860 H. A. Rowland—Diamagnetic Attachment to the Lantern. 
But as the above only applies to equal currents, I have gener- 
alized it in the following. Jn any two magnetic systems whatever, 
similar in all their parts and composed of any number of perma- 
nent or electro-magnets, wires carrying currents, or bodies under 
magnetic induction, the magnetic force at similar points of each will 
be the same when the following conditions are complied with ; 1st. 
the magnetic materials at similar points in the two systems must be 
exactly the same in quality and temper ; 2d, the permanent mag- 
nets must be magnetized to the same degree at similar points of the 
systems ; 3d, the coils of the electro-magnets and other wires or bun- 
dles of wires carrying the current must have similar erternal di- 
mensions in the two systems and must have the product of the current 
by the number of wires passing through similar sections of the two 
systems proportional to the linear dimensions of the systems. 
This will apply to the case we are considering when the 
product of the current by the number of turns of wire varies 
in direct proportion to the size of the apparatus. Hence in 
this case a a will vary inversely as ». Hence we 
see that n will be inversely proportional to the size of the ap- 
paratus: and although we have only proved this for the case 
when x is small, it is easy to see that it is perfectly general. 
The advantage of small diamagnetic apparatus is thus apparent, 
for the smaller we make it the more vibrations the bar will 
make in a given time and the more promptly will the results be 
shown. 
It might be thought that by hanging a very small bar in the 
field of a large magnet, we might obtain just as many vibrations 
as by the use of a small apparatus: but this is not so, for Sir 
Wm. Thomson has shown* that the number of oscillations of a 
from the origin. Developing R? as a function of x and y by 
Taylor's theorem, and noting that as R is symmetrical with re- 
ference to the planes XZ nent YZ, only the even powers of « and 
_ * Reprint of Papers, Art. 670. Remarques sur les oscillations d’aiguilles non 
t Hi , 
