396 
MR. W. CROOKES OK THE VISCOSITY 
Readings. 
Arcs. 
113-0 
200-0 
87-0 
154-4 
67-4 
119-2 
51-8 
92-0 
40-2 
71-0 
30-8 
54-8 
24-0 
42-3 
18-3 
Log. ares. 
Diff. 
2-3010 
0-1124 
2-1886 
0-1123 
2-0763 
0-1116 
1-9647 
0-1134 
1-8513 
0-1125 
1-7388 
0-1125 
1-6263 
0-1124 
The logarithmic decrement for the oscillation comes out 0'1124. 
645. The actual number obtained varies with each apparatus. The number does 
not represent an absolute, but a relative, quantity, to be compared only with the 
results obtained with the same apparatus at other pressures or with other gases. 
The first swing is seldom found to be in regular series. It is better to start an 
oscillation greater than is intended to be observed, so that the oscillation shall be 
fairly established when beginning to preserve the scale-readings. 
On comparing a large number of observations there appears to be a tendency for the 
logarithmic decrements to come alternately greater and less than the mean. It is quite 
conceivable that this may be real, and not accidental, as the body is moving opposite 
ways—-just as the resistance to a ship would be different according as she went prow 
foremost or stern foremost. Therefore it is well to take an odd number of arcs for 
final discussion, leaving an even number of intervals, so that the difference, if any, 
between fore and aft motion should be eliminated. 
646. Instead of taking the whole number of arcs it comes to the same thing to use 
the initial and final arc only, except for the sake of comparing the individual results 
with the mean of the whole. To take a particular instance,—say there are 7 arcs, 
cq, cq, to cq, The mean logarithmic decrement is— 
<K(log «i-log %) + ( lo g Os-log «3) + ( lo g «3“ lo g %) + ( lo g «4- lo g a o) + 
H-(log ft 5 log ft 6 ) + (log (* 6 —log cq)} 
which is the same thing as ^(log cq — log cq), and the same is evidently true whatever 
be the number of arcs. 
For instance, in the illustration already given much time will be saved by taking 
the observation thus :— 
