The gentlemans recreation in two parts : the first being an encyclopedy of the arts and sciences ... the second part treats of horsmanship, hawking, hunting, fowling, fishing, and agriculture : with a short treatise of cock-fighting ... : all which are collected from the most authentick authors, and the many gross errors therein corrected, with great enlargements ... : and for the better explanation thereof, great variety of useful sculptures, as nets, traps, engines, &c. are added for the taking of beasts, fowl and fish : not hitherto published by any : the whole illustrated with about an hundred ornamental and useful sculptures engraven in copper, relating to the several subjects.

CHAP. XXII.

GAGING.

ALL the difference between Gaging, and Mea∣suring other Solids, is only in this, that the

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Solids are Measured by Feet and Inches, the Vessels by Gallons, Quarts, &c.

In this Art are two things to be obser∣ved; First, that those Vessels, being for the most part of Irregular Forms how to reduce them to Regular Propotion; Secondly, to find the true quantity of the Gallons in Cubick Inches, or parts of a Foot: For the first of these, the best way is to measure the Diameter of the Cask, both at the Bung and Head; and by their Diameters find [ 10] out the Area of their Circles; then take 2 Thirds of the Area at the Bung, and 1 Third at the Head, which added together, will be the mean Area of the Vessel. And if you Multi∣ply this mean Area by the Length of the Vessel, it will shew how many Solid Inches the Vessel contains; which if you divide by the Number of Solid Inches in one Gallon, the Quotient will shew how many Gallons the Caskholds.

For Example, Sup∣pose [ 20] the Wine Cask A, having the Diameter at the Head 18 Inches, and the Diameter at the Bung 32 Inches, and the Length 40 Inches, what is the Content?

[illustration]

⅓ Of the Area at the Head is—84, 823 ⅔ of the Area at the Bung are—536, 166 The Sum of these two—620, 909 [ 30] being Multiplyed by the Length—40 959 makes Solid Inches—24839, 560 which being divided by the Solid Inches in one Gallon of Wine, which are 231 Inches, yields for the Content 107 Gallons, 530 Parts, that is, some∣what above ½ a Gallon.

But there is a difficulty to resolve, that is, How many solid Inches there are in a Gallon. [ 40]

As for the Wine Gallon it is generally conclud∣ed to contain 231 Cubick Inches; but some say it is some thing less; but this difference is not so much as others make it in the Ale-Gallon, for al∣though most Gagers, and the Coopers make the Ale-Gallon 〈◊〉〈◊〉 the Wine-Gallon 4 to 5, so that the Wine-Gallon being 231 Inches, the Ale-Gallon is 288 ¼ Inches; yet since the Excise, it is account∣ed by them but 282 Cubick-Inches.

According to these Rules and Observations, [ 50] this ensuing Table is calculated, shewing the ⅓ of the Area at the Head, and ⅔ of the Area at the Bung, of any Cask ready cast up in Gallons, and 1000 Parts for Wine measure; so that measuring the Diameter of any Cask at the Head, and Bung, and adding the Numbers together, and Multiply∣ing their Sum by the length of the Cask, you shall find the Content thereof in Wine-Gallons. For Ex∣ample, Suppose the Diameter at the Head to be 18 Inches,—0, 367 [ 60] at the Bung to be 32 Inches,—2, 321 the Sum of these two,—2, 688 Multiplied by the length 40 Inches,—40 make very near as before,—107, 502 that is, 107 Gallons, and 502 Parts of a Gallon, which is a little above one half of a Gallon.

A Table for Gaging of Wine Cask.

	Head.	Bung.		Head.	Bung.
	G Parts	G Parts		G Parts	G Parts
1	0 001	0 002	31	1 089	2 178
2	0 004	0 009	32	1 160	2 321
3	0 010	0 020	33	1 234	2 468
4	0 018	0 036	34	1 310	2 620
5	0 028	0 056	35	1 388	2 776
6	0 045	0 081	36	1 469	2 938
7	0 056	0 111	37	1 551	3 102
8	0 072	0 114	38	1 636	3 272
9	0 092	0 183	39	1 724	3 448
10	0 113	0 226	40	1 813	3 625
11	0 137	0 274	41	1 904	3 809
12	0 163	0 326	42	2 000	4 000
13	0 192	0 383	43	2 096	4 191
14	0 221	0 444	44	2 194	4 388
15	0 255	0 510	45	2 295	4 588
16	0 290	0 580	46	2 398	4 796
17	0 318	0 657	47	2 504	5 007
18	0 367	0 734	48	2 611	5 222
19	0 409	0 818	49	2 721	5 442
20	0 453	0 906	50	2 833	5 665
21	0 500	1 000	51	2 948	5 895
22	0 548	1 097	52	3 065	6 129
23	0 600	1 199	53	3 184	6 609
24	0 653	1 305	54	3 305	6 865
25	0 708	1 416	55	3 428	7 108
26	0 766	1 532	56	3 554	7 364
27	0 826	1 692	57	3 682	7 625
28	0 888	1 777	58	3 813	7 890
29	0 953	1 906	59	3 945	8 100
30	0 020	2 040	60	4 080

