227 



A considerable portion of the iron railing, now erected on 

 the wall in Nassau-street, had been, previously to its erection, 

 and during the absence of the writer in the summer, laid down 

 in a horizontal position in the College Garden, at the southern 

 side of the Observatory. The several pieces of which the rail- 

 ing is composed (each fourteen feet in length, and containing 

 twenty-eight bars) were found placed in a continuous line pa- 

 rallel to the south walk of the garden, and forming an angle 

 of 59° with the magnetic meridian. This line extended 7rom 

 a point nearly opposite the Observatory to a distance of 255 

 feet, and was distant from the declinometer magnet, at the 

 nearest point, by 153 feet. It would, of course, have been 

 impracticable to remove this great mass of iron, and to replace 

 it rapidly, or for many alternations. Instead of this, the effect 

 of a single piece of the railing was observed at a nearer dis- 

 tance, from which, and from the known laws of the mutual 

 action of magnets, the total effect was deduced by integra- 

 tion. 



Let a denote the perpendicular from the centre of the 

 moveable magnet upon the line of the bars ; and let a be the 

 angle which that perpendicular makes with the magnetic me- 

 ridian. Then, in the expression already given^for the mo- 

 ment of the force exerted by a fixed upon a moveable magnet, 

 (p + <j>' = a, and the moment of the force exerted by a single 

 bar is 



2^{sina + 3sin(a-20)j, 



m being the magnetic moment of the bar, and m' that of 

 the suspended magnet. The moment of the force exerted 

 by an element of the railing whose length is dx, is obtained 

 by multiplying this by ndx, n being the number of bars in 

 the unit of length. This is equilibrated by the earth's mag- 

 netic force, whose moment is 



