A more exact way to delineate the plot of any spacious parcel of land as baronies, parishes, and town-lands, as also of rivers, harbours and loughs, &c. than is as yet in practice : also a method or form of keeping the field-book, and how to cast up the superficial content of a plot most exactly.

A More Exact VVay to Delineate the Plot of any spa∣cious parcel of Land, as Baronies, Parishes and Town-Lands: as also of Rivers, Har∣bours and Loughs, &c. than is as yet in Practice

Sect. 1. How to keep the Field Book.

HAving taken and set down your notes (of Proprietors names and Lands, bounders, windings, &c.) in the Field on the left hand Pages of your Book, you may devide the right hand Page into six Columns, (as may be seen here∣after) in the first may be put the quantities of your lines measured in Chains and hundred parts, in the second Co∣lumn how many degrees and parts; the Lines you have traversed, are distant from the North or South part of the Meridian towards the East or West; the other four Co∣lumns are distinguished by the names of South, North, East and West: in the which are set down the Easting, VVest∣ing, Northing and Southing of the Degrees and Distances observed by a Table (the ma∣king and use whereof shall be shown) and for the easie understanding of which, we shall here affix a Table so divided and noted as aforesaid, answering to the Scheme adjoyning in which suppose the line from A. unto B. to be 73. Degrees to the South towards the VVest, and the length of the line A. B. to be 14. Chains and 70. links; again the line B. C. to be 75. Degrees and 36. from the South towards to VVest, and the length of the line B. C. to be 20. Chains :40. links, and also the line C. D. to be 87. Degrees from the South toward the VVest, and length C. D. 10. Chains :50. links; the line D. E. 9 Chains :70 links, and the Angle 73. Degrees 30, minutes from the South to the West,

and this Order is to be observed in all the rest till you have finished your surround, and may more plainly appear by the subsequent Table.

Distances.	Angles.	South.	North,	East.	West.	X	Z
14 :70	73 :00 S W	4 29			14 :06	4 :29	14 :06
20 :40	75 :30 S W	5 10			19 :79	9 :39	33 :85
10 :50	87 :00 S W	0 55			10 :49	9 :94	44 :34
9 :70	73 :30 S W	2 76			9 :30	12 :70	53 :64
29 :00	75 :30 S W	7 25			28 :11	19 :95	81 :75
7 :40	74 :30 S W	1 98			7 :12	21 :93	88 :87
10 :60	South.	10 60			00 00	32 :53	88 :87
14 :60	28 :30 S W	12 84			6 97	45 :37	95 :84
33 :95	82 :00 N E		4 :74	33 :61		40 :63	62 :23
25 :00	72 :00 N E		7 :74	25 :75		32 :89	38 :48
21 :40	78 :30 N E		4 :28	20 :97		28 :61	17 :51
21 :00	65 :30 N E		8 :71	19 :11		19 :90	1 :60
20 :00	4 :30 N W		19 90		1 60	00 :00	00 :00
238. 25		45. 37	45. 37	97. 44	97 :44	X	Z

Sect. II. Of the Construction and use of a Table for the more ready and exact laying down of any right Lined Figure.

THe making of this Table is very easie, out of the Tables of natural Sines for each De∣gree and half Degree of the Quadrant; (or nearer if one please) for if you multiply any distance run, by the Sine and Sine Complement answering that Degree of Azimuth you measured on, the Products shall be the number to be put in the North or South Co∣lumn, and East or West; for the reason is evident from the first Axiom of plain Trian∣gles, that if the Hypotenusa (in a right angled Triangle) be put as Radius the base, and Cathetus shall be Sines of their opposite Angles: Now in this case, the lines measured are put as the Hypote••usa, and supposed Radius and therefore the sides shall be in pro∣portion to the Sines of their opposite Angles, and the Ratio will be as Radius, is to the Distance of two places measured in their Rumbe: so is the Sine Complement of that Rumbe to a fourth number, to be put in the Meridian either Northward or Southward, according as the Rumbe lyeth North or South. Again as Radius is to the distance of two places measured in their Rumbe: so is the Sine of the Rumbe to a fourth number, to be put in the line of East or West, according as the Rumbe lieth Eastward or West∣ward; and this may suffice for the construction. Now to the use, supposing our Tables

already made, now this Table is made for every Degree and half Degree of the Quadrant from the North or South towards the East or West, and is only the Sine Complement of every of these Degrees and parts, made into a Table by Duplication, Triplication, Re∣duplication and Bipartition, &c. unto ten; by the help whereof, you may make the Numbers only by addition; which Numbers multiplyed unto ten I use whither my Num∣ber of Chains be under Ten, a Hundred, or a Thousand: only observe, that the Numbers in the Table stand for any Number of Chains under Ten; but if they shall amount unto Twenty Chains or above, and less than two Hundred, you are to adjoyn a Cipher to the Number found: but if your Number of Chains shall exceed two Hundred Chains, and less than two Thousand, you are to adjoyn two Ciphers to the Number found, &c. But if you shall have any odd Links, you are to seek them as if they were whole Chains, only with this caution, that if your Links exceed Ten, you cut off one Figures towards the right hand: but if under Ten, then you cut off two Figures towards the right hand; the residue you place under the Number of Chains, and then add them up into one Sum, and cut of the two last Figures toward the right hand, the remainder shall shew the Number of Chains and those two Numbers cut off, shall be the Number of Links. An ex∣ample or two will make all easie, and shew how the Numbers in the Columns of North, South, East and West in the little Table are made, which observe well.

