﻿of finding the Forces acting in Magnetic Circuits", 99 



results show that when the non-magnetic field is of sensible 



dimensions, the differences in the permeability of the samples 

 examined do not lead to any very abnormal results. The 

 curve is drawn by reduction for a bar one centimetre in 

 diameter ; and the air-gaps, which must be expressed in 

 diameters, appear therefore in centimetres. The ordinate* 

 give the values of the tractions at corresponding points in 

 terms of the calculated tractions when the surfaces are in 

 contact. 



One set of observations refers to square bars. In order to. 

 utilize the results, I assumed that the field would be distributed 

 very much as if the bar were round and of a diameter equal 

 to (he mean of the diameters of the inscribed and circum- 

 scribed 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 with the bars in contact at the proposed 

 induction. 



It will be seen that the factor is practically the same for all 

 inductions — hence one curve only is given. 



§ 16. In general it is more convenient to take the magneto- 

 motive 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 at constant induction-density, the reluc- 

 tances of the gaps should be, roughly, inversely as the linear 

 dimensions. I examined three sets of bars to see how near 

 such an approximation 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 centim. 

 in diameter. The induction was in these cases correctly 

 measured at the centres of the bars. It was necessary to use 

 the ampere-balances to get a sufficiently accurate knowledge 

 of the magnetizing currents. The results are contained in 

 Tables XIV. to XVI., and are also plotted for the mean of 

 all inductions. The reluctance of the iron and air circuits 

 was measured before the bars were cut and plotted against 

 inductions. It was assumed that by using bars of the length 

 employed, the air reluctance (other than that at the gap) 

 would not be materially changed bv pushing the bars up to 



H2 



