OF GASES AT HIGH EXHAUSTIONS. 
397 
Readings. 
113-0 
87 
24*0 
18-3 
Arcs. Log. 'arcs. 
200-0 2-3010 
42-3 1*6263 
6)0-6747 
0-1124 
647. In deducing the logarithmic decrement from the initial and final arcs it is 
advisable not to wait until the final arc has fallen very low, for then an error in the 
reading of the arc tells too much. In taking a long series a good plan is to group them 
into intervals of, say, 4 arcs, and take the logarithmic decrements for comparison with 
one another. Thus, let a x , a z , a 3 . ... be the arcs ; we may then take 
i (log <h -log a B ) 
4 (log «5 -logO 
i (log «9-log « 1 3 ) 
i (log -log a n)> 
and compare them with each other. They will be more regular than the logarithmic 
decrements for single intervals only, as the errors of observation will be divided by 4. 
648. The proportional error of observation of a small arc is of course much greater 
than that of a large one, but the absolute error, if anything, is rather less. Assuming 
the absolute errors to be the same in each case, the best arc to stop with so that a 
given error in the observation of the small arc shall produce a minimum error in the 
deduced logarithmic decrement, we find it (the last arc) should be -th part of the first 
arc used in the computation, e being the base of the Napierian logarithms, namely, 
2-71828 .... As the small arcs can be observed a little better than the large arcs, 
on account of the slowness of the motion, we may go a little lower, say to -^rd of the 
first arc preserved for calculation. 
649. The slight diminution in the log. dec. of air between pressures of 760 millims. 
and 1 millim. is clearly shown in figs. 5, 6, 7, and 8. The curved lines are copied 
from photographic traces made on a sensitive surface by the index ray of light. 
The experiments in which photography was employed will be described later on. 
3 f 2 
