348 
THE EEY. STEPHEN J. PERRY ON THE MAGNETIC 
The numbers for 1829 and 1850 have been calculated from the data given in M. A 
Quetelet’s treatise ‘ Sur la Physique du Globe and for 1850 I have made the suppo- 
sition, which I find to be most consonant with the observations cited in the same work, 
that the ratio between the values of Horizontal Force at Paris and Brussels is on the 
whole nearly constant, that ratio being 0-9G1. 
Table IX. 
1829. 
1839. 
1850. 
1854. 
1858. 
Aix-la-Chapelle 
37661 
3-8357 
3-8796 
3-9138 
3-8570 
3S208 
3-8971 
3-8730 
3-9349 
Ghent 
3-8553 
Liege 
3-798-4 
3-7355 
3-8316 
[3-8375] 
3-8755 
[3-8835] 
Louvain 
3-9077 
Namur 
3-8208 
3-8056 
Neglecting the two observations enclosed within brackets as being evidently too large,- 
we find, by comparing these numbers with those given in Table VIII., the following 
values of the secular variation : — 
Table X. 
Epoch 1850. 1855. 1860-5. 1862-5. 1864-8. 
Secular variation . . 0-00502 0-00547 0-00624 0-00552 0-00484 
These results give +0-00542 as the mean value of the yearly change of the Horizontal 
Force for the epoch 1858-56. If we compare this with the annual increase deduced 
from the numerous observations made at Brussels between the years 1828 and 1860, 
we obtain a strong confirmation of the approximate correctness of the above value. 
Hansteest, Lamoxt, and Quetelet have each expressed the laAV of increase of the Hori- 
zontal Force at Brussels in an analytical form, and these formulae give respectively, for 
the epoch 1850, 0-005422, 0-005183, and 0-005617, as the secular increase. The mean 
of these differs from the result found above only by 0-000031. The acceleration for the 
same date given by Hansteen’s formula is +0-000037 ; but Quetelet makes the increase 
of the yearly rate considerably more rapid. The concluded value of the secular variation 
of the Horizontal Force for Belgium is slightly in excess of that found for France from 
the surveys of 1868 and 1869. 
We will now pass on to the discussion of the results obtained from the combined obser- 
vations of the Dip and Horizontal Force at the several stations. Instead of forming 
new equations of condition with the values given in Table VII., and then solving them 
by the method of least squares, we can find the Intensity at each station by combining 
directly the computed as well as the observed values in Tables III. and VIII., and 
thence deduce the probable errors. Calling the Intensity deduced immediately from 
the observed Horizontal Force and Dip the observed Intensity, and that formed from 
the computed values the computed Intensity, we thus obtain the following results : — 
