﻿98 Prof. R. Threlfall on an Approximate Method 



diameters : — " With similar pole-faces and the same perme- 

 ability and induction-density, the induction (or filing) diagrams 

 are similar when the length of the air-gap is the same fraction 

 of a standard dimension of the pole- faces." 



If this be true, it follows as a consequence that with 

 similar air-gaps at similar induction-densities, the traction is 

 the same fraction of the traction with the poles in contact, 

 whatever be the actual dimensions of the poles. 



The greater part of the experimental work I have to offer 

 refers to this point, for, if established, we clearly have a method 

 which will enormously facilitate the calculation of magnetic 

 forces. 



§ 15. The observations made on this subject are sufficiently 

 detailed in the Tables I. to XIII., and the results will be under- 

 stood by looking at the curve. 



The tractions were measured by spring balances as before, 

 measured pieces of brass being inserted between the pole-faces. 

 Jn a series of observations the induction was kept constant by 

 varying the magnetomotive force. 



The observations were taken just as in the previous case. 

 A little care is necessary in defining what is meant by the 

 total induction. If the bars are long and thin, then of course 

 the solenoidal condition is fulfilled pretty closely, and there 

 is no ambiguity ; but with large air or brass gaps — say, 

 amounting to two diameters of the bars — the lines begin to 

 leave the iron just in front of the middle point of each bar 

 (at all events when the bars are about 50 diameters long). 

 The " total induction " therefore has no very exact meaning 

 with respect to the iron, unless it be specified where it is to 

 be measured. 



At the time the experiments were made, I did not (as I 

 now consider) sufficiently attend to this point, though I used 

 a testing-coil of about four times the diameters of the bars, 

 and kept the coil just to one side of the gap when the latter 

 was large. It is probable, therefore, that I have considerably 

 overestimated the tractions with the larger air-gaps, for the 

 induction must have been greater than I took it to be. I have 

 decided not to re-investigate this point, for the curve is of use 

 in giving approximate ideas of tractions only; and no one, after 

 looking at it, would design a mechanism with air-gaps as long 

 as those which are probably inaccurate. I have made a little 

 allowance for this (most unscientifically of course) in drawing 

 the curve. In fact my suspicions were first aroused by 

 examining the part of the curve corresponding to the larger 

 air-gaps. 



It will be seen that I examined a good many cases, and the 