[illustration] surveying diagram

Let the Line A. B. contain in length 14 Chains, 70 Links, and the Angle observed is 73 Degrees from the South part of the Meridian towards the VVest, under 73 Degrees in the Table, and against 10 in the side I find 292; also under 17 degrees (the Com∣plement of 73 Degrees to 90.) and against 10 in the side I find 956 these two Numbers I place thus, then in the same Table under 73 Degrees, I seek my four, Chains against 4 in the side, and I find 117 to be added to 292 afore found; also in the next Column under 17 Degrees, and against 4 in the side, I find 383 to be added to 956 found in the said Table as before.

292	956
117	383
20	67
4:29	14:06

Now here are 70 Links, which 70

I seek under 73 Degrees, and against 7 in the side, and find 205; also against 7 in the side, and under 17 Degrees I find 669; now according to the rule, because above ten Links I cut off the last Figure to the right hand, and they stand thus 20 : 67 to be added to the a∣foresaid Numbers, this done I sum up these Numbers, and they will be 429 and 14 06 but when I have cut off the two last Figures to the right hand, then they will be 4 : 29 and 14 : 06, that is 4 Chains 29 Links to be put in the South Column, and 14 Chains 6 Links to be put in the VVest; and alwaies observe to put the Number arising from the Degree you measured on, into the Column of South or North, according to his Title: and the Number arising from the Complement in the Column of East or VVest, with re∣gard to his Title. The second line B. C. is 20 Chains 40 Links, and the Angle 75 : 30 first I seek under 75 : 30 and against 2 in the side (because my Table gives not 20) I find 50 also under 14 : 30 the Complement of 75 : 30 in the Column adjoyning I find 194 to both these, I adjoyn a Cipher according to the rule, and they will stand thus also in the same Column, and against 4 I seek 40 Links and I find 100 and 387 which when I have cut off the last Figure to the right hand, they will stand thus 11 and 29 which added to the former Numbers and the two last Figures cut off it will be 5 Chains 10 Links for the South, and 19 Chains 79 Links to be put into the West, and so I proceed with all the rest until I have finished;

500	1940
10	39
5:10	19:79

and being thus returned unto my first station, I sum up severally these four Columns of South, North, East & West, and finding that the sum of the South Column is equal to that of the North, and the sum of the East is equal to the sum of the West, I conclude the work to be truly performed; whereas i•• there had been any difference it shews an Error, and if that difference had been great, it is necessary to examine the work again, and so to cor∣rect it; and thus much for our business in the Field, we come now to the plotting. And for our more quick dispatch, we add severally the several Numbers in each Column together, as in the Example following; and here I begin with the South Column, and put them into the Table noted with X thus, 4 : 29 4:29 & more by 5 : 10 is equal to 9 : 39. and 9 : 39 added to 0 : 55 is equal to 9 : 94 and 9 : 94 added to 2 : 76 is equal to 12 : 70. and 12 : 70 added to 7 : 25 is equal to 19 : 95. and 19 : 95 added to 1 : 98 is equal to 21 : 93. & 21 : 93 added to 10 : 60 is equal to 32 : 53. & 32 : 53 added to 12:84 is equal to 45 : 37. And thus is the South Column summed up, and the several Numbers in the Northern Column, are to be subducted out of the South Column; Thus 4 : 74 sub∣stracted from 45 : 37 there rests 40 : 63. and 7 : 74 subducted from 40 : 63 there rests 32 : 89. and 4 : 28 substracted from 32 : 89 there remains 28 : 61. and 8 : 71 subducted from 28 : 61 there rests 19 : 90. and 19 : 90 subducted from 19 : 90 there rests 00 : 00. And thus you see I have drawn the North and South Columns into the Column X. I shall proceed in the same manner with the East and VVest Columns, as to draw them into the Column Z. first 14 : 06 and 14 : 06 added to 19 : 79 is equal to 33 : 85. and 33 :85 added to 10 : 49 is equal to 44 : 34 & 44 : 34 added to 9 : 30 is equal to 33 : 64. and 53 : 64 added to 28 : 11 is equal to 81 :75. & 81 :75 added to 7 : 12 is equal to 88 : 87. and 88 : 87 added to 00: 00 is equal to 88 : 87. (and this is the reason of twice 88 : 87 in the Table Z) & 88 : 87. added to 6 : 97 is equal to 95 : 84. and so far is the West Column summed up: the East Column follows, and is to be subducted out of the West thus, 33 : 61 substracted from 95 : 84 there rests 62 : 23. and 23 : 75 subducted

from 62 : 23 there rests 38 : 48. and 20 : 97 subducted from 38 48 there rests 17 : 51. and 19 : 11 substracted from 17 : 51, which because I cannot do, I subduct 17 : 51 out of 19 : 11 there rests 1 : 60. East, from which I subduct 1 : 60 in the West, and there remains 00 : 00. And thus is my two Columns of X and Z made, by which I lay down the Scheme.

