FORCES ACTING IN MAGNETIC CIRCUITS. 207 
their resultant, and by the theory this is equal to O P, so that OQ 
isthe vector representing the pressures. A force represented by 
O M equal and parallel to P Q is therefore the resultant force, 
and clearly in this case is a repulsion whose magnitude along 
the normal produced is 
@LDy 4/2: Cos (Fee 0) 
an expression which gives no normal component at all when 
6=7/4. The force is therefore an attraction or repulsion accord- 
ing as Ois less or greater than 7/4, and isashear at this point. I 
tried to observe this, but could not get the lines to leave the 
surface at the exact angle. However the above way of looking 
at the matter is convenient when filings are used to trace the 
direction of the induction. This expression has been pointed out 
to me by Mr. Pollock as being identical with that given by Max- 
well in Section 643 for the special reduced case here considered. 
It is now evident why it was that Bosanquet got results ditfer- 
ing from those calculated from the formula for normal inductions; 
because as filings show, a very small gap is sufficient to produce a 
marked spreading of the field. 
12. By observing the distribution of filings about different air 
gaps it appeared probable to me that the following proposition 
might be true as referring to bars of different diameters. ‘ With 
similar pole faces and the same permeability 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, 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. 
13. The observations made on this subject are sufticiently 
detailed in the tables, (Nos. 1 to 13) and the results will be under- 
stood by looking at the curve. The tractions were measured by 