To Gage a Cask that is not full

A Table for Gaging Wine-Cask that are not full

G	Parts	G	Parts	G	Parts	G	Parts	G	Parts
0	000	13	2630	26	4338	39	5913	52	7672
½	295		2707		4400		5976		7758
1	470	14	2775	27	4462	40	6040	53	7829
	620		2847		4542		6094		7909
2	720	15	2918	28	4585	41	6158	54	7990
	830		2986		4646		6223		8072
3	935	16	3056	29	4706	42	6288	55	8154
	1038		3123		4766		6353		8236
4	1138	17	3189	30	4826	43	6418	56	8319
	1235		3255		4885		6483		8404
5	1339	18	3321	31	4943	44	6548	57	8491
	1420		3387		5000		6613		8580
6	1502	19	3452	32	5057	45	6679	58	8661
	1596		3517		5115		6745		8765
7	1681	20	3582	33	5174	46	6811	59	8862
	1764		3647		5234		6877		8962
8	1846	21	3712	34	5294	47	6944	60	9065
	1918		3777		5354		7012		9170
9	2010	22	3842	35	5415	48	7082	61	9280
	2091		3906		5476		7153		9398
10	2171	23	3960	36	5535	49	7225	62	9530
	2242		4024		5600		7297		9705
11	2328	24	4087	37	5662	50	7370	63	10000
	2405		4150		5724		7444
12	2481	25	4213	38	5787	51	7519
	2556		4276		5850		7595

The use of this Table is as followeth.

FIrst measure the Diameter of the Cask at the Head and Bung, and thereby you will find the Content of the whole Cask; Then measure how many Inches deep the Liquor in the Cask is, and then work by the Rule of Proportion; As for Example.

Let the Cask be as before, 32 Inches at the [ 10] Bung, and the Liquor 24 Inches deep.

• As the Diameter at the Bung in Inches 32
• To the depth of the Liquor in Inches 24
• So the Radius of the Table 10000
• To the part Proportional 7500

Find this Number 7500 in the Table, and it an∣swers very near to 50 ¼ Gallons.

Then work again thus, omitting the smaller Fractions, which are of little concernment. [ 20]

	Gal.	Part.
As the Gallons of the Radius	63	00
to the Proportional Gallons found	50	75
So the content of the whole Cask	107	50
to the Content of the Liquor being
24 Inches deep	86	61

That is somewhat above 86 ½ Gallons.

Note that one Foot Square is near ½ a Gallon; for there is 144 Inches in a Foot, which doubled makes 288, which should be the Content of the Ale Gallon, although here it is alittle lessened un∣to 282 Inches. [ 30]

To Gage a Ship, and cast up how many Tuns her Burthen is.

MEasure the Length of her Keel, the Breadth at the Mid-ship-Beam, and the Depth of the Hold; Multiply these three one by the o∣ther, and divide the Product thereof by 100, and so you shall find how many Tuns her Bur∣den [ 40] is; For Example.

Suppose a Ship having the Length of her Keel 50 Foot, and the Breadth at the Mid-ship Beam 20, and the Depth in the Hold 10 Foot; how many Tuns will the Ship carry?

Multiply 50 by 20, which makes 1000; and that Multiplyed by 10, makes 10000, which di∣vided by 100, cutting off the two last Figures, shews the Ships Burden to be 100 Tuns.

But this reckoning is only for the Kings Ships; As for Merchants Ships, who give no allowance for Ordinance, M••sts, Sails, Cables, and Anchors, which are all a Burden▪ but no Tunnage, you must divide your Product by 95; so the foresaid Ship will be found to be 105 Tuns, 25/95 Parts.

But this way of reckoning the Tunnage of Ships, though it may come near in some Ships, yet it may miss much in others; for all Ships are not built of the same Fashion; therefore it is the best and surest way to cast up the Content of the Ship more exactly according to the Rules of Art, with respect had to the Mold, and shape of the Ship, and so to find out how many Cubick Feet the Ship doth contain; and every Cubick Foot of Water according to some, weighs 55 li. Averdupoiz; but a Cubick Foot of Water according to some Artists, weigheth 62 li. 588 parts. Now every Tun being 20 hundred Weight, and every Hundred 112 li. which makes 2240 li. divide this by 62 li. 588 parts, it makes 35 Foot, 79 parts; so that about 36 Cubick Feet makes a Tun weight.

But observe that if you measure thus a Ship within, you shall find the Content or Burden the Ship will hold, or take in. If you mea∣sure the Ship on the out-side to her Light-mark, as she swims being unladen, you shall have the Weight or Content of the empty Ship; and if you measure from the Light-mark to her full Draught of Water, being laden, that will be the true Burden or Tunnage of the Ship.

Knowing the Measures of a Ship of one Burden, to make another Ship of the same Mold, which shall be double, or treble, or in any Proportion, more or less, to the said Ship.

Multiply the Measurs of the Length, Breadth, and Depth of the Ship Cubically, and then double, or treble the Cube, and extract the Cube-Root thereof.

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