A 
ON THE GAUSSIAN CONSTANTS FOR 1829. 93 
ant of these steps, they have a consolation in the fate of their predecessors 
in most similar labours: I allude to the long series of philosophers who de- 
voted themselves during the first thirty years of this century to ascertaining 
the mean values of magnetic elements for as many points on the surface of 
the globe as possible, and whose undertakings are so carefully recorded by 
one of them—I mean Col. Sabine, in his admirable report on magnetic in- 
tensity. They too were long enough under the necessity of restricting the 
immediate application of their operations to refuting some evidently super- 
ficial or erroneous theoretical views, and then, after detaching from their re- 
sults every accidental influence, to register them in the annals of science, as 
contributions to a theory which they only hoped might be attained. But M. 
Gauss’s admirable theorem, that any terrestro-magnetical element, that is 
_ to say, any observable part of the intensity of magnetic force at a given point 
of the earth, or any angle formed by this force with a given plane or line, can 
be represented by combining with given functions of the latitude and longi- 
tude of this point a limited number (probably twenty-four) of constant quan- 
tities, and the way pointed out by him for deriving these constants from a 
sufficient number of observed mean values of magnetic elements, have ina 
short time so completely realized these hopes, that a great encouragement 
was held out, both to former observers of mean magnetic elements, and 
to those who were then, and are still employed in less-advanced branches of 
physics: nevertheless this encouragement was but an imperfect one. To 
complete it, the possibility of applying those former observations had to be 
changed to a reality. On this account I am inclined to think that the com- 
mittee appointed to conduct the cooperation of the British Association in the 
system of combined magnetic and meteorological observations, have parti- 
cularly contributed to the satisfaction of their own observers, by encouraging 
the calculation of the Gaussian constants for 1829; for, by so doing, they in the 
first place have confirmed their adhesion to the general principle, that no set of 
observations whatever must remain longer than is indispensably necessary 
_ without reduction to theory; and secondly, they have made the immediate ap- 
_ plication of the mean magnetic values for 1845, that may be furnished by the 
combined British and Russian observatories, the more probable, as it will then 
_ be already preceded by a similar application of the analogous values for 1829. 
_ Besides this, to prove the influence of your resolution on the department of sci- 
ence most directly connected with it, I may remark that a more and more exact 
_ determination of magnetic constants (the Gaussian) is equally indispensable 
at the present moment (and for the same reason), as the obtaining of the con- 
_ stants for planetary orbits was formerly, from the moment in which Kepler’s 
_ and Newton’s discoveries opened a possibility of arriving at them. Whatever 
~ may be the analogies once to be found in magnetism for the secular varia- 
tions and other perturbations of planetary orbits, the entrance into these 
“untouched fields of science cannot fail to be effected by fixing the actual 
values of Gaussian constants. © 
It was under these circumstances that I long ago felt it to be a debt I had 
contracted towards science, that the magnetic elements which I observed 
_ from 1828 to 1830, at about 650 equidistant stations, on a line encircling 
| the globe, between latitudes 67° north and 60° south, conjointly, perhaps, 
with the magnetic elements that had been observed in Europe during the 
Same years, should be fully applied to the development of the now existing 
‘theory. For the undertaking of such a work, however, it was evidently ne- 
_ essary to have more time at my disposal than I have ever enjoyed. M. 
_ Henry Petersen, too, a most industrious and talented young mathematician, 
_ who in 1842 had undertaken and performed at my request a small part of 
| 
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