DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
355 
the radii of the pole-pieces and the core is 12'45 eras. Hence the area of 139° of the 
cylinder of this radios is 768'3 sq. cms., add to this a fringe of a width 0'8 of the 
distance from core to pole-pieces as already found necessary for the other machine, 
and we have 839'5 sep cms. as the value of A 2 . 
4 is 0‘8 cm. 
A 3 is 365 sq. cms. (i.e., the area of two magnet cores). 
4 is 26'0 cms. 
A 5 is taken to be 955 sq. cms., viz., double the smallest section of the pole-piece. 
4 is a very uncertain quantity; it is assumed to be 15 cms. 
The expression already used requires slight modification. Inasmuch as the pole- 
pieces are of cast iron a different function must be used. Different constants for waste 
field must be used for the field, the pole-pieces and the magnet core. We write 
Ai 
J 
4*mc = lj[ f)+ 24 f+kf( T ) + 2 hf 
vA 
A s 
the function f' is taken from Hopkinson, Phil. Trans., vol. 176 (18S5), p. 455, Plate 
52. v 2 , v 3 , and v 5 were determined by experiment as described below, their values are 
m = l'05 
Vo = 1T 8 
v b~ 1*49 
Comparing the curves on Plate 17 with that on Plate 19, the most notable differ¬ 
ence is that in the present case the armature core is more intensely magnetised than 
the magnet cores. No published experiments exist giving the magnetising force 
required to produce the induction here observed in the armature core, amounting to a 
maximum of 20,000 per sq. cm. We might, however, make use of such experiments 
as the present to construct roughly the curve of magnetisation of the material; thus 
we find that with this particular sample of iron a force of 740 per cm. is required to 
produce induction 20,000 per sq. cm. : this conclusion must be regarded as liable to 
considerable uncertainty. 
The observations on the two machines are plotted together, but are distinguished 
from each other as indicated. They are unfortunately less accurate than those of 
Plate 17, and are given here merely as illustrating the method of synthesis. 
Experiments to determine v 2 , v 3 , and v 5 . 
The method was essentially the same as is described on pp. 338 and 339, and was 
only applied to No. 1 machine. Referring to fig. 7 a wire AA was taken four times 
round the middle of one limb of the magnet, a known current was suddenly passed 
round the magnets, the elongation of the reflecting galvanometer was observed, it was 
found to be 214 scale divisions, giving 107 as the induction through the two magnet 
limbs in terms of an arbitrary unit. The coil was moved to the top of the limb as at 
BB—the elongation was reduced to 206 or 103 for the two limbs. We take the 
2 
