DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
353 
Referring to Table II. it appears that the efficiency approaches a maximum when 
the current, passing externally between the two machines, is about 400 amperes. Let 
C be the current in the armature, p its resistance, W the power absorbed in all parts 
of the machine other than the armature, then, if the speed is constant, the efficiency 
is approximately 
EC-W-CV 
EC 
where E is the electromotive force. 
This is a 
maximum when —+C p is a minimum, which occurs when W = C 2 p ; when the loss 
in the armature is equal to the sum of all other losses. For the machines under 
consideration the experimental results verify this deduction. But in actual practice 
the rate of generation of heat in the armature conductors, when a current of 400 
amperes was passed for a long period, would be so great as to trench upon the margin 
of safety desirable in such machines. Of the total space, however, available for the 
disposition of the conductors only about one-fourth part is actually occupied by 
copper, the remainder being taken up with insulation, and the interstices left by the 
round wire. If the space occupied by the copper could be increased to three-fourths 
of the total space available, while the cooling surface remained the same, the current 
could be increased 75 per cent, and the efficiency increased 1*3 per cent, approxi¬ 
mately, as all losses other than that in the armature-wires woidd not be materially 
altered. 
The loss in the magnets is also susceptible of reduction. It has already been shown 
that for a given configuration of the magnetic circuit and a given electromotive force 
the section of the wire of the magnet coils is determinate. The length is, however, 
arbitrary, since within limits the number of ampere convolutions is independent of the 
length. An increase in the length will cause a proportionate diminution in the power 
absorbed in the magnet coils. If the surface of the magnets is sufficient to dissipate 
all the heat generated, then the length of wire is properly determined by Sir William 
Thomson’s rule that the cost of the energy absorbed must be equal to the continuing 
cost of the conductor. 
Appendix. 
(Added Aug. 17.) 
Since the reading of the present communication experiments have been tried on 
machines having armatures wound on the plan of Gramme and with differently 
arranged magnets, the experiments were carried out in a closely similar manner to 
that already described. 
Description of Machines. 
The construction of these machines is shown in Plate 20, in which fig. 1 shows an 
elevation, fig. 2 a section through the magnets, fig. 3 a longitudinal section of the 
2 z 
MDCCCLXXXVI, 
