86 



NATURE 



[November 8, 19 17 



of stars of which the latitude of one star only 

 was observed, while that of the other was ob- 

 tained by means of Ptolemy's difference of lati- 

 tude. Therefore, the longitudes of only about 

 900 stars were actually observed, and the lati- 

 tudes of about 878 stars. But there is a strong 

 suspicion that the original observations should be 

 still further reduced, as there are some forty or 

 fifty stars the errors of the places of which resemble 

 the errors of Ptolemy, and thus suggest a deriva- 

 tion from the Almagest. These very interesting 

 results of Mr. Knobel's examination of the cata- 

 logue have escaped the attention of all previous 

 historians of astronomy. 



The comparison with modern star-places shows 

 that the accuracy of Ulugh Beg's observations 

 was not much superior to that of Ptolemy's. 

 Mr. Knobel reproduces a drawing of an altazi- 

 muth from a Persian MS. in the British Museum 

 (a treatise on astronomical instruments), which 

 shows the use of diagonal scales for subdividing 

 graduations. As the MS. dates from a.d. 1700, 

 the influence of knowledge derived from Western 

 sources is not excluded. But as diagonal scales 

 were known to Levi ben Gerson, a Spanish Jew 

 who died at Avignon in 1344, it is very possible 

 that some later Arabian observers may have 

 employed them. Judging from his star-places, 

 Ulugh Beg scarcely did so. We congratulate 

 Mr. Knobel on this completion of the long labours 

 of Prof. Peters and himself on ancient star- 

 catalogues. J. L, E. D. 



OUR BOOKSHELF. 



A Chemical Sign of Life. By Shiro Tashiro. 

 (The University of Chicago Science Series.) 

 Pp. ix+142. (Chicago: University of Chicago 

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 1917.) Price I dollar or 45. net. 

 Dr. Tashiro gives a useful and readable sum- 

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 the production of carbonic acid in nerve and in 

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 gas as a sign of life analogous to the "blaze 

 currents " described by Dr. Waller. The magni- 

 tude of the CO2 production which he observes in 

 nerve fibres has raised doubts as to the exact 

 significance to be ascribed to the results obtained. 

 The author deals with some of the criticisms 

 which his work has evoked. 



Morphology of Oymnosperms. By Profs. J. M. 



Coulter and C. J. Chamberlain, Revised edition. 



Pp. xi + 466. (The University of Chicago 



Press.) Price 5 dollars net. 

 This important work was reviewed at length in 

 the issue of Nature for August 10, 191 1 (vol. 

 Ixxxvii., p. 171). The revised edition is in no 

 sense rewritten, but important changes and 

 additions occur, the more important of which are 

 in the chapter on Cycadales and in the biblio- 

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 NO. 2506, VOL. 100] 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for 

 opinions expressed 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.] 



Tidal Energy Dissipation. 



Mr. Street is in error in attributing to me (Nature,, 

 October 25, p. 145) the "contention that viscous 

 action in a solid earth cannot be an appreciable cause 

 of the slowing of its rotation.'-' I have never made 

 any such assertion, it is opposed to my personal 

 opinion, and in the present state of knowledge it is 

 quite impossible either to affirm or to deny a state- 

 ment of such definiteness. His criticisms of the law 

 of viscosity used by me (M.N., R.A.S., vol. Ixxvii., 

 pp. 449-56) are confined to its precise mathematical- 

 form, to which I attach little importance, and do 

 not touch the physical conceptions underlying it, which 

 are fundamental. The mathematical argument was 

 only a numerical illustration of the order of magni- 

 tude of the effects to be expected from these. 



The theory that viscosity in the solid earth is the 

 cause of the lunar secular acceleration requires its 

 effect to be considetable for variable stresses with 

 periods of the order of a day. If, then, the viscosity 

 is of such a character as to permit an indefinite flow 

 when a constant stress is applied for a long enough 

 time, then for stresses with a period of a year or more 

 the substance will have time to flow like a liquid, 

 keeping approximately the hydrostatic form through- 

 out the changes. Hence the Eulerian nutation, a 

 long-period vibration depending for its existence en- 

 tirely on solid rigidity, could not persist. Similarly, 

 annual variations in the distribution of mass over the 

 surface would be compensated iby internal flow, and 

 there could therefore be no annual variation of latitude. 



If, on the other hand, the viscosity is not of a type 

 that permits indefinite flow, the strain when a constant 

 stress is applied must tend to a finite value, and 

 afterwards remain approximately constant. The effect 

 of viscosity must then be limited to the initial stage. 

 In the case of a periodic stress the period of which 

 is long compared with this initial stage^ the rigidity 

 will be of much more importance than viscosity, and 

 the substance will behave nearly as if perfectly elastic. 

 On the other band, if the period is short in com- 

 parison, viscosity will be of greater importance. This 

 is supported by the fact that if the viscous forces are 

 directly proportional to the rate of straining, as is 

 inherently probable on account of the analogy^ to elec- 

 tric resistance and fluid viscosity, the same is found 

 to hold. On such ideas the law I called that of 

 " firmo-viscosity " is based. If, then, the effect of such 

 vistosity is considerable when the period is twelve 

 hours, it must he more important than elasticity when 

 the period is only a few seconds, as in the case of 

 earthquake wave's. Thus the transmission of these 

 waves would he prevented. It follows that firmo-vis- 

 cosity is absent from the earth so far down as seismic 

 waves travel; it may, however, be important at still 

 greater depths. 



If on the application of a constant stress to a body 

 the strain at once assumed a finite value, then slowly 

 increased for a few days, and afterwards remained 

 constant, the viscous properties of such a body would 

 bear a close resemblance to those of the earth as a 

 whole. In this case, however, the rigidity found from 

 the Eulerian nutation should be much less than that 

 found from earthquakes, which does not appear to be 

 the case. This suggestion, therefore, alters the diffi- 

 culty without removing it. 



