April 4, 1895J 



NATURE 



533 



An Elementary Treatise on Theoretical Mechanics. 

 Part iii. Kinetics. By Alexander Ziwet, Assistant Pro- 

 fessor of Mathematics in the University of Michigan. 

 (New York : Macmillan and Co., 1894.) 



The first two parts of this excellent treatise have already 

 been noticed in these columns ; this third part keeps 

 up to the same excellence, and we look forward to a 

 sequel, in the absence of any indication that the treatise 

 is yet complete. 



We think the author would have done well to have 

 followed the opinion of his American colleague, Prof. 

 T. \V. Wright, and to have reserved absolute measure- 

 ments to the Metric system of units, whileusinggravitation 

 units only with the British foot and pound. These last 

 units are too insular and provincial ever to be employed 

 in cosmopolitan problems where results have to be 

 translated into absolute measure ; and James Thomson's 

 word, potential, is never likely to be of any practical use. 



Lagrange'sand Hamilton's generaldynamical equations 

 are expounded with clearness and elegance ; the ap- 

 plication of the principle of the Conservation of Areas to 

 the paradoxical motion of a kitten, let fall by his feet a 

 short distance above a table, has excited considerable 

 discussion recently at the Paris .Academy of Sciences ; 

 this problem would provide the author with an illustration 

 of the methods of generalised coordinates. 



The copious list of authorities at the end of the chapters 

 is a valuable feature of the book. G. 



LETTERS TO THE EDITOR. 



I hi Eiitor lioes not hold himself responsible jor opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonymous communications. ] 



Destruction of the Seismological Observatory at 

 Tokio, Japan. 



I REGRET to say that a letter, which has just arrived from Tokio, 

 informs me that Prof. John Milne has lost all his valuable seis- 

 mographic instruments, with his library and many manuscripts, 

 through a tire which has occurred at his house and observatory. 

 Prof. Milne wishe> me to announce that his address-book has 

 been destroyed, but he will be able to forward vol. iv. of the 

 Seismological yoiirnal \.o \.\\o%t entitled to it, iflhey will send 

 in their names to him, " care of the Japan A/ail office, Yoko- 

 hama." He further wishes me to state that he has 600 

 damaged copies of the Seismological Society's Transactions, 

 and that from these he will be happy lo complete sets. Ap- 

 plicants for the copies of the Transactions should address Prof. 

 Milne, care of the Geological Society, Burlington House, 

 London, W. 



I am sure that scientific men all over the world will feel the 

 deepest sympathy with Prof Milne in his great and, indeed, 

 irreparable loss. He was preparing to return to Europe when 

 the tire occurred, and he wishes to appeal to all who can furnish 

 him with separate copies of papers relating to earthquake 

 phenomena, to replace, so far as is possible, those he has lost 

 by the destruction of his library. John W. Judd. 



April I. 



On Mersenne's Numbers. 



In 1644 the mathematician Mersenne asserted that out of 

 the 56 primes not < 257, there were only 12 primes, viz. : — 



/ = l> 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257, 



which, taken as exponent (.7), make the number N = (2' - i) 

 also prime. No proof was published, and even up to now, 

 this statement has only been partially verified : the verification 

 is still one of the difficult problems of higher arithmetic. Ac- 

 cording to a paper by Mr. \V. W. Rouse Ball, in the Messenger of 

 Mathematics, vol. xx. p. 34, Mersenne's statement has been 

 verified (or the 18 prime values of </ < 60, and for 14 higher 

 values, and one additional number N has been shown to bo 

 prime l>y Prof. SeelholT, viz. when;/ = 61. This left 23 cases 



NO. 1327, VOL. 51] 



unverified, vi2. 3 supposed to be prime (when y = 67, 127, 257)> 

 and the remaining 20 .".upposed to be composite (when q — "I, 

 89, lOl, 103, 107, 109, 137, 139, 149, 157, 163, 167, 173, 181, 

 '93. 197. '99. 227, 229, 241). 



I have recently discovered the verification of one of the latter, 

 viz. that 



(2"'- i) is divisible by 74S7. 



This can be readily verified directly by the method of Con- 

 gruences. 



It has also been verified by actual division by Mr. R. Tucker 

 (Sec. London Mathematical Society), who has kindly sent me 

 the quotient consisting of 56 figures. The mode of discovery 

 of this factor has been communicated to the London Mathe- 

 matical Society, and will be sent to one of the mathematical 

 journals. ALLAN CUNNINGHAM. 



March 23. 



Tan-Spots over Dogs' Eyes. 



I TRUST you will allow me to point out that the drift of my 

 letter on the above subject in Nature, vol. I. p. 572, has not 

 been fully apprehended. Hitherto we seem to have no very 

 clear cases in which we can actually trace the operation of 

 "natural selection." I think, when examined, this will be 

 found to be an instance. 



The spots appear to have arisen in the dog as comparatively 

 recent permanent markings — for protective purposes — after semi- 

 domestication. .\s Mr. Worthington G. Smith says, they are 

 not seen among wild animals allied to the dog. 



They appear to have arisen since the original Red Dog — be 

 he Dhole, Pariah, or Dingo — became pied, and at times black, 

 through domestication. It is only on a black coat that the tan- 

 spots would be conspicuous, and simulate eyes. 



Perhaps Mr. A. R. Wallace may throw light on the matter. 

 The spots seem to be the only really permanent marking among 

 dogs, and are now being bred out. S. E. Peal. 



Sibsagar, Asam, February 19. 



Mr. Peal's suggestion appears to be a probable one, and is 

 supported by Mr. Worthington Smith's observations (Nature, 

 vol. li. p. 57). The spots may have been protective to the 

 animals during sleep, causing them lo look as if awake. The 

 reason that they do not occur in wild dogs may be that the 

 latter conceal themselves when sleeping, which the half- 

 domesticated animals were not able to do. 



Alfred R. Wallace. 



THE AGE OF THE EARTH. 



SINCE physicists do not seem to be in complete 

 accord on the question of the time which has 

 elapsed since the earth first permanently crusted over, 

 it may perhaps be as well to investigate the evidence to 

 be obtained from a study of stratified deposits. 



One of the first to raise a remonstrant voice against 

 the philosophers who demanded practically unlimited 

 time was Sir Archibald Geikie, whose original discussion 

 of the data known regarding the present working of 

 rivers gave us the fraction .jj'jjy as representing the 

 annual rate at which the Mississippi is lowering its 

 basin. The surprise with which this result was received 

 is now almost forgotten, in an unquestioning acceptance. 

 The question of the rate of deposition was next treated 

 by Dr. Haughton, in the year iSSo, with his usual mathe- 

 matical severity. Dr. Haughton, however, preferred to 

 take into consideration six other great rivers besides 

 the Mississippi, and thus obtained the fraction ,^.,q as 

 representing the average thickness of rock which is 

 annually worn away from the terrestrial surface by the 

 denudation of rivers. But the proportion of sea-bottom 

 to land surface is as 145 ; 52, so that if the suspended 

 sediment be spread evenly over the sea- floor, the average 

 rate of accumulation will be si-'i.-r of ^ foo' per annum. 

 The maximum thickness of the stratified series was 

 estimated by Dr. Haughton to be 177,000 feet, and thus 

 if the rate of deposition in the past was on the whole 



