Carroll's Pronunciation Guide
The new words, in the poem "Jabberwocky", have given rise to
some differences of opinion as to their pronunciation: so it may be
well to give instructions on that point also. Pronounce "slithy" as if
it were the two words "sly, the": make the "g" hard in "gyre" and
"gimble": and pronounce "rath" to rhyme with "bath".
--Preface to Through The Looking Glass
As this poem "The Hunting Of The Snark" is to some extent
connected with the lay of the Jabberwock, let me take this
opportunity of answering a question that has often been asked me,
how to pronounce "slithy toves". The "i" in "slithy" is long, as in
"writhe"; and "toves" is pronounced so as to rhyme with "groves".
Again, the first "o" in "borogoves" is pronounced like the "o" in
"borrow". I have heard people try to give it the sound of the "o" in
"worry". Such is Human Perversity.
This also seems a fitting occasion to notice the other hard words in
that poem. Humpty Dumpty's theory, of two meanings packed into
one word like a portmanteau, seems to me the right explanation
For instance, take the two words "fuming" and "furious". Make up
your mind that you will say both words, but leave it unsettled
which you will say first. Now open your mouth and speak. If your
thoughts incline ever so little towards "fuming", you will say
"fuming-furious"; if they turn, by even a hair's breadth, towards
"furious", you will say "furious-fuming"; but if you have that rarest
of gifts, a perfectly balanced mind, you will say "frumious".
--Preface to "The Hunting Of The Snark"
A hard "g" means the initial sound of "gun", as opposed to
the "j" sound in "gin". People with different accents
pronounce "bath" differently, so if the advice is followed,
then "rath" will be pronounced differently too.
Carroll/Dodgson would have had a British accent, so his
pronunciation of the word would use the vowel sound of
"bar", and not that of "bat".