of the Compound Dynamo. 463 
Let the values of the resistances be as indicated in the 
figure. Let the total electromotive force be H, that between 
Y and A eg, and that between A and X e,. The currents in 
7, and p; may be represented by c, and y,, and a similar nota- 
tion used for the other conductors. 
Finally, let the whole resistance be R, let the resistances of 
the multiple arcs between Y A and A X be R‘; and R’, respec- 
tively, and let c’ be the total current in each of these multiple 
ares. 
The current is to be conceived as flowing out of the arma- 
ture at Y, passing on to the three conductors pz, p;, and 7, 
and returning at X. 
All the existing forms of dynamo can be represented by 
leaving out some of the conductors shown in the above sym- 
metrical figure. Their properties are perhaps more easily 
recognized by regarding them as particular cases of a more 
highly generalized machine. The notation used has also 
another advantage. The shunt in the Compound Dynamo 
may be used in one of two ways—viz. as a shunt upon the 
armature alone, or as a shunt upon the armature and series- 
coils. It is usual to represent its resistance by a symbol which 
indicates only that it is a shunt, without showing in which of 
these ways it is used. If, however, it is agreed that 7, shall 
always represent the external resistance, 7, being in any prac- 
tical case infinite, then p, always represents the series-coils, 
and pq or pz the shunt-coil according as it is applied in the 
first or second of the methods above referred to. 
If we adopt Frolich’s equation we may write 
ee MM (so% + Sa¥at S171 + SoV2) : 
1 +0(so7¥9 + SaVa-F 8371 + S22) 
where n represents the number of revolutions ; 
M is a constant depending on the machine ; 
Say S;, and s, are the number of turns made by the 
magnetizing spirals pa, pi, and po ; 
and o isa small constant depending on the gradual weak- 
ening of the magnetizing effects of the currents as 
the iron approaches saturation. 
The product syy, represents the number of ampere-turns by 
which the initial magnetic field is, or may be supposed to be, 
produced. If, isan independent current, this quantity may 
be large. If it is only a fictitious current which is regarded 
as the cause of the permanent magnetism, s,y, is small. If 
the product of syy, and of o may be neglected, and if Ms,y,=, 
- we may write 
mM (sa¥at 8171 + S22) , 
L+o(sayat sy + 822)’ 
212 
H=nk+ 
