FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
329 
formed. Squaring- each, forming -^y-th part of the sum of squares, and multiplying 
its square root by 0'6745, the probable error is obtained. 
The quantity thus obtained is however a little too great. For, the number which 
26-25 
we have found for E„ contains A or 12 A nearly; and as the probable error of A 
1 3 
is about ^e, the probable error of 12 A is about and therefore we have on the 
right side of the equation an aggregate of terms whose probable error is \/ 
or nearly. The same is true for Eje and those near it. But for E 13 the factor 
of A IS 0 . Thus it will easily be seen that the quantity which we obtain is really 
nearly. The correction scarcely deserves notice. 
44 . In this manner the following (uncorrectedj values of Eo, Ej, &c. are found; 
arranged with reference to the Swings to which they relate. It will be remembered 
that the number 300 represents an error of 0®’! in absolute time, very nearly. 
First Series. 
Second Series. 
Third Series. 
Fourth Series. 
No. of 
Swing. 
Error of 
Comparison. 
No. of 
Swing. 
Error of 
Comparison. 
No. of 
Swing. 
Error of 
Comparison. 
No. of 
Swing. 
Error of 
Comparison. 
+ 
- 
+ 
- 
+ 
- 
+ 
- 
454 
923 
414 
276 
501 
476 
30 
211 
1 . 
27 ... 
53 
68 
128 
28 
54 . 
476 
69... 
254 
3... 
55 
29 ... 
7 
82 
89 
55 
575 
70 ... 
299 
266 
4... 
220 
30 
56 
52 
209 
353 
276 
74 
361 
71 ... 
5... 
702 
1180 
925 
874 
31 
88 
316 
57 ... 
72 ... 
124 
100 
6... 
32 
58... 
73 ... 
7... 
33 
56 
59 ... 
74 ... 
234 
217 
8 ... 
34- 
341 
121 
60 
75... 
9... 
378 
798 
651 
909 
322 
35 
61 
76... 
10... 
36 
59 
122 
62 
374 
196 
77... 
9 
223 
57 
339 
165 
277 
11... 
37 ... 
63 
78... 
12... 
38 
191 
403 
64 
145 
82 
79... 
13... 
14 .. 
79 
39 ... 
40 
56 
65 
66 
136 
80... 
81 
16... 
765 
707 
672 
517 
41 
94 
123 
146 
182 
67... 
234 
82... 
607 
16 
17 .. . 
18.. . 
19 ... 
296 
108 
392 
1135 
39 
42.. . 
43.. . 
44.. . 
45 
127 
109 
20... 
46 
21... 
22... 
439 
47 ... 
48 
52 
79 
23.. 
49 ... 
241 
164 
275 
24... 
25 
112 
60... 
51 
9 
26 ... 
7 
52... 
! 
From these are found the values of the probable error of a single comparison, treating 
the four series separately: 
2 X 
MDCCC'LVI. 
