I work in a large company in NYC which is very goyishe and there are times in the winter where a meeting may be scheduled which will go from say chatzos until after shkiah. What is the procedure for one who has missed davening mincha? Also may one daven seated at his desk granted being in a goyishe environment and not able to leave the workplace to go daven mincha with a minyan? Thanks for your clarification
One should make every effort to take the time out for mincha. Just as one can excuse himself for five minutes, to get a drink, use the bathroom or take an important call, this should be no different, a few minutes is all that is necessary. Only in unavoidable situations is one permitted to daven sitting down. In your case it doesn’t seem practical anyway as you may be interrupted by others. Speaking during Shmoneh Esrei is forbidden in any case.
One who misses mincha may make it up and daven 2 shmone esrei by maariv, however this is only when he did not knowingly miss it. Here the question is if in fact his job was on the line etc.if not and be could ave davened, he may not be eligible for the “make up” tashlumim by maariv.
If you just slighty miss shekiya, you may still daven mincha until halachic nightfall. The Biur Halacha recommends in this situation to make a stipulation that if this is no longer a kosher time for mincha, this shmone esrei should be for maariv, and the shmone esrei later [by maariv] should be for a make up of mincha [the make prayer always comes after the required one].