IL ELECTRICAL EHEOMETRY. 25 



slightest motion made with the circle of the currents in order to cause it to deviate 

 more, very often produces a comi^lete fall of the needle to within a very few de- 

 grees above zero, and thus it is very difficult to ascertain the maximum angles with 

 sufficient accuracy. Besides, all those who know how difficult it is to settle the 

 current exactly in the plane of the needle (even in the most simple case when it 

 is in the magnetic meridian), will be persuaded that there is great difficulty — 

 without a very excellent instrument and particular care — in keeping the currents 

 always exactly in the plane of the needle. Practice, however, and good construc- 

 tion, may obviate considerably the errors due to those causes, and a good instrument 

 cannot be too highly appreciated when it spares all the trouble of calculation. 



Formula (5) combined with (7) et seq. give the angle at which the needle will 

 rest after it has fallen from its maximum of deviation, since, dividing one by the 

 other, T and h being the same in both numerator and denominator, we have 

 Sin. D _ f{d)cos. jD — d') 

 Ik^' ~~ " / (0) ' 



from which, measuring I), we can calculate what ought to be the angle d^ which 

 could not be accurately observed. 



As from the formula we have deduced the explanation of this last case, so we 

 could explain a similar phenomenon which takes place when the plane of the cur- 

 rent is moved parallel to itself towards one of the sides of the needle ; we might 

 easily perceive that the deviation would increase until a certain maximum, after 

 which the needle would fall all at once and deviate a very few degrees. To deter- 

 mine this limit, it is only necessary to ascertain the value of d when the plane of 

 the circle is supposed to pass between the jaoles, and afterwards when it does not 

 do so, the value of Zq being the same. 



§ 7. Application of the Formula to our Experiments. 



The problem of Mr. Plana having for its object to determine the intensity of 

 action of several circular currents on the internal circumference of a globe, around 

 which they are disposed like so many meridians, and particularly on the various 

 points of its polar axis, it is evident that this is only a more complex case of our 

 formulae ; in these, the angle d^ varies within certain limits, and the sum of all the 

 actions is to be considered. This aggregate action is regarded by Mr. Plana as 

 exerted on a single element of a current, the verification of which by experiment 

 is impossible, and therefore a magnetic needle was substituted. This, however, is 

 obnoxious to a difiiculty, because, although it is true, as Ampere proves,^ that the 

 action of the pole of a solenoid is, for different distances, in the same constant ratio 

 with that of a simple element ; yet, notwithstanding this, by using a needle, the pro- 

 blem is completely changed, by the introduction of two centres of action, acting at a 

 certain distance from one another. This case, however, may coincide with that of 



• Theorie, page 104. 



