ONE HUNDRED THOUSAND FACTS FOR THE PEOPLE. 429: 



We will begin by plotting the field, A 

 B C, the measurement of which forms the 

 first example in the preceding section. 



Draw an indefinite line and set off 

 from the plotting scale the base A B, = 

 900 links, marking with the point of a 

 pencil the termination, A and B; set off 

 on A B the distance, A F, = 300 links, 

 from the point F raise an indefinite per- 

 pendicular and set off on it F C, = 480 

 links ; draw lines connecting the points, 

 A B, B C, A C, and the field is correctly 

 plotted. The field, A B C D, it will be 

 obvious, merely requires the erection of 

 the perpendicular, D E, = 510 links, 

 and drawing lines connecting the points, 

 A D, D B, in addition to the foregoing 

 operation. 



In the third example, where the boun- 

 dary, D d e f B, is irregular, on the line 

 D B set off a, = 150 links, a b = 270 

 links, be — 150 links and c B = 180 

 links, and from the points, a b c, raise the 

 perpendiculars, a d, = 150 links, b e = 

 90 links, and c /= 180 links, draw lines 

 connecting the points, D d, d e, e f, f B, 

 which finishes the plotting of the whole 

 field, ACB/^D. 



It is usual to place the north side of 

 the plan uppermost with a flower-de-luce 

 to indicate the north point, and in a 

 vacant place to insert a scale of equal 

 parts or chains and the title of the plan. 



3. The next thing to be done is the 

 computing the contents of the various 

 triangles and trapezoids, and bringing 

 out the total area of the whole survey, 

 which is equally simple with the preced- 

 ing operations. 



We cannot be expected in the limits of 

 this work to give a comprehensive treatise 

 on Mensuration and Superficies ; we shall, 

 therefore, confine ourselves to mentioning 

 two or three things, a knowledge of 

 which is indispensably necessary in the 

 calculation of almost every survey : 



1. The base and perpendicular of any 

 triangle multiplied into each other gives 

 twice the area of such triangle; or the 

 base multiplied by half the perpendicular 

 is equal to the area of the triangle. 



2. The sum of the parallel sides of any 

 trapezoid (that is, a four-sided figure 

 having two of its sides parallel) multiplied 

 by the perpendicular distance between 



them, gives twice the area of such trapez- 

 oid ; or, half the sum of the parallel sides; 

 multiplied by the perpendicular is equal 

 to the trapezoid. 



3. The number of square links in an? 

 acre, 100,000. Hence this rule — square- 

 links are reduced to acres by cutting off 

 five figures to the right, as a remainder, 

 which is to be multiplied successively by 

 4 for roods, 40 for poles, 30^ for yards,, 

 and 9 for feet, at each multiplication^ 

 cutting off 5 figures to the right; the 

 numbers on the left of the point being, 

 acres, roods, poles, yards and feet. 



The following calculation will suffi- 

 ciently illustrate the computing of sur- 

 veys. 



Required the area of the field, A C R 

 f e d D— 



LINKS. 



Triangle, A B C, = A B, 900, 



X C E, 480, = 432000 



Triangle, A B D, = A B, 900, 



X D E, 510,= --. 459000- 



OFFSETS. 



Triangle, D a d,= D a, 150, X 



a d y 150 = - - - - 22500. 

 Trapezoid, a d e b,-=. ad, 150 + 



b e, 90, X a b, 270,= - 64800 

 Trapezoid, b e J c, = b e, 90, -f- 



c f, 180, X be, 150,= - 40500. 

 Triangle, c fB,=c /, 180, X c 



B, 180, =- ... 32400 



According to Rule, divide by 2)1051200 



Square links, - 5.25600 



4 



1.02400 

 40 



.9608 



28.80000 

 24000 



29.04000 

 9 



.36000 

 * Contents of the field, 5 acres, 1 rood, 

 29 yards and about j4 of a foot. 



