The manner of raising, ordering, and improving forrest-trees also, how to plant, make and keep woods, walks, avenues, lawns, hedges, &c. : with several figures proper for avenues and walks to end in, and convenient figures for lawns : also rules by M. Cook.

CHAP. XLII. (Book 42)

Of measuring Timber and other solid Bodies, with several Ta∣bles usefull thereunto, &c. (Book 42)

IN Board, Glass, Land, &c. we onely took notice of the Length and Breadth, which was sufficient to find the superficial Content; but to measure solid Bodies we must take notice of the Length, Breadth and Depth. Most of solid Figures are measured by finding first the superficial Content of the Base, or one End, and multiplying that by the Length, if both Ends alike; but if tapering, then by ⅓ of the Length; and as superficial Measure hath 144 square Inches in one foot, and 72 square Inches in half a foot, and 36 square Inches in a Quar∣ter: So

• In solid Measure 1728 square Inches make one foot,
• And 8.64 square Inches make half a foot,
• And 432 square Inches make a quarter of a foot.

For every Inch square is like a Die, and so is a foot of solid Measure supposed to be; for what it wants either in Breadth or in Thickness, it must have in Length; so that in what form soever your solid Body is, that you measure, there must be 1728 solid Inches to make a foot; for 12 (the side of a foot) multiplyed by 12 gives 144 for one side; and 144 multiplyed by 12 (another side) gives 1728, the Cube-square Inches in a Cube-square foot.

Now to find the solid Content of any piece of Timber or Stone that hath the sides equal, first find the superficial Content of the End, in

Inches and parts; and multiply that by the Length in Inches, the Pro∣duct is the Content in solid Inches: Then divide that summe by 1728 (the Inches in a foot,) the Quotient sheweth you the Content in solid feet, and what remain are Inches. If you would work this by the Line of Numbers, the Rule is thus:

• Extend the Compasses from one to the Breadth in Inches;
• The same Extent will reach from the Depth to the Content of the End:
• Then extend the Compasses from one to this Content of the End;
• Keep your Compasses fixed, and that Extent will reach from the Length to the Content in solid Inches.

But if your solid Figure hath both Ends alike, and in form of a Re∣gular Polgone; that is, a piece of Timber hewed into 5, 6, 7 or 8 equal sides, &c. which is called by some A prisme: then take the Semi-circumference, and multiply that by the Radius or Semi-diameter, that product by the Length giveth the Content.

But if your solid Figure be a Cylinder, that is, a round piece of Timber or Stone; having both Ends equal Diameter, as a Rol∣ler, &c. here take the Semi-circumference, multiply it by the Semi-diameter, and the Area of that by the Length giveth the solid Con∣tent.

Now many of the Bodies of our Timber-trees will be near this form of a Cylinder, but Custom hath got such footing (though very false,) that men will not measure their Timber the true way, but will still keep their Error, which is, to gird the middle of the Tree about with a Line, and take the fourth part thereof for the true square, and so measure it as a four-square piece of Timber; but how false that is, may appear by the ensuing Tables. Whoever is pleased to trye, will find, that there may be four Slabs taken off, to bring that to a Square, and that squared piece then will be near equal to the Measure they first measured the piece of Timber by; so that when they have brought their piece square by hewing or sawing, they then have the Measure that it was measured for when it was Round.

But several men have demonstrated this false Rule to be false near ⅓, as Mr. Wing, Mr. Philips, and others: Yet Custom doth and will keep its Road.

I have already shewed how to measure Timber by the Customary way, by the Line of Numbers, in Chap. 35, and 36. before-go∣ing, and for further satisfaction I referre you to these Tables fol∣lowing.

A Table shewing the solid Content of one foot Length, of any piece of Timber according to the superficial Content taken at the End there∣of.

