July 19, 1917] 



NATURE 



405 



Oceanis Tidal Friction. 



In equaticm (26) of a paper in the current number 

 of the Proceedings of the Royal Society (93 A, pp. 348- 

 59) Mr. R. O. Street has g-iven an expression tor 

 the rate of dissipation of energy in the oceanic tides 

 which is probably the best yet obtained ; it is propor- 

 tional to the square root of the viscosity and to the 

 square of the surface velocit}'. In view, however, 

 of the uncertainty of many of the data involved, which 

 he carefully states, some further discussion of the 

 subsequent numerical application seems desirable. At 

 the end of the paper it is shown that a periodic surface 

 velocity with a maximum of 2 ft. per second all over 

 the ocean, with a viscosity of 1-4x10-^ ft.*/sec., wouW 

 account for a retardation of the earth's rotation of 

 amount 4' of arc per centary per century. Now it is 

 easy to find from equations (11) on p. 303 of Lamb's 

 *■ Hydrodynamics " that the surface velocity in mid- 

 ocean for a tide of height 2 ft. is only of order 004 ft. 

 per second ; on the other hand, the effective viscosity is 

 ver\' much increased on account of turbulence. The 

 available data on this question are scanty, but the 

 writer has shown elsewhere {Monthly Notices of 

 R.A.S., vol. Ixxvi., 1916, p. 512) that the effective 

 viscosity in the ocean is probably of order 4 cm.^ /sec.= 

 4-4X 10-- ft.^/sec Thus Street's retardation must be 

 multiplied by (o-02)-(3oo)i, giving 002' per centur\- per 

 century, which is inappreciable. No great part of the 

 observed lunar acceleration can therefore be attributed 

 to tidal friction in mid-ocean. The dissipation in 

 shallow regions near the coast may be greater, as fhe 

 velocity is greater there, but m view of the limited 

 area concerned the total is unlikely to be important. 

 As the retardation of the earth's rotation that is re- 

 quired to account for the lunar acceleration is about 

 io'-4 per century oer century {ibid., vol. Ixxvii. ; 1917, 

 p. 453), Street's result on the whole confirms those of 

 the earlier investigators, who regarded oceanic tidal 

 friction as very small in amount, and were disposed 

 to refer all the dissipation, if any, to the bodily tides. 



Harold Jeffreys. 



St. John's College, Cambridge. 



Gravitation and Thermodynamics. 



Attentio.v has been given in Nature to various de- 

 ductions from the results of Dr. P. E. Shaw's ex- 

 periments on "The Newtonian Constant of Gravita- 

 tion as affected by Temperature" (Phil. Trans., A, 

 544, 1916). So far as tne present writer is aware, 

 attention has not been directed to the suggestive re- 

 marks of the late Prof. G. F. Fitzgerald, to be found 

 in his Helmholtz memorial lecture (Transactions 

 Chemical Society, 1896, pp. 889-95). I" the course 

 of his reference to Helmholtz 's contribution to the 

 theory of vortex motion, Fitzgerald remarks : — " It is 

 difficult to weigh hot bodies accurately, and, in con- 

 sequence, there does not seem to be anv conclusive 

 proof that the weight of a body does not change with 

 its temperature. It ii: does not do so by a measurable 

 -amount, the simple vortex ring theorv'of matter can 

 hardlv be true." J. S. G. Thom.as. 



709 Old Kent Road. S.E.15, July 4. 



The First New ^oon in the Year 1 B.C. 



In making some computations Fast March about the 

 occurrence of new moon, an error of statement was 

 discovered in the ninth edition of the '■ Encyclopaedia 

 Britannica" under 'Calendar," vol. iv., p. 594, and 

 repeated in the eleventh edition, vol. iv., p. 993; it 

 is also given in Barlov.^ and Bryan's ".Mathematical 

 Astronomy," p. 215. Tlie erroneous statement is that 

 new rnoon occurred on January- i in i b.c. New 

 tnoon in January, i b.c, occurred on Januarv 25, 

 I2h. 26m. Jerusalem Mean Civil Time. 



Dominion Observatory, Ottawa. Otto Klotz. 

 NO. 2490, VOL. 99] 



PHOTOGRAPHS OF AURORA. 



\ TTEMPTS to measure the height of aurora 

 -^^ were made prior to the end of the 

 eighteenth century, and have been repeated at 

 intervals since that date. The most direct 

 method is obviously to determine the parallax as 

 given by synchronous observations at two 

 stations a sufficient distance apart. In the case 

 of the earlier attempts to apply this method, it 

 was only by the merest accident that observa- 

 tions would have been taken simultaneously, and 

 even in that event it was improbable that the 

 same point would have been selected for observa- 

 tion. Thus it was impossible to feel any great 

 confidence in the older results, though, as a 

 matter of fact, some of them were probably not 

 far wrong. After the invention of the telephone, 

 it became p>ossible for two observers a sufficient 

 distance apart to make simultaneous observations 

 with theodolites, but some uncertainty necessarily 

 prevailed as to the identity of the points selected 

 for observation. Observations made in this way 

 at Godthaab, in Greenland, with a 5-8-kilometre 

 base, discussed by Prof. Paulsen thirty years ago, 

 gave for the lower edge of aurora heights vary- 

 ing from o'6 to 67*8 km., the average being only 

 some 20 km. At Godthaab, however, the 

 parallax was too small to measure in some 20 

 per cent, of the cases. 



Towards the end of last century several people 

 succeeded occasionally in attempts to photograph 

 aurora, and in 1909 Prof. Carl Stormer, of 

 Christiania, devised a satisfactorily successful 

 method of securing photographs with only a few 

 seconds' exposure, and in 1910 he and his assist- 

 ants secured a good many pairs of photographs 

 from two stations 5 km. apart, near Bossekop, 

 in the north of Norway. 



In 191 3 Prof. Stormer took a much larger num- 

 ber of photographs, employing a longer base, 

 observations being made at Bossekop and Store 

 Korsnes, 27^ km. apart. His photographs in- 

 clude known stars as well as the aurora. An 

 auxiliary photograph of the face of a watch gives 

 the exact time, and thus the position of the star. 

 A series of corresponding |X)ints can usuallv be 

 recognised in the two photographs, and the 

 geographical position as well as the height of the 

 aurora — whether an arc, a band, a curtain, or 

 a ray — can be calculated. The accompanying 

 figures are reproductions of two pairs of photo- 

 graphs obtained by Prof. Stormer and his 

 assistant in 191 3. 



Prof. Stormer has recently discussed in 

 Terrestrial Magnetism a number of the measure- 

 ments made on the photographs which he took 

 in 191 3. The majority of his calculated heights 

 refer to the lower edge of the aurora, partly, no 

 doubt, because it is usually the best defined, and 

 partly because it possesses especial interest in 

 connection with the theory which he supports, 

 viz. that aurora arises from electrical corpuscles 

 discharged from the sun. On this theory, the 

 lower the visible limit of aurora, the more penetra- 

 ting the discharge. Out of about 2500 height 



