640 
Proceedings of the Royal Society 
This terminal velocity has to he considered along with the inten- 
sity ot gravitation, which intensity, if acting alone, would generate 
velocities proportional to the times ; wherefore the time in which 
the heavy body, falling freely, would acquire the terminal velocity, 
presents itself as the proper tabular unit of time, and, as a necessary 
accompaniment, the tabular unit of distance must he that over 
which the body would pass with its uniform terminal velocity in 
the time during which that terminal velocity was acquired ; or, in 
other words, must he double the height of the free fall needed for 
the acquisition of the final velocity. 
The accompanying table has been constructed for these assumed 
units ; the details of the rise are given on the left hand, those of 
the fall on the right hand side, the times being reckoned before and 
after the instant of culmination : — 
Time. 
Velocity. 
Rise. 
Fall. 
Velocity. 
Time. 
Time of 
Free Fall. 
Time of 
Actual 
Fall. 
- 0*0 
•00000 
•ooooo 
•ooooo 
•ooooo 
+ 0-0 
1-00000 
T 
T0033 
•00501 
•00499 
•09967 
•1 
•99918 
•2 
•20271 
•02013 
•01987 
T9738 
•2 
•99669 
•3 
•30934 
•04569 
•04434 
•29131 
•3 
•99265 
•4 
•42279 
•08223 
•07795 
•37995 
•4 
•98714 
-0*5 
•54630 
T3058 
T2011 
•46212 
+ 0-5 
•98026 
•6 
•68414 
T9197 
•17014 
•53705 
•6 
•97221 
*7 
•84209 
•26809 
•22727 
•60437 
•7 
•96313 
•8 
1-02964 
•36139 
•29075 
•66404 
•8 
•95321 
•9 
1-26016 
•47544 
•35983 
•71630 
•9 
•94260 
-1*0 
1-55741 
•61573 
•43378 
•76159 
+ 1-0 
•93143 
•1 
1-96476 
•79055 
•51194 
•80050 
•1 
•91988 
•2 
2-57215 
1-01512 
•59369 
•83365 
•2 
•90806 
•3 
3-60210 
1-31864 
•67850 
•86172 
•3 
•89608 
•4 
5-79789 
1-77215 
•76570 
•88552 
•4 
•88393 
-1-5 
14T0143 
2-64878 
•85544 
•90515 
+ 1-5 
•87204 
•94681 
•92167 
•6 
86005 
1-03968 
•93541 
•7 
•84824 
1T3381 
•94681 
•8 
•83637 
1-22898 
•95624 
•9 
-82516 
1-32500 
•96403 
+ 2-0 
•81394 
Opposite the time 1*3 in the first column, we find the velocity 
3-60210, this means that if the stone he thrown upwards with the 
