124 MESSRS. A. Y. HARCOURT AND W. ESSON ON THE LAWS OE CONNEXION 
corresponds the interval t'—t during which the quantity y has diminished to the quan- 
tity y'. So that the modified form of the equation which is applicable to the preceding 
Table is 
Now this may be written in the form 
or taking the logarithms of both sides of the equation, 
}og^,=(t'-t)cc\oge, 
which expresses the fact the logarithms of the ratio of any two successive residues is 
proportional to the corresponding interval. For calculation it is convenient to express 
the equation in the deduced form 
log log ^ — log (U—t)= log a+ log log e. 
If, then, the differences between the corresponding values of log log J7 and log (t'—t) are 
found to be constant within the errors of experiment, it may be presumed that the hypo- 
thesis above stated is correct. 
These values and their differences are given in the following Table. 
Table II. 
log log A. 
y 
log (t'—t). 
log log — , — log (t’ — t). 
y 
2-327 
0-660 
3-667 
2-349 
0-681 
3-668 
2-373 
0-710 
3 663 
2-395 
0-730 
3-665 
2-421 
0-756 
3-665 
2-449 
0-786 
3-663 
2-478 
0-814 
3-664 
2-509 
0-847 
3-662 
2-543 
0-880 
3-663 
2-579 
0-919 
3-660 
2-619 
0-056 
3-663 
2-663 
0-997 
3-666 
2-711 
1-049 
3-662 
2-766 
1-101 
3-665 
2-829 
1-165 
3-664- 
2-902 
1-239 
3-663 
2-991 
1-325 
3-666 
1-103 
1-440 
3-663 
T-255 
1-590 
3-665 
1-495 
1-831 
3-664 
