108 Mr. J. A. Toinkins on the 
even if there were no other objections. Hence it becomes 
necessary to examine systems with more than one ring. 
§ 29. The effect of the presence of other rings besides the 
one considered is twofold : — (1) Each ring contributes a term 
to the resultant specific moment of the system, so that the 
second terms in (36) and (38) must be replaced by sums of 
terms, one for each ring. (2) Each ring modifies the con- 
trolling field of every other ring, partly on account of its 
own steadv motion, partly on account of its disturbance ; the 
P 
result is that the quantities T , S and R in equations (21) 
and (25) are altered. In particular T , which is zero in 
our models, becomes negative, and the rings become linked 
together. In consequence the total moment due to all the 
rings is by no means the sum of the moments they "would 
contribute if independent of each other. AVben the linking 
is very loose the total moment is paramagnetic, but less than 
the sum of the separate moments, possibly less than that of a 
single ring ; so that it may Aery well happen that the resulting 
moment of the system of sphere and rings is negative for 
certain arrangements of rings. The problem is, however, too 
complicated to be pursued further here, but it does suggest 
that magnetic properties are functions of the structure of the 
atom, depending on the number and arrangement of its 
electrons, just as directly as do the atomic weight and atomic 
volume. 
/ 
XIII. Note on the Focometry of a Concave Lens. 
By J. A. Tomkins, A.R.C.Sc. (Lond.)*. 
IX a recent number of the Philosophical Magazine f 
Prof. Anderson described a simple method for the de- 
termination of the focal length of a concave lens in which/ 
is calculated from observed values of u and v. 
The following methods, in which the focal length of a 
concave lens is measured directly, occurred to the writer 
after reading Prof. Anderson's article. They correspond to 
two well-known methods which are employed in the case of a 
convex lens. They do not appear, however, to have been 
previously described. 
I. Light from the cross-wires C (fig. 1) of an optical bench 
is brought to a focus at F by means of a convex lens L 1# The 
concave lens L is then placed in the position shown and 
* Communicated by the Author. 
t Tliil, Mag. June 1906. 
