OF RADIANT HEAT THROUGH DIFFERENT BODIES. 13 
modifications which the active part of this force is made to undergo by 
the different inclination of the needles to the direction of the currents ; 
and these modifications are quite analogous to those which take place 
in the portion of gravity that acts on the pendulum in different ares of 
oscillation. 
Now the force necessary to make the pendulum vibrate from one in- 
clination to the other, is proportional to the difference of the cosines of 
the angles which the two directions form with the vertical. Whence it 
is clear that it remains sensibly constant in the ares that are not far re- 
moved from the line of rest. The same effect must therefore be pro- 
duced in the galvanometer also ; or, in other words, the force required 
in this apparatus to increase the deviation of the index by a degree will 
be constant near the line of zero, as is shown by experiment. 
From what we have just said it will be easy to see that the relation 
between the degrees of the galvanometer and the forces which cause 
the deviations of the needles, must depend on the sensibility of the 
astatic system and the distribution of the wire on the frame*. It will 
vary, therefore, according to the construction of the instrument, but 
may be always determined by the method we have mentioned. 
Experiment having shown that in my galvanometer the proportion of 
* Tn order to understand this clearly, it is sufficient to suppose a galvanome- 
ter in which the circumvolutions of the wire are more numerous towards the 
extremities than towards the central part. It is evident that under the action 
of such a system the forces which produce the deviations, instead of increasing 
or being merely proportional in the arcs near zero, must decrease as we approach 
the extremities of the frame, in order to increase afterwards when the index has 
passed these positions. 
As to the influence of the sensibility of the astatic system, we shall be able to 
form a tolerably exact idea of it, if we imagine a galvanometer with the two 
needles possessing very different degrees of magnetism. Then the terrestrial 
globe will very powerfully affect both combined; and, in order to produce the 
least deviations, electric currents must be employed possessing much greater 
force than those required to produce small deviations in a more perfect astatic 
system. In the positions near zero, the electro-magnetic action produced by 
the most distant currents, that is, the action of the currents situated at the ex- 
tremities of the frame, will possess an energy sufficient at least to overcome the 
resistance arising from the twisting of the suspension thread and the inertia of 
the astatic system. It will therefore always contribute to move the oscillating 
mass. Hence it is evident that if the needles are displaced in the slightest de- 
gree, the consequence will be a loss in the moving force; for if the system ap- 
proaches a certain arc at a certain extremity, it recedes at the same time double 
the distance from the opposite extremity. Now we have already seen that, in 
delicate galvanometers, the moving force is constant when the angles are small ; 
and we have assigned the cause of this fact upon the incontestible principle that, 
in small deviations of the instrument, the action of the currents situated towards 
the extremities of the frame must be disregarded, not indeed because they have 
no value, but because it becomes, in consequence of its distance, extremely 
feeble, and incapable of surmounting the obstacles opposed to it by the torsion 
of the silk thread and the inertia of the needles. 
