TRACT 26.
MEAN DENSITY OF THE EARTH.
21
three cases, in which the constant angle formed by the sectionand the base was a right angle; and one case in which thevertical angles were not taken at the beginning of the sectionline, but at the other end of the base line, where the horizon-tal angles were also observed. It may be necessary therefore,to insert and explain an example of each of these cases, andthe more so, as they point out the fittest means of measuringthese sections, so as to save most part of the labour in thecomputation, in which the trouble chiefty consists.
Of the case of the right angle, the first ,.-| V
section is an instance, where also rs is thebase, as before, and the angle rs p being y y
— 90°. .
Poles.
Dep. andElev.ats.
Horiz.Ang. atR.
Tang, ofvert.. Z’sat s.
Tang, of
/. *S R.
Sum ofColumns4 and 5.
6th + rs= Log.Alt.
Depth
and
Alt.
i
5 16*d
O t
10 0
8-96533
9-24632
8-21165
1-36105
23 d
2
0 30 r
31 35
7-94086
9-78874
7-72960
0-87899
7*a
3
4 15
41 56
8-87106
9-95342
8-82448
1-97388
94
4
6 14*
49 25
9-03861
10-06722
9-10583
2-25523
180
5
8 16
55 51*
9-16224
10-16870
9-33094
2-48033
302
6
10 13
59 57*
9-25582
10-23783
9-49365
2-64305
440
7
11 37
62 56*
9-31297
10-29174
9-60471
2-75411
568
8
12 25
65 3*
9-34276
10-33257
9-67533
2-82472
668
9
13 21
66 41*
9-37532
10-36568
9-74100
2-89040
777
10
14 10
67 36*
9-40212
10*38519
9-78731
2-93671
864
11
15 17
68 42*
9-43657
10*40925
9-84582
2-99522
989
12
17 46
70 58
9-50572
10-46221
9-96793
3-11733
1310
13
19 33
72 48
9-55035
10-50927
10-05962
3-20902
1618
14
20 6
74 30
9-56342
10-55701
10-12043
3-26983
1861
1
2
3
4
5
6
7
8
In this form there are three columns less than in the former,by which it happens, that about one-third of the labour issaved. The method of solution is thus; as radius 1 : tang, r: : rs : sp ~ RS x tang, r ; and again, as 1 : tang, verticalangle s :: sp : sp X tang, s = rs x tang, r x tang. s. Or,in logarithms, log. rs + tang, r + tang, s = log. of the ver-tical perpendicular: and by this theorem, it is evident, thecolumns of this table are constructed.