The artillerist's manual and British soldier's compendium

by F. A. Griffiths

TABLE OF SQUARES, CUBES, AND ROOTS.

No.	Sqr.	Cube.	Sqr. root.	Cube root.	No.	Sqr.	Cube.	Sqr. root.	Cube root.
1	1	1	1·0000000	1·000000	51	2601	132651	7·1414284	3·708430
2	4	8	1·4142136	1·259921	52	2704	140608	7·2111026	3·732511
3	9	27	1·7320508	1·442250	53	2809	148877	7·2801099	3·756286
4	16	64	2·0000000	1·587401	54	2916	157464	7·3484692	3·779763
5	25	125	2·2360680	1·709976	55	3025	166375	7·4161985	3·802953
6	36	216	2·4494897	1·817121	56	3136	175616	7·4893148	3·825862
7	49	343	2·6457513	1·912933	57	3249	185193	7·5498344	3·848501
8	64	512	2·8284271	2·000000	58	3364	195112	7·6157731	3·870877
9	81	729	3·0000000	2·080084	59	3481	205379	7·6811457	3·892996
10	100	1000	3·1622777	2·154435	60	3600	216000	7·7459667	3·914867
11	121	1331	3·3166248	2·223980	61	3721	226981	7·8102497	3·936497
12	144	1728	3·4641016	2·289428	62	3844	238328	7·8740079	3·957892
13	169	2197	3·6055513	2·351335	63	3969	250047	7·9372539	3·979057
14	196	2744	3·7416574	2·410142	64	4096	262144	8·0000000	4·000000
15	225	3375	3·8729833	2·466212	65	4225	274625	8·0622577	4·020726
16	256	4096	4·0000000	2·519842	66	4356	287496	8·1240384	4·041240
17	289	4913	4·1231056	2·571282	67	4489	300763	8·1853528	4·061548
18	324	5832	4·2426407	2·620741	68	4624	314432	8·2462113	4·081656
19	361	6859	4·3588989	2·668402	69	4761	328509	8·3066239	4·101566
20	400	8000	4·4721360	2·714418	70	4900	343000	8·3666003	4·121285
21	441	9261	4·5825757	2·758923	71	5041	357911	8·4261498	4·140818
22	484	10648	4·6904158	2·802039	72	5184	373248	8·4852814	4·160168
23	529	12167	4·7958315	2·843867	73	5329	389017	8·5440037	4·179339
24	576	13824	4·8989795	2·884499	74	5476	405224	8·6023253	4·198336
25	625	15625	5·0000000	2·924018	75	5625	421875	8·6602540	4·217163
26	676	17576	5·0990195	2·962496	76	5776	438976	8·7177979	4·235824
27	729	19683	5·1961524	3·000000	77	5929	456533	8·7749644	4·254321
28	784	21952	5·2915026	3·036589	78	6084	474552	8·8317609	4·272659
29	841	24389	5·3851648	3·072317	79	6241	493039	8·8881944	4·290841
30	900	27000	5·4772256	3·107232	80	6400	512000	8·9442719	4·308870
31	961	29791	5·5677644	3·141381	81	6561	531441	9·0000000	4·326749
32	1024	32768	5·6568542	3·174802	82	6724	551368	9·0553851	4·344481
33	1089	35937	5·7445626	3·207534	83	6889	571787	9·1104336	4·362071
34	1156	39304	5·8309519	3·239612	84	7056	592704	9·1651514	4·379519
35	1225	42875	5·9160798	3·271066	85	7225	614125	9·2195445	4·396830
36	1296	46656	6·0000000	3·301927	86	7396	636056	9·2736185	4·414005
37	1369	50653	6·0827625	3·332222	87	7569	658503	9·3273791	4·431047
38	1444	54872	6·1644140	3·361975	88	7744	681472	9·3808315	4·447960
39	1521	59319	6·2449980	3·391211	89	7921	704969	9·4339811	4·464745
40	1600	64000	6·3245553	3·419952	90	8100	729000	9·4868330	4·481405
41	1681	68921	6·4031242	3·448217	91	8281	753571	9·5393920	4·497942
42	1764	74088	6·4807407	3·476027	92	8464	778688	9·5916630	4·514357
43	1849	79507	6·5574385	3·503398	93	8649	804357	9·6436508	4·530655
44	1936	85184	6·6332496	3·530348	94	8836	830584	9·6953597	4·546836
45	2025	91125	6·7082039	3·556893	95	9025	857375	9·7467943	4·562903
46	2116	97336	6·7823300	3·583048	96	9216	884736	9·7979590	4·578857
47	2209	103823	6·8556546	3·608826	97	9409	912673	9·8488578	4·594701
48	2304	110592	6·9282032	3·634241	98	9604	941192	9·8994949	4·610436
49	2401	117649	7·0000000	3·659306	99	9801	970299	9·9498744	4·626065
50	2500	125000	7·0170678	3·684031	100	10000	1000000	10·0000000	4·641589

PILING OF SHOT, AND SHELL.

Shot, and shells, are usually piled in horizontal courses, the base being either an equilateral triangle, a square, or a rectangle. The triangular, and square piles terminate each in a single ball, but the rectangular pile finishes in a row of balls.

To find the number of balls in a complete pile.

Rule.—Add the three parallel edges together; then one-third of the product of that sum, and of the number of balls in the triangular face, will be the number sought.

Note 1.—The parallel edges in a rectangular pile are the two rows in length at the base, and the upper ridge. In the square pile the same, except that the upper row is only a single ball. In the triangular pile, one side of the base, the single ball at top, and that at the back, are considered the parallel edges.

Note 2.—The number of balls in the triangular face is found by multiplying half the number in the breadth at the base, by the number in the breadth at the base plus 1.

Note 3.—In all piles the breadth of the bottom is equal to the number of courses. In the oblong pile, the top row is one more than the difference between the length, and breadth of the bottom.