The principle is pretty easy. A normal dipole in free space normally has a 72 Ohm feed point impedance. A quarter wave ground plane is half this...about 36 Ohms.
By extending the antenna from a quarter wave to a three-eight wave, the maximum current point moves from the base to further up the radiating element. This has the effect of lowering the angle of radiation which is a plus.
The longer three-eight wave antenna now has a reactive feed point (inductive) as it's too long. This is tuned out with a series capacitor and it should be able to get close to 50 Ohms.
This antenna would suit someone who can only put up a quarter wave ground plane for 10 metres and wants better performance.
The article from the March 1983 edition of Short Wave Magazine is shown below...
* * * * * * * * * *