Ahem... Isn't "IHS" the acronym for the Latin phrase "In Hoc Signo," meaning "In this sign (conquer)" ?
It's my understanding that the Latin transcription of the Greek abbreviation for Jesus preceeded all other uses of the monogram.
The use of an abreviation for sacred names is a practice drawn from prehistoric taboos on the speaking of a god's name.
You beat me to it. My ancient history course and my Latin are rusty, after 60 years with little occasion for use. I think the story, etc. is this. The Emperor Constantine's mother, Sophia, became a Christian. (It is she who went to Jerusalem in search of relics, and returned with a relic of the Holy Cross according to tradition). And it is she for whom the Basillica of St. Sophia in Constantinople was named (now called Hagga Sophie, or something like that since it is now a mosque in Instanbul). She pressed Christianity on her son, Constantine. He converted after seeing a cross in the sky, and said in this sign we will conquer. Thereafter the Roman Empire shifted from various cults to Christianity.