6s wet fs aa (chromosome inversions, duplications, translocations, deletions, etc.) and remain viable. However, although only a very small fraction of alpha interactions give rise to viable mutated ceils, these survive to proliferate, whereas cells which suffer lethal changes are eliminated from the cell population. Thus in the case of long-term exposure of . tissue to internal alpha emitters at low dose rates ‘here is a cumulative ' dmerease in the population of cells which have survived one or more chromosome structural changes. However it 4s equally obvious that a cell whose nucleus is subjected to repeated alpha interactions within the frean life of the cell has only a negligible chance of survival. -It is likely that the production of a radiation-induced tumor begins with the formation of @# single malignant cell characterized by a combina~ tion of two or more chromosome changes and/or gene mutations. The alpha radiation-induced bone tumor incidence in dogs is observed to be propor- tional to the square of the alpha dose (19) implying that a sequence of two or more low probability events must de involved. This is consistent with the two-mutation and multiple-mutation theories of cancer on the age distribution of cancer in man. (20,21) based On the basis 6f these consider- ations the production of a malignant cell involves a sequence of events, as follows: cr) production of a viable mutated cell; (2) clone growth from the mutated cell; (3) production of a second viable mutation in one or more of the clone:-(4) growth of a clone of doubly-mutated cells; --etc. Thus, for a two-mutation sequence, the tumor risk would be proportional to the Re (t/t), where R is the alpha dose rate, t is the time of | exposure, and Ty) is the mean life of the normal cell and singly mutated cell. The term (t/t) represents the influence of the growth of the clone of the singly-mutated cell on the long-term risk. This tumor risk relationship makes it abundantly clear that a linear