FORCES ACTING IN MAGNETIC CIRCUITS. 209 
square bars. In order to utilise the results I assumed that the 
field would be distributed very much asif the bar were round and 
of a diameter equal to the mean of the diameters of the inscribed 
and circumscribed circles. 
To use the curve it is only necessary to express the length of 
the air gap as a fraction of the diameter of the pole face, and 
refer to the table to find the proper factor to multiply the traction 
when the bars are in contact at the proposed induction. 
14. In general, itis more convenient to take the magnetomotive 
force as given, and in this case the induction cannot be estimated 
without a knowledge of the reluctance of the circuit. Now 
methods of building up the characteristic curve of the magnet have 
been given when the air gaps are narrow, by Drs. J. and E. 
Hopkinson and others, but I thought that I might possibly be 
able to extend the method of similar systems, so as to include 
air gap reluctances. In similar induction systems the reluctances 
of the gaps should be roughly inversely as the linear dimensions. 
I examined three sets of bars to see how near such an approxima- 
tion really was, but it will be noticed that the results would not 
reduce so as to give a single curve by any such simple process. 
The curves are therefore kept separate ; they cover bars of from 
about one to three cm. in diameter. The induction was in these 
cases correctly measured at the centre of the bars. It was neces- 
sary to use the Ampere Balances to get a sufficiently accurate 
knowledge of the magnetising currents. The results are contained 
in tables 14—19, and are also plotted for the mean of all induc- 
tions. The reluctance of the iron and air circuits was measured 
before the bars were cut and plotted against inductions. It was 
assumed that, using bars of the length employed, the air reluctance 
(other than that at the gap) would not be materially changed by 
pushing the bars up to two diameters apart. The proper reluc- 
tance for the iron and air circuit was taken from the curve in 
finding the reluctance of the air gap. 
Except with the largest bar there is no definite indication of 
the reluctance depending on the induction density. In this case 
N—July 5, 1993, 
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