Induced emf in the armature E = P * φ * Z * N / A * 60 volts.
Where Z and A are constant.
N ∝ Eb / φ
N ∝ V – Ia ra / φ.
We can consider that the Ia ra drop is very small and there by in the place of V – Ia ra we can consider only V. If it so then N ∝ V/ φ.
So speed may be varied by varying either applied voltage to the armature and by varying field flux or field strength per pole or total field flux.