1060 
DR. T. R. ROBINSON ON THE DETERMINATION OE 
the arc an auxiliar balance, so that its action would begin only at the minor limit of 
the arm’s motion, and increase, so as to prevent it from reaching the major limit. It 
consists of an iron tube O' '75 diameter, containing 12" , 5 deep of mercury. In this is 
immersed a rod of iron 0” , 3 diameter, reaching to the bottom, and with a cross piece 
at top resting on the tube; from this cross piece descend two wires carrying weights 
just sufficient to balance the flotation of the mercury. To the top of the rod is attached 
a cord, passing over a pulley to the arc. It is easily shown that if the rod be raised 
an inch the cord will be pulled with a force-weight of a cylinder of mercury 0"‘3 
diameter and 1"T91 high. (For this also I formed an interpolation table, but in it S' 3 
is nearly insensible.) 
To use it the spring balance is tended till it keeps the arm near the middle of the 
opening of the box; the arm is then pressed back to touch the box, the cord is looped 
on the pin already mentioned and shortened till the cross just rests on the tube, and 
the 9 read which gives the zero of the auxiliar. Deducting this from the mean 6, we 
have 9', the measure of the auxiliar tension.* 
The largest oscillation which I have observed under this arrangement was 54°; 
the wind was moderate, Y being only 16 m . This is equivalent to a change of tension 
= 764 grains at the cups, nearly 0 '4 of the entire tension there. I cannot account for 
the great irregularities of this friction, but I believe similar facts have been observed 
on a large scale in applying Peony’s brake to machinery. The extent and frequency 
of the oscillations do not seem to follow any regular law of Y or v, though they 
evidently are related to them. 
(67.) The process described in paragraph (58) gives for each observation an equation 
containing three unknown quantities, a, x, y, and two unknown variables, Y and V', 
or Y Tw, w being the difference of wind at the two instruments. It is shown by 
Table XX. that w may be considerable for a few seconds, but when the time is a few 
minutes it is probably confined within the limits fiz3. Even when (as in the whirling 
experiments) we know Y approximately, and have not Y' to consider, the coefficients 
are so related that it is impossible to get accurate values of the constants by the usual 
methods of elimination, and here the difficulty is still greater. I have therefore 
thought it best to assume probable values for a and y, and determine x so that the 
mean Y — V' may vanish. In the first approximation to this, supposing U the true 
value of the wind at K, we have JJ=\-\-edx—Y9c: wJ r e 'dx ; e being = 
Hence S(Y' — Y)ff:Stt;=AxX S(<?— e). 
* A far better mode of retarding tlie motion of E would be to have on its shaft a sheave connected 
with an apparatus like that described in paragraph (6), so that the instrument in revolving might draw 
up the driving weight. The moment of this at the cups would be constant and accurately known, and 
the observer would only have to continually unwiud the cord. Unluckily, this did not occur to me till 
the series of Table XXI. was nearly completed ; and I was unwilling to repeat the measures, for, owing 
to deficiency of v r ind, that series had occupied several months. 
