22

CALCULATIONS TO ASCERTAIN THE. TRACT 2,to

But nearly the same saving, in the great labour of compu-tation, would be made, if the vertical and horizontal angleshad both been taken at the end of the base farthest from thebeginning of the section. And this method would also bemuch the easiest in making the survey on the ground, asthere would then need only one observer, with an instrumentto measure both horizontal and vertical angles ; and any per-son, without an instrument, could direct in a line the personwho moves and places the poles, or he may even direct him-self after his first pole has been placed, by means of a backobject, as is commonly done in land surveying.

Of this kind there happens to havebeen one section taken, proceeding fromG, and making with gp an angle of 85°,p being the Northern obervatory, andwhere both the bearings and depressionsof the points p in the section line wereobserved.

Log.

pg 3-68262 'j this gives a constant number from whichsin. G 9 99834 h t j le s ; nes 0 f ^ j n £[ le co ] umn> are

Sum 3-68096 J to be deducted.

P P

p

From ISO 0Take 10= 852 f + 2p= 95

. jVertic.« (Angles(2 (at p.

HorizAngleat p.'

•vj * ,°

II 1

Sines ofZ’s at p*

PC + J.G-i.p =

P P

Tang, ofDepr.

Sum ofC 0 I. 6 &7. — p p.

Depth

below

p

1

0 1

8 45d

0 /

9 15

8°5 45

9-998S0

3-68216

9-18728

2-86944

740

2

&-46

16 25

78 35

9-99132

3-68964

9-18812

2-87776

755

3

9 58

27 16

67 44

9-96634

3-71462

9-24484

2-95946

911

4

8 38

30 52

64 8

9-95415

3-72681

9-18136

2-90817

809

5

7 6

34 30

60 30

9-93970

3-74126

9-09537

2-83663

686

6

5 23

37 55

57 5

9-92400

3-75696

8-97421

2 73117

538

1

2-

3 ■

4

5

6

7

8

9

Here, it is evident, is a saving of two of the most laboriouscolumns in the table. This happens because that, in everytriangle pg/j, there are now constant those two parts whichenter the proportion made use of in the calculation, viz, pg