SURVEY OF THE EAST OF FRANCE. 
17 
Were we to omit the observations taken at the stations of Marseilles, where the site 
was quite exceptional, and of Grenoble, where the geological formation appears very 
unfavourable for deducing a correct mean value, the solution of the remaining equations 
would give us a value for r identical with that already obtained, but would induce a very 
considerable change in the resulting angle between the lines of equal intensity and the 
prime meridian. The probable errors would be greatly diminished. The several quan- 
tities would become 
4T260 for the H. F. at the central station. 
0-00135 =r and u=- 75° 22' 35". 
Probable error at any one station ±(>00654, and at the central station ±0-00154. 
I will now form a Table, similar to that for the Dip, for comparing the general results 
obtained during the two surveys of 1858 and 1868-69. 
Table X. 
Epoch. 
H. F. at Central 
Station. 
Distance between 
lines of equal H. F. 
which differ by 01. 
Angle of lines of 
equal H. F., N.E. of 
meridian. 
Number of stations. 
Jan. 1st, 1858, W 
4-0521 
miles. 
68-0 
72 40 51-7 
20 
Jan. 1st, 1858, E 
4-0707 
73-5 
78 49 36-0 
22 
Sept. 1st, 1868, W 
4-1150 
71-4 
74 25 31-5 
13 
Sept. 1st, 1869, E 
4-1259 
74-1 
76 27 16-5 
20 
We see at once that the lines of equal Horizontal Force lie much closer in the west 
of France, but that this difference is diminishing rapidly at present, although it still 
remains considerable. The mean angle formed by these lines with the meridian of Paris 
is only slightly different for 1858 and for 1868 and 1869, whilst the angle deduced from 
both sets of observations taken in the east is very much greater than that found for the 
west; the difference, however, is here again less for 1868-69 than for 1858. 
The secular variation for the W. ±0-00590, and for the E. ±0-00473, obtained from 
the preceding Table, agrees well with the results deduced from the few stations which 
are common to the two surveys. 
We next come to the discussion of the values of the Total Force, found by combining 
the observations of the Dip and Horizontal Force taken at each successive station. 
The figures in Table VII. enable us to form at once the required equations of con- 
dition, and these combined furnish the three equations, — 
17-8759=20 F— 2521 #± 3057 y, 
— 2167-3049= — 2521 F ±421413#— 447498 3 /, 
2352-5148 = 3057 F -447498 #±910595 y, 
whose solution give F=T0608, #=0-0003444, y= — 0-0008084. 
Thus the isodynamics that differ by 0-1 are 113-8 miles apart, and they lie at an angle 
of 66 ° 55' 24"-9 to the N.E. of the geographical meridian. The intensity of the earth’s 
MDCCCLXXII. D 
