A military dictionary

by William Duane

Multiply the base by the base + 1, this product by the base + 2, and divide by 6.

Square Pile.

Multiply the bottom row by the bottom row + 1, and this product by twice the bottom row + 2, and divide by 6.

Rectangular Piles.

Multiply the breadth of the base by itself + 1, and this product by three times the difference between the length and the breadth of the base, added to twice the breadth + 1, and divide by 6.

Incomplete Piles.

Incomplete piles being only frustums, wanting a similar small pile on the top, compute first the whole pile as if complete, and also the small pile wanting at top; and then subtract the one number from the other.

Table, of square Piles of Shot.

side	con- tent	side	con- tent	side	cont’t	side	cont’t	side	cont’t
2	5	20	2871	38	19019	56	60116	74	137825
3	14	21	3311	39	20540	57	63365	75	143450
4	30	22	3795	40	22140	58	66729	76	149226
5	55	23	4324	41	23821	59	70210	77	155155
6	91	24	4900	42	25585	60	73810	78	161239
7	140	25	5525	43	27434	61	77531	79	167480
8	204	26	6201	44	29370	62	81375	80	173880
9	285	27	6930	45	31395	63	85344	81	180441
10	385	28	7714	46	33511	64	89440	82	187165
11	506	29	8555	47	35720	65	93665	83	194054
12	650	30	9455	48	38024	66	98021	84	201110
13	819	31	10416	49	40425	67	102510	85	208335
14	1015	32	11440	50	42925	68	107134	86	215731
15	1240	33	12529	51	45526	69	111895	87	223300
16	1496	34	13685	52	48230	70	116795	88	231044
17	1785	35	14910	53	51039	71	121836	89	238965
18	2109	36	16206	54	53955	72	127020	90	247065
19	2470	37	17575	55	56980	73	132349	91	255346

Explanation. The numbers gradually increasing, from 2 to 91, express the number of shot at the base of each square pile; and the numbers opposite, the quantity of shot in each complete square pile. Example. No. 20 gives 2871, and No 30 gives 9455; and so of the rest.