Who Invented the Self Starter -- Charles Franklin Kettering or Clyde Coleman?

I am very interested in looking at the inventive work of Charles F. Kettering within a broader context of his times. That is moving me into the period 1900-1910  and an incredibly complex story related to starter and ignition systems. There were so many individuals working at the same time on basic and fundamental automotive problems, and it is difficult to determine who was looking over the shoulder of whom. 

In my 2nd edition of The Automobile and American Life, I mention the work of Clyde Coleman. Above is the image from one of his patents, first filed in 1901.

Note that the patent begins with:

According to my invention means are provided for starting the' engine by the application of power thereto and for utilizing the power of the engine when the engine is self actuated fo'r the purpose of storing energy, these means and the engine being connected by differential connecting devices, and according to m y invention these means comprise a. motor-dynamo so connected. 

My invention also includes the provision of means constructed so asto be readily actuated by the operator and initially operating the starting-motor and by further movement connecting the running-gear of the vehicle with the engine, such means permitting the engine to be started by the starting-motor while relieved of its load. 

My invention also includes provision for the discontinuance of the self-actuation of the starting-motor after the engine has been started, so that such starting-motor has only to perform the work of starting the engine.

Now as to Coleman's ignition system see figure 4 and read his description:

The electrical connections are diagram m atically shown in Fig. 4. The source of electric storage battery 40, and this storage battery is charged when the motor-dynamo is operating as a dynamo and supplies electric current to the motor-dynamo to energize and actuate the same when-the motor-dynamo is used as a motor and also during the operation of the engine supplies an electric current to an electric igniting or sparking circuit for igniting the gases within the engine-cylinder. The igniting or sparking circuit is closed at the switchrplates b and b through the controlling-lever 24, which is of conductive material or is conductively connected with its pivot, and the primary cir cuit flows from the battery 40 through the wire 41, a primary coil ofan induction-coil 42 and through a make-and-break device 42 and Wire 43 to the switch-plate b or b, and from either switch-plate through the controland the wire 44 back'to battery. The secondary coil of the induction-coil is thus inductively energized and energizes the sparking device or plug 36, which would be located within the cylinder of the engine 3. 1f the ignition of the engine were accomplished by other than electrical means, this circuit would of course be unnecessary.

I have a long way to go with this research, but any insight you have on this topic would be most appreciated.