645 
of Edinburgh, Session 1877-78. 
consulting the column marked Fall, we find that the original level 
is reached between the instants + ’60 and + *70, by interpolation at 
•611, so that the whole time of its flight has been 1*111. Also, in 
the columns marked Hor. Distance, we find *6984 for that covered 
during the rise, and -4726 for that passed over during the fall, 
making the total horizontal range 1*1710. The velocity with which 
the ball strikes the ground is seen to be -7777, while the impact is 
at an angle of 39° ‘TO'. The squares of the initial and final velo- 
cities are nearly in the ratio of 55 to 7 ; that is to say, of the work 
done by the gunpowder in putting the ball in motion, 48 parts are 
spent on the air, and 7 parts only remain to represent the destruc- 
tive effort. 
Thus we can readily compute the range, the time of flight, and 
the incidence of the ball. A table of these, such as the following, 
forms a convenient adjunct to the fundamental table 
Velocity at Summit = L00000. 
Elev. 
Velocity. 
Range. 
Time. 
Velocity. 
Depr. 
5°”26' 
1-11630 
•20372 
•20347 
•91142 
6°”13 / 
10 ”12 
1-27188 
•41740 
•41452 
•84497 
13 ”22 
14 ”17 
1-48161 
•64538 
•63470 
•79993 
21 ”26 
17 ”42 
1-77176 
*89405 
•86649 
•77594 
30 ”01 
20 ”27 
2-18190 
1-17100 
1-11087 
•77768 
39 ”19 
In order to apply these results to business, we must ascertain the 
values of the tabular units in terms of the actual units of time and 
distance. This is easily done if the terminal velocity be known. 
As an example, let us take a bullet whose terminal velocity is 800 
feet per second, in which case the tabular velocities must all be 
multiplied by 800. A heavy body falling freely acquires velocity 
at the rate of 32 feet per second for each second of time, and would 
acquire this velocity of 800 in 25 seconds, wherefore all the tabular 
times must be multiplied by 25. Lastly, the unit of distance 
is described with the unit velocity in the unit of time, where- 
fore 800 x 25 = 20000 feet is the actual linear unit of the 
tables as applied to this particular projectile. The above ex- 
ample, therefore, expressed in English feet and in seconds of 
time, becomes 
VOL. ix. 4 Q 
