This section is from the book "The Science And Art Of Phrase-Making", by David Wolfe Brown. Also available from Amazon: The science and art of phrase-making.
182. In each of the following phrases, on is to be made upward:
on all
on all sides
on being
on bes(t) information
on bes(t) terms
on both
on both sides
on business
on demand
on different occasions
on each side (I. D.)
on them
*In these cases will is represented, according to Graham, by prefixing the l hook to the tick.
on themselves
on this
on it
on its merits
on its own
on several
on that
on that side
on the
on this occasion
on these things (I. D.)
on those cases (I. D.)
on which
on your
183. In each of the following phrases, on, except where otherwise indicated, is to be made downward, because of convenience of junction:
on account on account of *on his on his own on his own part on important matters on many on many days on many occasions on me on my
on my assurance on my matter on my protest on my refusal
on one
on one another
on one side
on short notice
on so important
on so little
on so many
on so necessary
on (the) (con)trary
on (the) part (of)
on (the) subject
on their objection
on their receipt
on their terms
on what
 
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