The Interstellar Gas Experiment (IGE) exposed thin metallic foils aboard the LDEF spacecraft in low Earth orbit in order to collect neutral interstellar particles which penetrate the solar system due to their motion relative to the sun. By mechanical penetration these atoms were imbedded in the collecting foils along with precipitating magnetospheric ions and, possibly, with ambient atmospheric atoms. During the entire LDEF mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. After the foils were returned to Earth, a mass spectrometric analysis of the noble gas component of the trapped particles was begun. The isotopes of He-3, He-4, Ne-20, and Ne-22 were detected. We have given a first account of the experiment. In order to infer the isotopic ratios in the interstellar medium from the concentrations found in the foils, several lines of investigation had to be initiated. The flux of ambient atmospheric noble gas atoms moving toward the foils due to the orbital motion of LDEF was estimated by detailed calculations. Any of these particles which evaded the baffles in the IGE collector could be entrapped in the foils as a background flux. However, the calculations have shown that this flux is negligible, which was the intent of the experiment hardware design. This conclusion is supported by the measurements. However, both the concentration of trapped helium and its impact energy indicate that the flux of magnetospheric ions which was captured was larger than had been expected. In fact, it appears that the magnetospheric particles constitute the largest fraction of the particles in the foils. Since little is known about this particle flux, their presence in the IGE foils appears fortunate. The analysis of these particles provides information about their isotropic composition and average flux.