Forgot to look at the clef . . . . . corno basso, if it's a horn transposing at a 9th, will be in treble clef. So this is still a mystery.
Having made a cursory look at the bassoti parts, the range fits the fingered range of all clarinets -- in some cases a passage goes down to low E and then turns around again, low E being our lowest written note (band instruments usually don't have the extensions that you find on some orchestral instruments). And in one pattern where other instruments descend from a low F# to a D, the bassotto part has a rest on the D, which would be off the range of a clarinet.
So I think it's fairly safe to say these are clarinets. As to the keys, most wind bands have alto and bass clarinets. It seems Rimsky-Korsakov was writing for a group that used F basset horn rather than Eb alto, and it isn't too much of a stretch to assume that he used the word bassotti to mean any low clarinet. So the Bb bassotti would be bass clarinet.
I don't know if my university has a modern edition of this, if at all, but the next comparison would have to be to a modern score to see who has been given these parts. Master Music puts out an edition arranged by Clark McAllister, and his scoring does include alto and bass clarinet, although whether he gave those instruments the exact notes in the bassetti parts is something I don't know.
In the brass department, McAllister scores "4, 4+2, 3+1, 2"-- 4 horns, 4 trumpets, 2 cornets, "3+1" for trombones, and "2" for tubas. The IMSLP score does have 4 horns, 4 trumpets, 2 cornets, and 2 tubas, so the only thing left is the 3 trombones and the corno basso. Obviously "3+1" refers three trombones and something, I would guess euphonium?
A brass specialist would have to say whether the corno basso part could be played on a euphonium, although I'm still perplexed as to why a bass clef part is sitting between two treble parts. How would a bass trumpet fit this part?
Doronk wrote:( couldn't he have just written out the instruments in english
The problem is in the history and development of military bands. The English, American, Russian (and Turkish, for that matter) military bands all developed differently and used different instruments, sometimes including ophicleides, saxhorns, serpents, and all sorts of things not used today. Any modern performance has to move these parts to a modern instrument.
This score is entirely do-able with a modern band (with just the one proviso that someone needs to say what a good subsitute for the corno basso part is).
In fact, since most clarinettists can do Major 2nd transposition at sight, playing the basset clarinet part on an alto clarinet doesn't even require re-writing the part (and the part itself is relatively simple).