Prof. E. Bouty's Studies on Magnetism. 87 



that tana — tana' is extremely small, we have, excepting quan- 

 tities of the second order : — 



, T tan a+ tan a' /M . 



*=M ^ ( 5 ) 



It will therefore be sufficient to take the mean of the two obser- 

 vations to correct the result of the imperfection of the apparatus*. 



Again, in the preceding we have supposed that the magnetic 

 meridian is invariable, which is not rigorously true ; besides, our 

 apparatus realizes a veritable compass of variations ; consequently 

 the error resulting from the variations of the declination is an 

 appreciable quantity in the conditions in which we are placed. 



Except the case of abrupt and irregular variations, this cause 

 of error will be eliminated by making a third measurement after 

 restoring the needle to its first position, turning it end for end. 

 If the observations have been made at nearly equal intervals, the 

 mean of the first and third measurements may be taken, and the 

 mean of this and measurement 2 will not be sensibly affected by 

 the variation of the declination. In all cases the equality of 

 Nos. 1 and 3 will be a guarantee of the accuracy of the mea- 

 surement. 



For the purpose of making an observation, the oscillations of 

 the apparatus are first eased by hand, in order to abridge the 

 duration of an experiment. Besides, as soon as the amplitude 

 of the oscillations is sufficiently small, the divisions n Y and n q 

 of the scale, corresponding to the commencement and the end of 

 an oscillation, are noted, and the division n 3 , corresponding to 



the end of the following oscillation. The mean, N = — — , 



is taken several times ; and thus the position of equilibrium is 

 determined with great exactness. 



The number N also has to be corrected when the deviation is 

 rather considerable, in such a manner that the arc cannot be con- 

 founded with its tangent. To effect the reduction a Table is 

 employed, giving the values of tana when tan 2a is known f. 

 The distance of the scale from the mirror being known approxi- 

 mately, it is easy to draw up a Table giving the reduced values 



* The two readings n and n', corresponding to the deviations u and &', 

 will differ very little from one another, if the scale be exactly perpendicular 

 to the optic axis of the telescope. This condition will be realized by ro- 

 tating the scale, in a horizontal plane, about its centre until the two read- 

 ings n and n', obtained with one and the same needle direct and reversed, 

 differ the least possible one from the other. 



t See a Table of this sort in Wiedemann's Galvanismus, vol. ii. p. 207 

 (2nd edition). 



