the step between hand cranked starting and electric starting, for a 1913 Pirece Arrow, was a compressed air powered starter system

The 1913 cars also had a self-starter of the compressed air variety.

The 1913 cars, known as Series One, had grown from the 1910 versions. The 66-A-1 was mounted on a 147 1/2 inch wheelbase. The engine in the 66 had also grown to a 5x7 bore and stroke. This pushed the displacement to 824 cubic inches, the largest production automobile engine ever made.

https://www.pierce-arrow.org/history/history3.php

The compressed air tank was under the right side, and the air starter system pumped compressed air was into the cylinders to move the pistons and turn the engine.

http://www.conceptcarz.com/z18227/Pierce-Arrow-Model-38-C.aspx