MAGNET STEELS AND PERMANENT MAGNETS 391 



It was to be expected, of course, that the values of Brrm would ap- 

 proach Br as a limit for high values of length of bar, since the end effect 

 diminishes as the length increases and the condition of an infinitely 

 long bar or a closed ring is simulated. The functional relationship 

 which the quantity LV//,.//)\'i^r bears to the ration Brem/Br is not 

 known. A fairly good fit of the observed data is given by the ex- 

 pressions: 



q1.5 



r = YJc q = to q = 1.25 and 



0.8 

 ff2.75 



r = e '"■"' q = 1.25 to g = oo 



in which r = BremjBr and q = L^HcjD^Br, but aside from the direct 

 proportionality of Brem and Br, the equations appear to have little 

 meaning. However, they do indicate that for a given dimension ratio, 

 there is a practical upper limit to He, beyond which very large increases 

 in lie are necessary to produce small increases in the ratio of Brem 

 to Br. Considerable interest attaches to the fact that the dimension 

 ratio LjD and \Hel^Br are of equal weight in affecting the remanence 

 of a magnet. It is also worth noting that the value of Brem is inde- 

 pendent of the contour of the cross-sectional area. It is possible that 

 this would not hold for dimension ratios less than one, but it does 

 appear to hold for dimension ratios of practical importance. As 

 shown in Fig. 5, a line drawn through the origin and tangent to the 

 dotted curve of that figure has its pomt of tangency at values of 

 Brem/Br aud L^HdD^Br of approximately 0.65 and 1.25 respectively. 

 It will be shown later that this is the point of maximum efficiency, 

 i.e., the point at which are obtained the highest values of Brem or 

 external magnetic energy per unit volume of steel. 



It follows, if this is true, that magnets should be designed so that 

 L^HelD^Br = 1.25, and with this as a basis, the nomogram of Fig. 7 

 was laid out. The use of this chart to design a magnet for maximum 

 efficiency, is illustrated by the dotted lines of the figure. In the case 

 shown a total flux in the magnet of 3,000 maxwells is desired, and a 

 steel with a Br of 10,000 gauss and a coercive force of 54 oersteds is 

 assumed. The correct values of A and L are found to be 0.461 

 cm. 2 and 13 cm., respectively, and the dimension ratio is 17. 



It should be borne in mind throughout this discussion that Figs. 4, 

 5, 6 and 7 apply directly only to straight bar magnets. Formed 

 magnets with short air-gaps with or without pole pieces, will have 

 higher remanence values than are shown by the curve of Fig. 6. This 



