The data from six neutron-intensity monitors distributed over a wide range of geomagnetic latitudes have been used to study the large and temporary increase of cosmic-ray intensity which occurred on February 23, 1956, in association with a solar flare. During the period of enhanced intensity a balloon-borne neutron detector measured the absorption mean free path and intensity of the flare particles at high altitudes. From these experiments the primary particle intensity spectrum as a function of particle rigidity, over the range <2 to> 15-30 Bv rigidity, has been deduced for different times during the period of enhanced intensity. It is shown that the region between the sun and the earth should be free of magnetic fields greater than ~10-6 gauss and that the incoming radiation was practically isotropic for more than 16 hours following maximum flare particle intensity. The decline of particle intensity as a function of time t depends upon the power law t-32, except for high-energy particles and late times, where the time dependence approaches an exponential. The experiments lead to a model for the inner solar system which requires a field-free cavity of radius greater than the sun-earth distance enclosed by a continuous barrier region of irregular magnetic fields [B(rms)~10-5 gauss] through which the cosmic-ray particles must diffuse to reach interstellar space. This barrier is also invoked to scatter flare particles back into the field-free cavity and to determine the rate of declining intensity observed at the earth. The diffusion mechanism is strongly supported by the fact that the time dependence t-32 represents a special solution of the diffusion equation under initial and boundary conditions required by experimental evidence. The coefficient of diffusion, the magnitude of the magnetic field regions, the dimensions of the barrier and cavity, and the total kinetic energy of the high-energy solar injected particles have been estimated for this model. Recent studies of interplanetary space indicate that the conditions suggested by the experiments may be established from time to time in the solar system. The extension of the model to the explanation of earlier cosmic-ray flare observations appears to be satisfactory. The solar flare event was superposed by chance upon a large but typical intensity decrease of nonsolar cosmic rays which began several days prior to February 23. Hence, the flare particles have been used as probes to explore the intensity modulation mechanism responsible for this decrease of background cosmic-ray intensity.