  The cosine law of field enhancement factor variation was recently derived for
a hemi-ellipsoidal emitter and numerically established for other smooth emitter
shapes (Biswas et al, Ultramicroscopy, 185, 1 (2018)). An analytical derivation
is provided here for general smooth vertical emitter shapes aligned in the
direction of the asymptotic electrostatic field. The law is found to hold in
the neighbourhood of the emitter apex from where field emisson pre-dominantly
occurs.
