Fuse Switchbox for furnace
Background:
The 20A fuse is a Type S, meaning it is a &quot;time delay&quot; type fuse that allows things with motors to get to speed without making the fuse blow. The 30A fuse is a Type W with is not time delay, it is a &quot;fast acting&quot; type of fuse.
Best guess...
The furnace originally had Type S 20A fuses, but something was wrong so fuses kept blowing and after getting frustrated (but not finding out why), someone just put a larger Type W fuse in there so that it would not blow. Totally the wrong thing to do and is one of the biggest problems with fuses, which is why they are not used in houses any more.
Some time later your house was upgraded to using circuit breakers (circuit breakers would not have been used in 1924) and the installer wisely put a 20A breaker on that circuit, rendering the fuses irrelevant (assuming the wire is 12ga or larger).
But... here's another potential problem. Your drawing seems to imply that there is a 1 pole 20A breaker on the one wire feeding this, then the photo seems to show that there is a fuse (the 30A) on the white wire, which would be typically indicating the neutral circuit. It is illegal and DANGEROUS to have a fuse on the neutral circuit! If the breaker is 2 pole and this is a 240V circuit going to the furnace, then it's fine, other than the use of a white wire (white is only to be used for neutral circuits).
If none of this makes sense to you, I suggest getting a qualified electrician to look at it and, if possible, just remove those fuses.