The theory of geomagnetic effects on cosmic radiation is discussed for the case in which the point of observation is above the surface of the earth. Parts of the older geomagnetic theory are readily modifiable for application under the new conditions; the manner in which ordinary Störmer theory and the Lemaitre‐Vallarta theory of the main cone can be adapted is discussed. However, the simple shadow cones of Schremp appear now in a new light; as the point of observation rises from the earth, the simple shadow effect which exists at the earth makes a smooth transition to a new kind of earth's shadow effect. Associated with this effect are principal shadow cones which are defined by reference to the properties of certain families of trajectories. For observation points above the earth a modification in our view of the penumbral region is required; this is discussed very briefly. Extensive computations of principal shadow cones have been carried out by machine integration of the equations of motion and subsequent abstraction of data from these trajectories. Sample computed cones are given for representative particle rigidities, geomagnetic latitudes, and altitudes of observation. The centered dipole approximation for the magnetic field of the earth is used througho