Action of a Galvanic Coil on an external small Magnet. 359 



hand. The courses selected for consideration are those indicated 

 by the small magnets on the upper side of the right-hand half 

 of the diagram ; and the longitudinal velocity will be taken to be 

 positive in the direction of issuing, and the transverse velocity 

 positive in the direction from the axis. Hence, putting /l&X 1 and 

 fiY 1 for these velocities respectively, and substituting m l for 

 (G»-Q 2 + 2 2 )-^ and m % for (Qtf + /) 2 + £ 2 )~^ we have by the 

 formulae in art. 15, 



Y i _ qim^ — m^ 



Xj (p + l)m 2 —(p—l)m l 



21 being the length of the coil, and p, q the longitudinal and 

 transverse coordinates of any one of the positions of the centre 

 of the small magnet. If a line drawn in the direction opposite 

 to that of the motion at any position cuts the axis of the coil at 

 an angle of inclination co reckoned always from the negative di- 

 rection from the point of intersection, we shall have tan &>= — ~, 



and co will in all cases be positive, varying from zero for a posi- 

 tion on the transverse axis to 180° for a position on the longitu- 

 dinal axis. 



The calculation of co by means of the formula above gives the 

 theoretical determination of the angle of position of the small 

 magnet, so far as the action of the coil is the same as that of a 

 magnet ; and the observed position is readily determined by means 

 of the values of the longitudinal and transversal forces for a coil 

 without core, given (in p. 491) in the memoir before cited. I 

 have besides calculated the same angle by Ampere's theory, 

 availing myself for that purpose of the results of Mr. Stuart's 

 theoretical calculation of X and Y contained in p. 497. The 

 value of / for all the observations is 6*7 inches, and the values of 

 the coordinates jo and q for the different positions of the small 

 magnet are those subjoined. Both the experimental and the 

 theoretical values of co were calculated to minutes of arc, but it 

 was thought sufficiently accurate, considering the circumstances 

 of the observations, to express them to the nearest tenth of a 

 degree. After these explanations the following statement of the 

 results of the calculations will be intelligible. 