The Inches at the End.	f. pts.
1	0.007
2	0.014
3	0.021
4	0.028
5	0.035
6	0.042
7	0.049
8	0.056
9	0.062
10	0.069
20	0.139
30	0.208
40	0.278
50	0.347
60	0.417
70	0.486
80	0.556
90	0.625
100	0.694
200	1.389
300	2.083
400	2.778
500	3.472
600	4.167
700	4.861
800	5.556
900	6.250
1000	6.944
2000	13.888
3000	20.833
4000	27.778
5000	34.722
6000	41.666
7000	48.711
8000	55.555
9000	62.500
10000	69.444
20000	138.888

Finding the super∣ficial Content at the End of your Timber∣stick or Stone, &c. let it be Round or Square, so it hath but the same Compass from one end to the other, against that Number is the feet and parts of one foot Length; and by mul∣tiplying that by the Length of your Stick, sheweth the Content in square feet.

Example:

The superficial Con∣tent at the End being 200 Inches and 5 foot long, against 200 is 1 foot 389 parts, 〈 math 〉〈 math 〉 which multiplyed by 5 (the Length,) yieldeth 6 foot and 945 parts, that is near 7 foot of Timber: But if the Num∣ber that is at the End be not in the Table, then adde two Numbers together, and then take the Number which an∣swereth them, and adde them together, and multiply the Length by that summe, as before, &c.

A Table shewing the true Quantity of one foot length, in any true squared piece of Timber, for Inches and half Inches, from half an Inch square to 36 Inches square.

I.	fo. pts
	0.002
1	0.007
	0.016
2	0.028
	0.043
3	0.062
	0.085
4	0.111
	0.140
5	0.174
	0.210
6	0.250
	0.293
7	0.340
	0.390
8	0.444
	0.502
9	0.562
	0.627
10	0.694
	0.765
11	0.840
	0.919
12	1.000
	1.085
13	1.174
	1.266
14	1.361
	1.460
15	1.562
	1.668
16	1.778
	1.891
17	2.007
	2.127
18	2.250
	2.377
19	2.507
	2.641
20	2 778
	2.918
21	3.062
	3.210
22	3.361
	3.516
23	3.673
	3.835
24	4.000
	4.166
25	4.340
	4.513
26	4.694
	4.877
27	5.063
	5.250
28	5.445
	5.670
29	5.840
	6.043
30	6.250
	6.460
31	6.673
	6.890
32	7.111
	7.333
33	7.562
	7.780
34	8.028
	8.263
35	8.507
	8.750
36	9.000

If you would enlarge this Table further, the Rule is this; As the square of 12 Inches (which is 144,) is to 1000, So is the square of another Number to another.

Example.

As in 36; the Square of it is 1296; then as 144 is to 1000, So is 1296 to 9 foot, &c. as is in the Table.

〈 math 〉〈 math 〉

The Ʋse of the Table.

The Square of a piece of Timber being found in Inches, and the Length thereof in Feet, to know the Content, take the Number answering to the Square of Inches, out of the Table, and multiply it by the Length in feet.

Example.

A piece of Timber 18 Inches square, and 25 foot long; the Number answering to 18 Inches square, is— 〈 math 〉〈 math 〉 Which multiplyed by 25 (the Length)

Which is 56 foot and one quarter.

A piece 18 Inches square at the End, and one foot long, is 2 foot and 1/40.

A Table shewing by the Compass of Round Timber, what is contained in a Foot length thereof.

Co.	fo. pa.
10	0.055
11	0.066
12	0.079
13	0.093
14	0.108
15	0.124
16	0.141
17	0.159
18	0.179
19	0.200
20	0.221
21	0.243
22	0.267
23	0.292
24	0.318
25	0.343
26	0.374
27	0.403
28	0.433
29	0.465
30	0.497
31	0.531
32	0.566
33	0.602
34	0.639
35	0.677
36	0.716
37	0.756
38	0.798
39	0.840
40	0.884
41	0.929
42	9.974
43	1.021
44	1.070
45	1.119
46	1.169
47	1.220
48	1.273
49	1.327
50	1.381
51	1.437
52	1.496
53	1.552
54	1.612
55	1.671
56	1.732
57	1.795
58	1.860
59	1.923
60	1.988
61	2.056
62	2.124
63	2.193
64	2.264
65	2.335
66	2.406
67	2.480
68	2.555
69	2.631
70	2.707
71	2.785
72	2.864
73	2.945
74	3.026
75	3.108
76	3.191
77	3.276
78	3.362
79	3.449
80	3.537
81	3.625
82	3.715
83	3.807
84	3.866
85	3.990
86	4.084
87	4.183
88	4.279
89	4.377
90	4.475
91	4.576
92	4.677
93	4.780
94	4.882
95	4.987
96	5.093
97	5.200
98	5.307
99	5.416

The Ʋse of this Table is as followeth:

Look for the Compass of the Tree in Inches, and in the Column annexed you have the Quantity of Timber in one Foot length; which multiply by the Number of feet that the Tree is in Length, and the Product is the Content thereof.

