10272.07
2140 | 20.551 | .000226 | .888499 | 28.66 | 10300.95
2150 | 20.811 | .000222 | .888725 | 28.44 | 10329.61
-----+--------+---------+---------+-------+---------

+------+---------+------------+----------------------------------+
| v. | m. | log k. | Cr = gp = f(v) = {v^m}/k. |
+------+---------+------------+----------------------------------+
| 3600 | 1.55 | 2.3909520 | v^{1.55} x log^{-1} [=3].6090480 |
| 2600 | 1.7 | 2.9038022 | v^{1.7} x log^{-1} [=3].0961978 |
| 1800 | 2 | 3.8807404 | v^2 x log^{-1} [=4].1192596 |
| 1370 | 3 | 7.0190977 | v^3 x log^{-1} [=8].9809023 |
| 1230 | 5 | 13.1981288 | v^5 x log^{-1}[=14].8018712 |
| 970 | 3 | 7.2265570 | v^3 x log^{-1} [=8].7734430 |
| 790 | 2 | 4.3301086 | v^2 x log^{-1} [=5].6698914 |
+------+---------+------------+----------------------------------+

The numbers have been changed from kilogramme-metre to pound-foot units by
Colonel Ingalls, and employed by him in the calculation of an extended
ballistic table, which can be compared with the result of the abridged
table. The calculation can be carried out in each region of velocity from
the formulae:--

(25) T(V) - T(v) = k [Integral,v:V] v^{-m} dv,
S(V) - S(v) = k [Integral,v:V] v^{m+1} dv,
I(V) - I(v) = gk [Integral,v:V] v^{-m-1} dv,

and the corresponding integration.

The following exercises will show the application of the ballistic table. A
slide rule should be used for the arithmetical operations, as it works to
the accuracy obtainable in practice.

_Example_ 1.--Determine the time t sec. and distance s ft. in which the
velocity falls from 2150 to 1600 f/s.

(a) of a 6-in. shot weighing 100lb, taking n = 0.96,
(b) of a rifle bullet, 0.303-in. calibre, weighing half an ounce, taking
n = 0.8.

------+------+---------+---------+--------+----------+----------+--------
V. | v. | T(V). | T(v). | t/C. | S(V) | S(v) | s/C.
------+------+---------+---------+--------+----------+----------+--------
2150 | 1600 | 28.6891 | 27.5457 | 1.1434 | 20700.53 | 18587.00 | 2113.53
------+------+---------+---------+--------+----------+----------+--------

----+-------+------+-------+--------+-------+---------+-----------------
| d. | w. | C. | t/C. | t. | S/C. | s.
----+-------+------+-------+--------+-------+------