| Value of | Value of | Value of | Value of | Value of | |||||
| X. | S. | X. | S. | X. | S. | X. | S. | X. | S. |
| 1 | 1 | 6 | 56 | 11 | 286 | 16 | 816 | 21 | 1771 |
| 2 | 4 | 7 | 84 | 12 | 364 | 17 | 969 | 22 | 2024 |
| 3 | 10 | 8 | 120 | 13 | 455 | 18 | 1140 | 23 | 2300 |
| 4 | 20 | 9 | 165 | 14 | 560 | 19 | 1330 | 24 | 2600 |
| 5 | 35 | 10 | 220 | 15 | 680 | 20 | 1540 | 25 | 2925 |
Table giving the Number of Balls contained in a Square Pile, the Base of which is X,
and in a Rectangular Pile, the Sides of which are X and X + N.
| Value of X. | Differences | Value of N. | Differences | ||||||||||||
| 2d. | 1st. | 0. | 1. | 2. | 3. | 4. | 5. | 6. | 8. | 9. | 10. | 11. | 1st. | 2nd. | |
| 2 3 4 5 | 7 9 11 13 | 9 16 25 36 | 5 14 30 53 | 8 20 40 30 | 11 26 50 85 | 14 32 60 100 | 17 38 70 115 | 20 44 80 130 | 23 50 90 145 | 26 56 100 160 | 29 62 110 175 | 32 68 120 190 | 35 74 130 205 | 3 6 10 15 | 3 4 5 6 |
| 6 7 8 9 10 | 15 17 19 21 23 | 49 64 81 100 121 | 91 140 204 285 385 | 112 168 240 330 440 | 133 196 276 375 495 | 154 224 312 420 550 | 175 552 348 465 605 | 196 280 384 510 660 | 217 308 420 555 715 | 238 336 456 100 770 | 259 364 492 645 825 | 280 392 528 690 880 | 301 420 564 735 935 | 21 28 36 45 55 | 7 8 9 10 11 |
| 16 17 18 19 20 | 35 37 39 41 43 | 286 324 361 400 441 | 1496 1785 2109 2470 2870 | 1632 1988 2280 2660 3080 | 1768 2091 2451 2850 3290 | 1904 2244 2622 3040 3500 | 2040 2397 2793 3239 3710 | 2126 2550 2964 3420 3920 | 2312 2703 3135 3610 4130 | 2448 2556 3806 3800 4340 | 2584 3009 3477 3990 4550 | 2720 3162 3648 4180 4760 | 2856 3315 3819 4370 4970 | 136 154 111 190 210 | 17 18 19 20 21 |
| 21 22 23 24 25 | 45 47 49 51 53 | 484 529 576 625 676 | 3311 3795 4325 4900 8525 | 3542 4048 4600 5200 5850 | 3773 4301 4876 5500 6175 | 4004 4554 5152 5800 6500 | 4235 4807 5428 6100 6825 | 4466 5060 5704 6400 7150 | 4697 5313 3980 6700 7475 | 4928 5566 6256 7000 7800 | 5159 5819 6532 7300 8125 | 5390 6072 6803 7600 8450 | 5621 6325 7084 7900 8775 | 231 253 276 300 325 | 22 23 24 25 26 |
The number contained in a square pile is found in the column opposite the number X.
In a rectangular pile let the smaller side be 19 = X, the longer side be 26 = X + N. Then N = 7. Under 7 and opposite 19 we have 3,800. This table may be indefinitely extended by the aid of the columns of differences.
PRESERVATION OF SHOT AND EMPTY SHELL.
98. All round shot and shell are to be cleaned from rust and covered with a thin lacquer of such composition as may be directed by the Bureau when they are first received and when they are restowed.
99. For the present the following colors are established when put on board ship: All shot, black; shell, red; shrapnel, white; length of fuze stencilled on the shell. Special kinds of shell, as may be directed by Bureau. (Crane's shell, yellow; Pevey, blue.)
100. Empty shell, whether in store or in transportation, shall be most carefully protected from damp, and are to have the fuze-bouching coated with such composition as may be directed, and be stopped by a plug of very soft wood, well coated with a mixture of oil and tallow, screwed into them. The ends of the plugs should not be sawed off even with the shell, but left square and project sufficiently to allow them to be unscrewed by means of a wrench, and whenever these plugs are removed for the purpose of fitting the shells for service, they are not to be thrown away but preserved for future use.