Distances.	Angles.	South.	North.	East.	West.	X	Z
14 :70	73 :00 S W	4 29			14 :06	4 :29	14 :06
20 :40	75 :30 S W	5 10			19 :79	9 :39	33 :85
10 :50	87 :00 S W	0 55			10 :49	9 :94	44 :34
9 :70	73 :30 S W	2 76			9 :30	12 :70	53 :64
29 :00	75 :30 S W	7 25			28 :11	19 :95	81 :75
7 :40	74 :30 S W	1 98			7 :12	21 :93	88 :87
10 :60	South.	10 60			00 00	32 :53	88 .87
14 :60	28 :30 S W	12 84			6 97	45 :37	95 :84
33 :95	82 :00 N E		4 :74	33 :61		40 :63	62 :23
25 :00	72 :00 N E		7 :74	25 :75		32 :89	38 :48
21 :40	78 :30 N E		4 :28	20 :97		28 :61	17 :51
21 :00	65 :30 N E		8 :71	19 :11		19 :90	1 :60
20 :00	4 :30 N W		19 90		1 60	00 :00	00 :00
238. 25		45. 37	45. 37	97. 44	97:44	X	Z

Sect. III. How to Delineate the Scheme.

COnsidering which way the Ground lies, I take a point for my first Station; So as the whole may fall conveniently within the Plot, which let be the point A. By which point I draw a Meridian and Paralel, namely two right lines intersecting one an∣other at right Angles, whereof let N S be the Meridian running North and South, and E W. the Paralel running East and West: And first I look to the South and North Co∣lumns, and there in the South Column, and against the first station I find 4:29. and even with it in the VVest I find 14 : 06 then with my Compasses, on a Scale of equal parts, I measure this 4 : 29 on the Meridian line, from A. towards S, to 1. Also I take the length of 14 : 06 of the Seale, and set it on the line of East and West, from A to 1; then keep∣ing your Compasses at that distance, set one point in the Meridian line at 1, and with the other point describe a small Arch towards B. then set the Compasses to the first distance 4 : 29 and setting one point in 1 on the line of East and West Cross the aforesaid Arch, and in the point of crossing note it with a prick, and a line drawn from this point to the point A represents my first line A B 14 : 70. Then I observe against my second Station in the Column X Z. for the South 9 : 39 and for the West 33 :85. First I take the 9 : 39 on the Scale of equal Parts and lay it as before on the Meridian line N. S. from A. to 2; also I take the length 33 :85 and measure it on the line of East and West from A to 2: then

keeping your Compasses at that distance set one point in the Meridian line at 2. and with the other foot describe an Arch toward C. then setting the Compasses at the former di∣stance 939 set one point in the Line of East and West at 2. and with the other foot Cross the aforesaid Arch, and note the point of crossing for a line drawn from thence to the point B. is my second line 20 :40, and thus you may lay down the distances C.D.E. &c. till you have included the figure, the practice of this but once makes all perfect.

[illustration] surveying diagram

Sect. IIII. How to cast up the Superficial Content.

NOw for the exact casting up the Area, the very bare Inspection will Declare it; for in the first Triangle A. B. 1, it is plain by the Table that the Base is 14 : 06, the Cathetus 4 : 29; the second Triangle B. C. Q. the Base 19 : 79 and the Cathetus 5 : 10; also the Parallelogram 1. B. 2. Q. hath for his sides the Cathetus of the first Triangle 4 : 29, & Base of the second Triangle 19 : 79; So it is obvious for all the rest; then ha∣ving considered the length & breadth of the Rectangle Figure a b c d (within which the greatest extent of your Plot is contained) drawn into one another, and from the product you shall subduct the products of all those Triangles, and Parrallelograms comprehend∣ed within the said Rectangle Figure, and perimeter of your Plot; the remainder shall be the Superficial Content of that Figure: as in the foregoing Scheme the sides of the Rectangle Figure containing the Plot are 45 :37 and 97: 44, which drawn into one ano∣ther, is 44208528; and the Products of the several Triangles and Parrallelograms are 23799003; which subducted from the former, there rests 204 : 09525, which are the Number of square Links in the Plot, and if your Chain be four Pole; than are you to cut off the five last Figures towards the right hand, the residue shall be the Numbers of Acres,

as thus, 204 : 09525 is 204 Acres, and 9525 Links; but if your Chain be two Pole, than the fourth pare of this number shall be the Number of Acres, viz. 51 Acres and 2381 Links, or almost 4 Perch; for like Plains are in a Duplicate Ratio to their Homologal sides by 20. Eucl. 6. (that is) as a Quadrat to a Quadrat; and therefore if three Lines are proportional, it shall be as the first is to the third: So is the superficies upon the first, to the superficies on the second; For example, 1. 2. 4, are proportional therefore as 1. is to 4: so is the square of 1. to the square of 2. upon this depends the reason of reduction of Plots or quantities, either bigger or lesser.

FINIS.