Look between the Vee and flat way on the tailstock end of the bed and you will see the Lot number and machine number. There should be a letter stamped there which tell of the model of the lathe. Also you can check the swing and line it up with the model:
9 $ 11" Model K or Junior (first built around 1920)
12" Model E (first built around 1918)
14 & 16 Model A (first model Monarch made starting in 1909)
18 & 20" Model B (first built 1910)
22, 24, 26, 28 & 30" Model D (first build in early teens)
Model C was used to designate their toolroom lathes of the above swings. CA, CB etc. Monarch carried this on in all their "lettered" models.
These are the cone head lathes Monarch built from 1909 into the early 1920's.
My guess is a Model A, as this was the most numerous cone head lathe Monarch made, with WWI war production 2,000 to 4,000 lathe in 1917 and 1918. And head head end leg is what you find on the smaller swing lathes. The chip pan does not look to be factory supplied.
Hope this help,
John