In discussing x-ray induced mutations in drosophila flies, Schrodinger denotes the method and target as such: No matter the type of radiation source (speaking in terms of x-ray to gamma rays here) as the dosage goes up, so does the mutation rate. The target for measuring this ionization here, aside from those irradiated drosophila flies, is called the 'standard substance,' that being air. It's chosen "not only for convenience, but also for the reason that organic tissues are composed of elements of the same atomic weight as air. A lower limit for the amount of ionizations or allied processes (excitations) in the tissue obtained simply by multiplying the number of ionizations in air by the ratio of the densities. It is thus fairly obvious, and is confirmed by a more critical investigation, that the single-event, causing a mutation, is just an ionization (or similar process) occurring within some 'critical' volume of the germ cell" (p. 44).
So, given a dosage of radiation, this 'critical volume' demonstrates the effects of irradiation through ionization. Ionization is when an atom is hit by a 'packet of energy' enough to excite the electron in its outermost shell, causing it to break off (ionization). In large enough examples, ionization, is at the heart of the photoelectric effect. That is, if you heat something (i.e., add energy to it) you cause that something to give off light. Imagine a person's hand giving off light after being hit by a gamma ray burst from a criticality event. Bad news, dude, bad news.
Now what is this 'critical volume of the germ cell?' That's the specific size (in volume) of genetic material that gets hit by a dose of radiation. Citing the seminal paper on this study of x-ray induced mutation, Schrodinger writes. "He arrives there at a size of only about ten average atomic distances cubed, containing thus only about 10^3 = a thousand atoms. The simplest interpretation of this result is that there is a fair chance of producing that mutation when an ionization (or excitation) occurs not more than about '10 atoms away' from some particular spot in the chromosome" (p. 44).
Armed with this knowledge Schrodinger notes that threats to humanity through ionizing radiation aren't of great concern if known sources of this radiation are regulated. He produces a simple example and leaves with a cautionary note. "To put it drastically, though perhaps a little naively, the injuriousness of a marriage between first cousins might very well be increased by the fact that their grandmother had served for a very long period as an X-ray nurse. It is not a point that need worry any individual personally. But any possibility of gradually infecting the human race with unwanted latent mutations ought to be a matter of concern to the community" (p. 45).
As an aside, I had read a book in my youth called 'The Therapy of Desire' by Martha Nussbaum wherein she outlines the developmental projects of various schools of Greek philosophy, resting upon their approach to both the passions and their obverse, stagnation. The point of her book, and the preliminary work of these Greek schools of thought, was to teach individuals how to regulate themselves optimally as a matter of a personal ethic. Her source material on the Epicureans and the Stoics reveal whole tranches of what would become Christian teaching that it struck me very hard how much of Christianity as it passed through Greek hands carried that very flavor of the learned community working with the basic story of the Χρίστος (Christos). Likewise, here I feel as if Schrodinger is setting the groundwork for a generation of X-men comics and their backstories, namely the fear of irradiation and the prospects that 'just the right dose' could produce a 'superman.' And as we all know, Kal-El, the original Superman derived his source of power from the sun's radiation.
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