80 Mr. R. H. M. Bosanquet on the Magnetic 
when we remember that in the bar the lines of force are 
crowded closely only at the equatorial section. 
The formula by which Rowland represented his results was 
of the type 
, phen Steere, 
in which A, C, D, and a are constants depending upon the 
kind and quality of the metal used. This type of formula is 
unmanageable; and it seemed to me necessary to attempt a 
more direct expression of the facts. 
Rowland’s formula offers the suggestion that we may regard 
values of « which occur in these experiments as corresponding 
to the first half of a periodic change, the whole of which would 
be completed for a value of 9% corresponding to about twice 
the saturation-value. This being so, it is theoretically pos- 
sible, according to Fourier’s theorem, to express any set of 
the experimental values of uw by a series of sines and cosines 
of an angle proportional to the induction and of the multiples 
of that angle; and the only difficulty is to find the coefficients 
of the different terms of the series. 
Unfortunately the distribution of the values obtained does 
not admit of the application of the simplest form of harmonic 
analysis; so that the accurate determination of the coefficients 
is attended with a good deal of difficulty; and after trial of 
various methods of solution of equations, including an extended 
application of the method of least squares, it was found that 
a process of trial and error was capable of giving better results 
than could be obtained in any other way. 
The representations thus obtained are not in all cases very 
close, but they are quite sufficient to show, by comparison of 
the different rings of the same iron, the uselessness of attempt- 
ing to define minutely the properties of a given kind of iron. 
For the analysis of the different sets these are as valuable, on 
account of the clearness of the expressions, as the representa- 
tions founded on my subsequent theory, which are as close or 
closer. 
As to the size of the rings. There are five rings of crown 
iron, H, F, G, H,K. Of these, E, H have approximately the 
same mean diameter; IF, G, IK have mean diameters rather 
more than twice as great. HH, K have about the same bar- 
thickness, H, F bar-thickness nearly twice as great, and G a 
bar-thickness between three and four times as great. But when 
we examine the expressions for u, we fail to find any syste- 
matic differences which appear to correspond with these dif- 
ferences in the dimensions. So that, so far as this small 
number of experiments goes, the fundamental suppositions are 
