The well-known GEIGER-NUTTAL relation in alpha radioactivity postulates a positive trend in the variation of disintegration constant ~ with alpha energy E. A number of energy groups within the different alpha ray spectra deviate from the above linear relation and have been designated as anomalous in some recent works. The present study will show that this anomaly is only apparent and there exists some regularity ill the variation of ~ with energy E of the spectral components. Instead of the positive gradient of the GXlGER-IN-UTTAL relation, the new systematics for the alpha ray spectra give both positive and negative trends in the log 2 vs. E-relation. It will also be observed that for highly complex spectra the positive and the negative trends follow one another regularly, with one or two exceptions. These negative gradients do not agree with the alpha decay theories of GAMOW and of others and the discrepancy factor, 2theoreticaI/~observed, is shown to be in general of the order of t03 while in some cases it exceeds t0 la (Table i). The theoretical implications of the new systematics have been qualitatively studied and a possible way of explaining the above disagreement is indicated. Besides, another important correlation, viz., the FOURNIEI~ curves for alpha decay energy vs. mass number, has been reconsidered in the light of alpha ray spectra, and it is found that interesting suggestion can be made about the possible existence of subshells at neutron numbers 128 and t34. Alternative speculation of some weak components ill the alpha spectra of Po 213, Bi ~13, and tZa 2a4, is less probable.