Example.

〈 math 〉〈 math 〉

The Circumference or Compass of a Tree 47 Inches, and 12 foot long; the Number against 47 Inches is, 1.220: So there is so much in one foot Length, Which multiplyed by 12 gives the Content, That is, 14 foot and above half a foot.

This Table shews how many Inches in Length make one Foot of Tim∣ber, according to the Compass of the piece of Timber, from 10 Inches Compass, to 100 Inches Compass.

Co.	In. pts
10	217.15
11	179.46
12	150.80
13	128.49
14	110.79
15	94.312
16	84.822
17	75.137
18	67.020
19	60.151
20	54.286
21	49.228
22	44.865
23	40.904
24	37.690
25	34.743
26	32.122
27	29.787
28	27.697
29	25.820
30	24.127
31	22.596
32	21.206
33	19.936
34	18.784
35	17.736
36	16.755
37	15.862
38	15.038
39	14.276
40	13.572
41	12.916
42	12.310
43	11.744
44	11.211
45	10.723
46	10.262
47	9.830
48	9.425
49	9.044
50	8.686
51	8.349
52	8.030
53	7.730
54	7.447
55	7.178
56	6.924
57	6.684
58	6.455
59	6.238
60	6.030
61	5.836
62	5.649
63	5.471
64	5.301
65	5.140
66	4.985
67	4.837
68	4.696
69	4.561
70	4.432
71	4.308
72	4.198
73	4.075
74	3.965
75	3.861
76	3.760
77	3.663
78	3.569
79	3.479
80	3.393
81	3.310
82	3.230
83	3.152
84	3.078
85	3.006
86	2.936
87	2.869
88	2.804
89	2.742
90	2.681
91	2.622
92	2.566
93	2.511
94	2.458
95	2.406
96	2.356
97	2.307
98	2.261
99	2.216
100	2.171

The Ʋse of this Table.

Having taken the Circumference of the Tree in Inches, look that Compass in the Table, and against it you may see how many Inches or parts of an Inch make one Foot of Timber; then with a Ruler or a pair of Compasses (which are better,) measure how many times you can find that in the Length of the piece of Timber, and so many Foot is in that piece of Timber: This is a most usefull Table to measure your Timber-trees by.

Example.

The Compass of a Tree being 84 Inches about, then three Inches and 078/1000 make one Foot; take with your Compasses three Inches 078 from off a Scale, and so many times as there is that Length in your Tree, so many foot of Timber are there, &c.

If any Tree be above 100 Inches Circumference, then take half that Circumference, and find the Number belonging thereto in the Table, then take one fourth part of it, and that makes one foot of Timber: Suppose a Tree to be 146 Inches about, the half of it is 73, against this in the Table is 4 Inches 075 parts; one quarter thereof, (viz. one Inch 019 parts) makes one foot of Timber at that Circumfe∣rence.

These Tables, with what hath been before said, will be sufficient to measure any Cylinder by, and how to measure a Cone I have shewed already. A Cone is such a Figure as the Spire of a Church, having a Circular Base, and ending in a sharp point. It is measured by the su∣perficial Content of the Base, multiplyed by one third part of the Al∣titude or Length. A Pyramid, or Pyramis, is such a Figure as hath an angular Base, and ends in a sharp point, which is measured as the Cone is. A Sphear or Globe, is a solid Figure, every where equally distant from the Centre; it is measured by cubing the Diameter, and multiplying that by 11, and dividing that product by 21, the Quotient sheweth the solid Content of the Sphere.

There be several other sorts of solid Figures, as several parts of the Sphear, but they all depend on the proportion of a Circle, and its Dia∣meter.

Also the Hexaedron, which hath 6 Bases; Octaedron 8 Bases; Do∣decaedron 12 Bases; and several other; which to name I shall for∣bear.