The Philosophical magazine; a journal of theoretical, experimental and applied physics . -1 Iodine. 52-2 Rhodium. 129 Antimony 52-2 llutheuium. 184 Tantalum. 53-3 Palladium. 197 Gold. 56 Cadmium. 208 Bismuth. If we glance at this list we notice some peculiarities, but noveiy striking ones. We might ask, for instance, Why shouldthere be so many elements cougregated about No. 28; and,again, about 52 ? Why should there be only one atomic weightbetween 80 and 99, and then a group of four ? The following letter, kindly sent me by Professor De Morgan,will give the data for calculating the probabilit
The Philosophical magazine; a journal of theoretical, experimental and applied physics . -1 Iodine. 52-2 Rhodium. 129 Antimony 52-2 llutheuium. 184 Tantalum. 53-3 Palladium. 197 Gold. 56 Cadmium. 208 Bismuth. If we glance at this list we notice some peculiarities, but noveiy striking ones. We might ask, for instance, Why shouldthere be so many elements cougregated about No. 28; and,again, about 52 ? Why should there be only one atomic weightbetween 80 and 99, and then a group of four ? The following letter, kindly sent me by Professor De Morgan,will give the data for calculating the probabilities of this. Iintroduce it on account of its applicability, not only to this par-ticular case, but to others which will occur in these observations. Univ. Coll., Loncl.,Dec. 18,1852. Dear Sir,—The following, though but an imperfect viewof the whole question, will be enough, I think, for your pur-pose. I send formula and all, that who likes may verify it. If there be n numbers, each of which may be drawn at anytrial, and all equally likely, and if the following denominationsbe &c. Atomic Weights of analogous Elements. 315 Then, speaking of one assigned number, the chance that thatnumber shall not appear in m trials, is P; that it shall appearonce and once only, is Q; twice and twice only, is R; and soon. Further, the chance that it shall appear once or more is 1 — it shall appear twice or more, the chance is 1 —(P + Q).Three times or more, 1 —(P + Q + R); and so on. For calculation, mP Q=R = S = n —1 (m-l)Q 2(w-l) (m-2)R, 3(/i-]) and so on. Let there be 100 numbers, and 60 trials to be made. I find p= •54716 Q= •33161 R= •09881 S = •01929 T = •00278 U = •00031 +Q+R+S+T+U= •99996 1-00000 •00004. Chance of six or moreof a given number. It is then 99996 to 4, or 24999 to 1, against the appearanceof a predicted number six or more times. Now suppose the question to be what is the chance thatsome one number, not named, shall occur six or more ti
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