In order to find environmental signals based on the dust and calcium-ion concentrations in ice cores, we determine the constituent elements of residue particles obtained after melting ice samples. We have designed a sublimating system that operates at −45°C, below the eutectic temperatures of major salts. This system permits us to obtain a great many non-volatile particles. After studying the non-volatile particles, we immersed them in water to remove soluble particles and compounds. We thereby analyzed a total of 1272 residue particles (from the melted sample), 2418 non-volatile particles (after sublimation) and 1463 insoluble particles taken from five sections of Last Glacial Maximum ice from the Dome Fuji (Antarctica) ice core. Their constituent elements were determined by scanning electron microscopy/energy-dispersive X-ray spectrometry (SEM-EDS) and compared to the dust, calcium-ion and sodium-ion concentrations measured by ion chromatography. Our results indicate that >99.9% of the insoluble particles contain silicon but no sulfur, nitrogen or chlorine. A significant number of the non-volatile particles, however, contain sulfur and chlorine. We conclude that insoluble dust consists mostly of silicate, that almost all calcium ions originate from calcium sulfate and that almost all sodium ions originate from sodium sulfate and sodium chloride.