643 
of Edinburgh, Session 1877 - 78 . 
length, is limited in the time of its description ; while the branch 
VC, also unlimited in length, is unlimited as to time, but is limited 
as to the extent of its horizontal range. 
A 
The intensity of gravitation being known ; if the terminal velo- 
city, the direction, and the velocity at any point be given, we can 
compute the position, the velocity, and the direction at any pro- 
posed instant. These three data serve to determine the curve, and 
in general any three data are sufficient, as, say, the inclination, the 
range, and the time of flight. The direct computation from the first- 
named three arguments is very operose; in the other cases it is 
much more so, because we can only proceed by the method of suc- 
cessive trials, or, what comes to the same thing, we must have 
recourse to tabulated results. 
My object at present is to describe the arrangement of tables of 
this kind, and to explain their uses. 
If we launch two masses at the same angle with speeds pro- 
portional to the terminal velocities, the paths are similar in shape 
though on different scales and performed in different times. This 
circumstance is the first and principal guide in the arrangement of 
the tables, because the computations for the one trajectory are easily 
made to serve for the other. We naturally select for tabulation that 
one in which the terminal velocity is unit. 
These ballistic curves differ in character as well as in size. The 
characteristic of the shape may be taken as the angle A (fig. 4), 
made by the two asymptotes, or we may adopt the velocity at some 
definite direction, say the velocity at the summit Y. The former is 
general in its application, it includes the cases of projection obliquely 
