" ON THE GAUSSIAN CONSTANTS FOR 1829. 97 
cases, and which consists in the formation for each primary equation of a 
supplementary term s, equal to the sum of the other, viz. in one case, in the 
calculation of 
s=coeff. Ag*:° + coeff. Ag*:! + coeff. Ah*:!+.....+ coeff. Ag!:! + coeff. Ah!)!, 
whereby we obtain as controlling equations, . 
[sz] =[n.c.Ag*° ] + [n.c.Ag*!] + [n.c.Ah*!] +... + [2.c.Ag'!] + [.c.Ah'1], 
[s.c.Ag*]=[ (e.g) (c.Ag#")] +[(eAg*®)(e.Ags!)] tut [(cadg'?)(ALY)], 
MIAE (C0. AblA)(oiAg4\] 44 calen scscccsccneeceoE Gecdhl)(@AROI) I> 
independently of the extension which is given to the sums marked by [ ]. 
If we now consider, in the first place, the linear primary equations con- 
tained in the Tables annexed, we shall find that the values of the Gaus- 
sian constants hitherto accepted sufficiently approximate to the truth to 
authorise the supposition from which we start, that the powers of their cor- 
rections superior to the first can be neglected ; but, on the other hand, that 
these values are still so erroneous, that the elements calculated by them differ 
from the empirical ones by far more than can be ascribed to errors of obser- 
vation, and in quite another manner than would arise from local irregularities 
of terrestrio-magnetic power. Indeed we see that when the places of obser- 
vation are in similar parts of the globe, the values of 2 belonging to them 
remain nearly enough equal to each other; whereas on the longitudes of the 
places increasing, these values of m are gradually lessened, and at length 
replaced by a series of values with opposite signs. Of course, to observe this 
regularity of progress, we must only compare such values of 7 as relate to 
magnetic elements of a similar character; as for instance, all to 2, or all to 
_ w, and so on. 
_ The value [nn ]=233423, marked in the Table of Final Equations as re- 
' sulting from 283 equations, shows that for the part of the earth on which 
the observations hitherto considered have taken place, the inean difference 
between an observed magnetic element and the corresponding calculated one 
amounts to 29, the intensity of the whole force at Loaten being =1372 ; and 
_ in agreement with this result, we find, for example, by immediate inspection 
of the Table of Primary Equations,— 
Lat. 56. | 56. | 67. | 54. | 59. 56. 
The mean difference —E——E—————EEE— EE 
Long. 43. | 60. | 67. | 100.) 145.| 222. 
Tn northern horizontal force} +46, |+39)+23/— 6/—28 4.35 
In western horizontal force +18 |+19/+40) O|—25 
| In perpendicular force ...... +11 {+13)+35)—15|/+30) +38 
in whole hori- 
zontal force 
The concluding table contains besides, as already mentioned, twenty-four 
final equations for the twenty-four unknown quantities, by which, mathema- 
tically speaking, the whole problem in question would appear to be ready for 
a definitive and now most easy solution. In practice, however, this is evi- 
dently far from being the case. Thus indeed it is plain, even at a first 
glance, that each observation, hitherto registered, has already contributed 
to the solubility of the problem all that it will ever be able to do; there 
is not in this circumstance alone a sufficient reason for that solubility being 
re and then that, on the contrary, the probability of the value to 
— -:1846. H 
