth of a division. But 
the tensions thus obtained are too large : the anemometer’s motion is accelerated 
up to the point where aV /3 =T+F ; there it has acquired a velocity which carries 
it on beyond this. The force which brings it back is now T — aV ' 3 — F, and it will rest 
when aV' 2 — T — F. f Even the a thus obtained must be a trifle too large, for V' ought 
to include, as a component, the radial vortex-motion Z. I subjoin the measures which 
I have taken in the following tables. Of the headings, D, S, N, b, V, W, and f" 
have been explained ; C is the reading of the circle, T the corresponding tension in 
grains, 6 the angle made by the highest of the cups with the horizon. 
* It seemed unnecessary to give these tables. 
f This supposes that the moment due to the final velocity is greater than 2F, which is a minor limit 
of a. I have used it as giving results nearest to those obtained by minimum squares. If the moment 
does not exceed F, a— y,^ ■ 
