196 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Drss. VI. 



observing the earth's magnetism and its changes. 

 The instruments devised by them were a De- 

 clination Instrument and a Bifilar Magnetometer. 

 The first is a heavy magnetized bar some feet in 

 length, suspended by a bundle of parallel silk fibres. 

 It is suffered to place itself in the magnetic meridian, 

 and the small displacements due to hourly, annual, 

 or irregular fluctuation, are ascertained by viewing 

 with a telescope the reflection of a fixed scale of equal 

 parts placed at some distance in a small mirror 

 which is attached to the magnetic bar. The bifilar 

 instrument is for ascertaining changes of intensity in 

 the earth's magnetism. It is a bar like the last, sus- 

 pended by two parallel threads or wires. By twist- 

 ing round the points of double suspension, the bar 

 is forced by torsion into a position at right angles 

 to the magnetic meridian, where it is held in 

 equilibrium by the force of the earth's magnetism, 

 and that of the torsion of the wires. Supposing the 

 latter force to be constant, if the former vary, the 

 bar will change its position, which is observed by the 

 mirror and telescope as before. 



(900.) To these instruments, Professor Lloyd, of Dublin, 

 added another for measuring the vertical component 

 of the magnetic intensity. It is a magnet suspended 

 horizontally on knife-edges like those of a balance. 

 Its deflection from the horizontal line indicates va- 

 riations in the vertical portion of the earth's mag- 

 netism. 



(901.) The dip is determined in the usual way ; the va- 

 riations of dip, however, are ascertained by comparing 

 the variations of horizontal and vertical intensity. 



(902.) Gauss did not content himself with suggesting 

 The Got- new forms of apparatus, and recommending them to 



tmgen others. With the active assistance of M. Weber, he 

 magnetical , . , _ .. . . , 



observa- erected, in 1833, at Gottingen, a magnetic observa- 

 tions, tory free from iron (as M. de Humboldt and Arago 

 had already done on a smaller scale), where he 

 watched with patience the incessant movements of 

 the newly-constructed needles or bars. It was from 

 the same observatory that he sent telegraphic 

 signals to the neighbouring town, thus showing the 

 practicability of an electro-magnetic telegraph (856). 

 Pie farther instituted an association (magnetischer 

 Verein), composed at first almost entirely of Ger- 

 mans, whose contimious observations on fixed Term- 

 days extended from Holland to Sicily. 1 The marvel- 

 lous coincidence of the occurrence of even the minute 

 irregularities of the earth's magnetism was thus 

 more fully established. 



(903.) r^e Mathematical Theory of Terrestrial Magnetism 

 of Gauss 2 is intended to replace all arbitrary assump- 



tions whatever as to the distribution of magnetism Gauss's 

 in or over the earth. It proposes to express by an mathema- 

 empirical law, involving as little of hypothesis as ofterre 

 possible, the direction of the freely suspended mag- trial mag- 

 netic needle and its directive force at any point of the netism. 

 earth's surface, the data being of course derived from 

 a limited number of observations. 



The theoretical assumption with which Gauss ( 904 

 starts is merely this, that the elementary force of 

 magnetism varies inversely as the square of the dis- 

 tance, and that it is distributed over the matter of 

 the terrestrial globe in a way or according to a law 

 presumed to be entirely unknown. 



Following up the methods employed by Laplace (905.) 

 and others, for representing the attractions of a Theorems 

 sphere or spheroid, he proposes to discover the form 

 of that remarkable function (sometimes called the 

 Potential) 3 whose differential coefficients express the 

 resolved components of the total magnetic force. 

 This quantity V, and also its differential coefficients 

 (representing the attractions in given directions), 

 may always be expressed by a series with indetermi- 

 nate coefficients, which is known to converge more 

 or less rapidly ; and since the component forces 

 or attractions are given by observation, the coeffi- 

 cients of the terms of the series representing them 

 may be deduced from a comparison with the data. 

 The convergency is greatest if the magnetic matter 

 be disposed towards the centre of the sphere, least if 

 it reside near its surface. 



Retaining quantities of the fourth order, there are (906.) 

 twenty-four constants, which, rigorously speaking, 

 may be deduced from complete observations of the 

 three magnetic elements (888) at only eight stations 

 anywhere situated on the surface of the globe. With 

 great patience and skill, Gauss collected as many avail- 

 able data as possible for determining these constants 

 with accuracy, and he thence deduced by calculation 

 the values of V, those of the declination, horizontal 

 and vertical force, and that of the dip for all points 

 of the globe. The beautiful charts which he caused 

 to be constructed show a remarkable general ac- 

 cordance with the complex facts of magnetism as 

 then known. But in many instances more accurate 

 data have since been obtained applicable to the im- 

 provement of the empirical theory. Perhaps the 

 most surprising fact which Gauss considers to be 

 demonstrated is this, that the average amount of 

 magnetic force associated with every cubic yard of 

 the earth's volume (supposing the distribution uni- 

 form) is equal to that contained in six saturated steel 

 bars each a pound in weight. 



1 The volumes of their publications, from 1836 to 1839, contain much interesting information on the history of this subject. 

 8 Allgemeine Theorie des Erdmagnetismus. Leipzig, 1839. 



3 



See Art. 877. This function V represents the integral f , were dm is the attracting or repelling element, and f its 



distance from the point acted on. Gauss represents in his charts the values of the function V at different points of the earth's 

 surface. The lines of equal values of V are everywhere perpendicular to the direction of the needle, and the horizontal inten- 

 sity is inversely as the distance between two adjacent lines. 



