Im thinking thats a signal direction finder
That is a directional antenna.
It appears it could be a transmitter-receiver outfit.
It also appears the right rear fender has had the crap knocked out of it.
And it's not a Dodge Brothers, by the splash apron & fenders.
Maybe it's an early MapQuest street scene car???
It's an early attempt at a car radio. Seriously.
NSA beginnings !
An the versatile 1921 Doctor's Coupe as a radio car. (Sorry for the formatting, two oversize illustrations)
I bet they didn't listen and drive because the coils would aggravate that radio to death with sparking sounds.
I know the power unit for the sawmill out in the side yard has copper spark plug wires and when it is running,you can't play a radio in the house without hearing it.