REPORTS 



ON 



THE STATE OE SCIENCE. 



Ueport OH the Gaussian Constants for the year 1829, or a Theory of 

 Terrestrial Magnetism founded on all available observations. By 

 H, Petersen and A. Erman. 



It was in 1838 that the illustrious C. F. Gauss published the principles of 

 a method which made all the phenomena of terrestrial magnetism as fully 

 calculable as are astronomical phenomena by Newton's theory of gravita- 

 tion. This beautiful accession to natural philosoi^hy may be summed tip as 

 follows: — 



For every point of space, the position of which is given by its distance r from 

 the earth's centre, and by the angles u and X denoting respectively its angular 

 distance from the geographical north pole and its longitude east from Green- 

 wich, there exists a mathematical expression relating to the terrestrial magnetic 

 qualities of this point, and containing only r and trigonometrical functions 

 of u and X, together with numerical values that are the same for the whole 

 extent of space. This expression is called the magnetic potential of the 

 point ; and as to the said numerical values, we give them here, as we did in 

 the Eeport on our computation made during the years 1846 to 1848, the 

 name of the Gaussian Constants. This must be iinderstood as relating to 

 their invariability as to space, but by no means to independence of time. 



For every point on the earth's surface, or above it, up to infinite distance, 

 the magnetic potential has a finite value, and in consequence thereof must be 

 calculable as soon as the Gaussian constants are known. There exists no 

 visible or measurable phenomenon which for every given point agrees with 

 the value of the magnetic potential ; but this remarkable quantity is 

 for every place in explicit connexion with the intensity and the direction 

 of the magnetic force which is exerted there by the causes considered. These 

 two measurable phenomena are therefore given as soon as the potential can 

 be ascertained; and the same is the case with every one of the components 

 which we are wont to form of terrestrial magnetism for the sake of easier 

 observations — as, for instance, with the three rectangular components, which 

 in their turn are equivalent to the horizontal and vertical intensities and to 



1872. B 



