March 20, 1919] 



NATURE 



^5 



ment and personnel at his disposal. At least observa- 

 tions of potential-gradient and conductivity (prefer 

 ably both positive and negative) should be made 



(4) Meteorological observations in accordance with 

 the observer's equipment should be made at con- 

 venient periods (as short as possible) throughout the 

 interval It is suggested that at least temperature 

 should be read every fifth minute (directly after the 

 magnetic reading for that minute), 



(5) Observers in the belt of totality are requested to 

 take the magnetic reading every thirty seconds durint* 

 the interval, ten minutes before and ten minutes after 

 the time of totality, and to read temperature also 

 every thirty seconds before the magnetic readings. 



It is hoped that full reports will be forwarded 

 as soon a^ possible for publication in the journal 

 Terrestrial Magnetism and Atmospheric Electricity 

 Those interested are referred to the results of the 

 observations made during the solar eclipse of June 8, 

 19 18, the publication of which was begun in the 

 September (19 18) issue of the journal. A summary 

 of the results obtained is given in the March (19 19) 

 issue. Louis A. Bauer. 



Carnegie Institution of Washington, Depart- 

 ment of Terrestrial Magnetism, Washing- 

 ton, D.C., February 15. 



A Proof that any Aggregate can be Well-ordered. 



All the critics of my method sketched or described 

 in my two letters to Nature (vol. ci., pp. 84 and 304, 

 1918), in my two notes in Comptes rendus (vol. clxvi., 

 pp. 520-23 and 984-86, 1918), in Mind for July, 1918, 

 and in Science Progress for October, 1918, wish to see 

 a certain particular case sotved in detail. Although this 

 case does not throw so much light on the problem 

 as the equally simple method of dealing with the 

 general case, which I happen to have discovered 

 long before I applied it to special cases, I here give 

 the treatment of the particular case referred to. 



Suppose that an aggregate M is such that there 

 are classes x„ x^ . . ., where x„ is the class of all 

 those chains of M of type n, and the suffixes of the 

 x's are all the finite ordinal numbers (that is, 

 those less than w); we are to prove that M has a 

 chain of type w. We will define by complete induc- 

 tion a rule for actually constructing out of the x's 

 many (we can prove afterwards that the many are 

 all; we do not, of course, merely postulate that there 

 is a non-null class of all such classes) classes of direct 

 continuations of which each contains one chain from 

 each X. The rule, though it is, accordingly, split 

 into two parts, is to be regarded as one whole; and 

 it can be so regarded, since it does not involve an 

 infinity of arbitrary selections. 



(i) With each member Kj of X2, class that member 

 of X, which is the sole segment of K^. Thus each 

 member of Xi is classed with many of Xj, and each 

 member of x^ is classed with a definite one of », so 

 that together these members form a class of direct 

 continuations with members of types i and 2. 



(2) In general, for 2<n<w, with each member 

 K,j of Xn classify (a^i that member (K„_,) of jr„_, which 

 is a segment of K,„ and (b) also those chains of 

 types n — 2, . . . 2, i previously classed with K„_i by 

 the rule. Remember not to regard here a class of 

 y and 2 as anything more than just y and z. For 

 instance, each member of x, forms, with the chains 

 classed with if, a class of direct continuation with 

 three members; and we easily see that, in general, 

 every class of direct continuations with n members 

 is added to, provided that the whole rule is applied 

 and not merely a part of it which stops at n. 



Thus we have defined a means of rearranging all 



NO. 2577, VOL. 103] 



the members ofi all the ^'s so that thev form classes 

 of direct continuations of the kind we wished and 

 stated above. Since any class of direct continuations 

 which IS formed from the members of M, and con- 

 tains chains of all types less than .. plainly defines 

 a chain of type o,, each of the classes of direct cSn- 

 inuations formed by the rule defines a cha n o 

 f}pe o,. This IS what we had to prove. We have 



hafinh T "^i'^^^'^f °f direct c^ontinuations sucS 

 that each class has at least two terms, and, if it has 

 terms it has n+i. P„iup E. B. Jourdain 



The Bourne, Basingbourne Road, 

 Fleet, Hants, March 11. 



Coal in Thrace. 



Antigonos a Greek writer about the beginning of 

 our era, made a collection of the accounts of^the 

 natural wonders of his time. Among them he men 



h°?~i'''^"''^'t ^""^"^ '^^ ^'^^ edition of is^r* 

 that they say that in the wild (uncultivated) region 

 of Thrace there is a river called Pontos, which brfngs 

 down in »ts course stones resembling anthrax (char- 

 coal), and that these burn, but differ in combustion 

 trom charcoal, inasmuch as the use of bellows extin- 

 guishes the fire. On the other hand, sprinkled wi"h 

 water they burn all the better." Wher^ was this river ? 

 Kiepert does not mention it, but it seems to have 

 flowed into the Black Sea, then called Pontos. It 

 would be interesting to know if anthracite has been 

 tound so near Constantinople. 



QUI r^ Edmund M'Clure. 



80 Kccleston Square, S.W.i, February 27. 



reimMf i' "^^.^^rranty for suggesting that "stones 

 resembling anthrax" are anthracite; they are far 

 more likely to have been bituminous coal or 

 lignite, both of which burn more readily than does 

 anthracite, which latter is decidedly difficult of igni- 

 tion Whilst European Turkey has not been fullv 

 explored for coal, the existence of coal is known in 

 various places; a bituminous coal-seam is reported 

 near Keshan, in the province of Adrianople, and along 

 parts of the northern coast of the Sea of Marmora ; 

 and there are lignite deposits known near Rodosto, 

 near Dedeagatch, and even within a short distance 

 of Constantinople. Obviouslv any of these deposits 

 might have given rise to the stones referred to bv 

 Canon M'Clure. 



It would be interesting to know whether the Greek 

 text excludes the possibility of its Reference being 

 to the district of Pontos, on the south shores of the 

 Black Sea, as the best-known coal-mines of all the 

 region are those to the south of Heraclea in that 

 ^"trict. Hbnry Louis. 



Armstrong College, Newcastle-upon-Tyne, 

 March 3. 



Curious Markings on Chalk. 



Dr. .\ndrews (Nature, March 13, p. 25) probably 

 knows more about the natural forms assumed by 

 chalk than I do, but I think, nevertheless, that the 

 specimen described by me in the February issue of 

 Man (p. 17, pi. B) cannot be disposed of quite so 

 summarily as he supposes. And I would suggest that 

 it is generally considered unwise, in such matters, to 

 publish a definite opinion before an examination of 

 the actual specimen has been made. 



It is my hope that before long Mr. Gathome- 

 Hardy may exhibit his discover\' at a meeting of 



