Primordial He-3, together with neon enrichment in Ne-20 and Ne-21 relative to Ne-22 compared with atmospheric values, have been identified in many samples derived from the Earth's mantle. To explain the enrichment of Ne-21 and Ne-20 in the mantle source regions for these samples, it is necessary to mix at least two distinct non-atmospheric neon components. The two most likely candidates are nucleogenic and solar neon. Nucleogenic Ne-21, produced by local decay of U and Th, elevates Ne-21/Ne-22 ratios. Solar neon is the only known component which has a Ne-20/Ne-22 ratio greater than both the atmospheric value and the Ne-20/Ne-22 ratios observed in terrestrial samples. We suggest, therefore, as a working hypothesis to account for the observed non-atmospheric neon, that there has been mixing of two neon components, solar and nucleogenic, in the mantle. If the Earth's primordial composition was solar, then we expect to see a correlation between the helium and neon isotope systematics. This is because primordial helium and neon would all be solar, and variations in the observed He-3/He-4 and Ne-21/Ne-22 ratios in the mantle would be due to the time integrated ingrowth of radiogenic He-4(He-4*) and nucleogenic Ne-21 (Ne-21*), having a constant He-4*/Ne-21* production ratio. This relationship can be explicitly stated as: Ne-21*/Ne-22(s)={(He-4/He-3)(Mantle) - (He-4/He-3)(s)}Ne-21*/He-4*(He-3/Ne-22)(s), where subscript S denotes the solar composition. Using the above equation we can calculate hypothetical He-3/He-4 ratios related to the neon isotopic compositions in the mantle sources. We are able to correlate the observed He-3/He-4 ratios of all available samples having non-atmospheric neon isotopic ratios with the slopes of neon mixing lines between mantle and present-day atmospheric neon in Ne-20/Ne-22-Ne-21/Ne-22 space. Thus, the helium and neon isotopic signatures in the mantle can be explained by mixing of a primordial solar component, different fractions of radiogenic and nucleogenic components produced by radioactive processes inside the Earth, and a present-day atmospheric component. The correlation between observed helium and neon isotopic ratios in samples derived from the mantle provides strong support for the notion that a significant primordial noble gas component in the Earth was of solar composition. This provides a critical boundary condition for models regarding how and when the Earth acquired its volatiles, and how its atmosphere evolved