SIMPLE SHADOW CONES FOR TEN POINTS OF INCIDENCE HAVE BEEN EVALUATED FOR SEVERAL LATITUDES, LOGITUDES AND PROTON ENERGIES. THE TRAJECTORIES WERE COMPUTED IN THE EARTH´S DIPOLE AND QUADRUPOLE MAGNETIC FIELD. THE PURPOSE OF THIS NEW COMPUTATION WAS A) TO CALCULATE THE CORRECT SIMPLE SHADOW CONES AND ESTIMATE THE ERROR IN THE CONES CALCULATED BY SCHREMP IN 1938 AND B) TO STUDY THE LONGITUDE EFFECT OF THE SIMPLE SHADOW CONES. A NEW COMPUTATION OF SIMPLE SHADOW CONES HAS ALSO RECENTLY MADE BY J. E. KASPER FROM THE UNIVERSITY OF IOWA. THE CONES CALCULATED BY KASPER AND SCHREMP PRESENT TO LONGITUDE EFFECT, AS THESE AUTHORS CONSIDERED THE MOTION OF CHARGED PARTICLES IN THE MAGNETIC FIELD OF A CENTRAL DIPOLE.THE AGREEMENT BETWEEN KASPER´S AND OUR CONES AND DISCREPANCY WITH THE SCHREMP CONES DEMOSTRATES THAT THE SCHREMP CONES ARE ERRONEOUS AND PREDICT A SHADOW EFFECT TO THE EARTH LANGER THAN THE CORRECT ONE, THE DISCREPANCY BETWEEN OUR CONES AND SCHREMP´S IS MOSTLY DUE TO THE ERROR IN THE SCHREMP CALCULATIONS AND ONLY IN A SMALLER DEGREE TO THE LONGITUDE EFFECT. THE COMPARISON BETWEEN KASPER´S AND OUR CONES ALLOWS TO ESTIMATE THE LONGITUDE EFFECT. THIS EFFECT IS IMPORTANT AT LOW LATITUDES FOR SMALL PARTICLE ENERGIES AND DECREASES WITH THE INCREASE OF LATITUDE. THE SHADOW CONE OF THE DIPOLE FIELD FALLS BETWEEN THE TWO CONES CORRESPONDING TO TWO DIFFERENT LONGITUDES OF THE DIPOLE AND QUADRUPOLE MAGNETIC FIELD. THE LIMITATIONS OF THE METHOD OF INTEGRATION WHEN USED FOR HIGHER ENERGIES, ARE DISCUSSED.SIMPLE SHADOW CONES FOR TEN POINTS OF INCIDENCE HAVE BEEN EVALUATED FOR SEVERAL LATITUDES, LOGITUDES AND PROTON ENERGIES. THE TRAJECTORIES WERE COMPUTED IN THE EARTH'S DIPOLE AND QUADRUPOLE MAGNETIC FIELD. THE PURPOSE OF THIS NEW COMPUTATION WAS A) TO CALCULATE THE CORRECT SIMPLE SHADOW CONES AND ESTIMATE THE ERROR IN THE CONES CALCULATED BY SCHREMP IN 1938 AND B) TO STUDY THE LONGITUDE EFFECT OF THE SIMPLE SHADOW CONES. A NEW COMPUTATION OF SIMPLE SHADOW CONES HAS ALSO RECENTLY MADE BY J. E. KASPER FROM THE UNIVERSITY OF IOWA. THE CONES CALCULATED BY KASPER AND SCHREMP PRESENT TO LONGITUDE EFFECT, AS THESE AUTHORS CONSIDERED THE MOTION OF CHARGED PARTICLES IN THE MAGNETIC FIELD OF A CENTRAL DIPOLE.THE AGREEMENT BETWEEN KASPER'S AND OUR CONES AND DISCREPANCY WITH THE SCHREMP CONES DEMOSTRATES THAT THE SCHREMP CONES ARE ERRONEOUS AND PREDICT A SHADOW EFFECT TO THE EARTH LANGER THAN THE CORRECT ONE, THE DISCREPANCY BETWEEN OUR CONES AND SCHREMP'S IS MOSTLY DUE TO THE ERROR IN THE SCHREMP CALCULATIONS AND ONLY IN A SMALLER DEGREE TO THE LONGITUDE EFFECT. THE COMPARISON BETWEEN KASPER'S AND OUR CONES ALLOWS TO ESTIMATE THE LONGITUDE EFFECT. THIS EFFECT IS IMPORTANT AT LOW LATITUDES FOR SMALL PARTICLE ENERGIES AND DECREASES WITH THE INCREASE OF LATITUDE. THE SHADOW CONE OF THE DIPOLE FIELD FALLS BETWEEN THE TWO CONES CORRESPONDING TO TWO DIFFERENT LONGITUDES OF THE DIPOLE AND QUADRUPOLE MAGNETIC FIELD. THE LIMITATIONS OF THE METHOD OF INTEGRATION WHEN USED FOR HIGHER ENERGIES, ARE DISCUSSED.