I agree with Frank, when he said:
Generally, the radiation in small instruments, like old sextants, is not a serious issue, mostly because the total exposure time is quite low (unless you sleep with your sextant under your pillow). It depends on the amount of Radium, but if it's comparable to an old watch or clock face, you should be ok.
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I do have one very specific concern, which has not been addressed. Ingestion. Paint is not permanent. It can and will degrade, producing dust. The degradation is neither enhanced nor inhibited by the addition of radium. As the radium infused dust moves about, it will migrate out of your instrument, onto your hands and then into your body. One can argue that the amount is minuscule, yet no level of ingestion is safe.
So instead of keeping your radium safe in the garage, you store it in your liver. Instead of under your pillow, its in your internal organs. Keeping it in the garage is likely to enhance the dust and flake production, due to the unequal thermal coefficient of expansion of the metal the paint is applied to and the paint itself.
What possible benefit do we derive from a radium containing sextant as opposed to one that is not so infused? Risk v Reward: what is the reward?? How is the radium an enhancement that cannot be obtained otherwise?
In my view, this is the safest method: Far, far away from me. Being reassured of your safety by some random science journalist for the NYT [we never make fun of science journalists] or a fellow correspondent on NavList may not be the best approach.
I won't keep radium in my house. If you think it safe, keep it in yours.