338 
DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
when the magnetising current is more than 5'62 amperes its value should be a little 
greater. 
The function f(a) is taken from Hopkinson, Phil. Trans., vol. 176 (1885), p. 455 ; 
the wrought iron there referred to was not procured at the same time as, and its 
properties may differ to a certain extent from, the wrought iron of these magnets. 
The curves now explain themselves, the abscissae in each case represent the line 
integral of magnetising force in the part of the magnetic circuit referred to, the 
ordinates, the number of lines of induction which also pass through the armature. 
The results of the actual observations on the machine are indicated, those when the 
magnetising force is increasing +, when it is decreasing ©. The measurements of the 
currents in the magnets which were separately excited, and of the potential difference 
between the brushes, the circuit being open, were made with Sir W. Thomson’s 
graded galvanometers, standardised at the time of use. The irregularities of the 
observations are probably due to the variation of speed, the engine being not quite 
perfectly governed. The second construction exhibits quite as close an agreement 
between observation and calculation as could be expected; the deviation at high 
magnetising forces is probably due to three causes, increase in the value of v when 
the core of the armature is partially saturated, uncertainty as to the area A 3 , 
difference in the quality of the iron. It is interesting to see how clearly theory 
predicts the difference between the ascending and descending curves of a dynamo. 
Consideration of the diagram proves that this machine is nearly perfect in its 
magnetic proportions. The core might be diminished by increasing the hole through 
it to a small, but very small, extent without detriment. Any reduction of area of 
magnets would be injurious, they might, indeed, be slightly increased with advantage. 
An increase in the length of the magnets would be very distinctly detrimental. 
Again, little advantage results from increasing the magnetising force beyond the 
point at which the permeability of the iron of the magnets begins to rapidly diminish. 
For iron of the same quality as that of the machine under consideration, a magnetising 
force of 2‘6Xl0 3 or 28'4 per centimetre is suitable. To get the same induction in 
other parts of the circuit, the diagram shows that for the air space a magnetising force 
of 21 X 10 3 is required, for the pole-pieces O'J X 10 3 , for the armature 0'2x 10 3 , for the 
yoke O'GXIO 3 , making a total force required of 24‘5X10 3 . Any alteration in the 
length or the area of any portion of the magnetic circuit entails a corresponding 
alteration in the magnetising forces required for that portion, at once deducible from 
the diagram. Similar machines must have the magnetising forces proportional to the 
linear dimensions, and, consequently, if the electromotive force of the machines is the 
same, the diameter of the wire of the magnet coils must be proportional to the linear 
dimensions. If the lengths of the several portions of the magnetic circuit remain the 
same, but the areas are similarly altered, the section of the wire must be altered in 
proportion to the alteration in the periphery of the section. 
