GAUSS AND WEBER ON TERRESTRIAL. MAGNETISM. 'Jl 



needle produces a force or moment of rotation when the needle is 

 not in the magnetic meridian : this moment of rotation is greater, 

 the more the needle deviates from the magnetic meridian ; and is 

 greatest when the needle is at right angles to that meridian. This 

 maximum of effect is always to be understood when the moment 

 of rotation simply is spoken of; it may be represented by a given 

 weight acting on a lever of given length, and consequently by a 

 number, if the weights and lengths are expressed in numbers, 

 according to arbitrary units. Now this moment of rotation 

 and the time of vibration are very simply connected, by means 

 of an intermediate quantity, dependent on the figure and 

 weight of the needle, called its moment of inertia, and which 

 may be calculated according to known rules. If the needle is 

 not a perfectly regular body, or if it carries any appendage 

 when in vibration, other means are required for the determina- 

 tion of its moment of inertia, the description of which would 

 lead us too far ; suffice it to say, that it is always possible. The 

 moment of inertia then being known, the moment of rotation 

 produced by the earth's magnetism on the magnetism of the 

 needle, may be concluded from the observed time of the vibra- 

 tion of the needle." 



If we designate by the letter C, the moment of inertia, after 

 it has been multiplied by tt-, i. e., 9'8G96 . . . and divided by 

 twice the height of the fall of a heavy body in the unit of time, 

 we may conclude from C, and from the observed time of vibra- 

 tion t, the greatest moment of rotation caused by the earth ; it is 



_ C 



~ t^' 



" It is possible to determine the moment of rotation by direct 

 experiment, without observing the time of vibration. An appa- 

 ratus, expressly adapted to this purpose, has been recently placed 

 in the Gottingen Astronomical Observatory, and is susceptible 

 of great accuracy ; but for the present purpose it is unnecessary 

 to dwell on this point. 



" The moment of rotation, produced by the earth's mag- 

 netism on a given needle, offers a new way of measuring the 

 force of the earth's magnetism, or, to speak more accurately, a 

 new form of the previous mode of measurement, over which it 

 has this advantage, that one portion of the individuality of the 



