yan. 20, 1887] 



NA TURE 



28 



SOCIETIES AND ACADEMIES 



London 



Royal Society, November 25, 1S86. — " On the Dynamical 

 Theory of the Tides of Lon<j Period." By G. II. Danvin, 

 LL. D. , F. R. S. , Fellow of Trinity College, and Plumian Professor 

 in the University of Cambridge. 



Laplace sought to show that, as regards the oscillations of 

 long period, called by him "of the first species," friction would 

 suffice to make the ocean a-sume at each instant its form of 

 equilibrium. His conclusion is no doubt true, but the question 

 remains as to what amount of friction is to be regarded as sufific 

 ing to produce the result, and whether oceanic tidal friction can 

 be great enough to have the effect which he supposes it to 

 have. 



In oscillations of the class under consideration, the water 

 moves for half a period north, and then for half a period south. 

 Now in systems where the resistances are proportional to 

 velocity, it is usual to specify the resistance by a modulus of 

 decay, namely, that period in which a velocity is reduced by 

 friction to 1-^2783 of its initial value; and the friction 

 contemplated by Laplace is such that the modulus of decay is 

 short compared with the semi-period of oscillation. 



The quickest of the tides of long period is the fortnightly 

 tide, hence, for the applicability of Laplace's conclusion, the 

 modulus of decay must be short compared with a week. Now 

 it seems practically certain that the friction of the ocean bed 

 would not much affect the velocity of a slow ocean current in a 

 day or two. Hence we cannot accept Laplace's hypothesis as to 

 the effect of friction. 



This paper then gives a solution of the equation of motion 

 when friction is entirely neglected. The method is indicated 

 in a footnote to a paper by Sir William Thomson {Philosophical 

 Magazine, 1875, ^°'' S°> P- 280), but has never been worked out 

 before. 



It appears in the result that with an ocean 1200 fathoms 

 deep, covering the whole globe, the fortnightly tide has about 

 l/7th of its equilibrium value at the pole, and nearly a half at the 

 equator. If the ocean be four times as deep we get analogous 

 results, and it appears that with such oceans as we have to deal 

 with the tide of long period is certainly less than half its 

 equilibrium result. 



In Thomson and Tait's "Natural Philosophy" (edition of 

 1883) a comparison is made of the observed tides of long period 

 with the equilibrium theory. 



This investigation was undertaken in the belief of the cor- 

 rectness of Laplace's view as to the tides of long period, and 

 was intended to evaluate the effective rigidity of the earth's 

 mass. 



The present result .shows that it is not possible to attain any 

 estimate of the earth's rigidity in this way, but as the tides of 

 long period are distinctly sensible, we may accept the investiga- 

 tion in the "Natural Philosophy" as generally confirmatory of 

 Thomson's view as to the great effective rigidity of the whole 

 earth's mass. 



There is one tide, however, of long period of which Laplace's 

 argument from friction must hold true. In consequence of the 

 regression of the nodes of the moon's orbit there is a minute tide 

 with a period of nearly nineteen years, and in this case friction 

 must be far more important than inertia. Unfortunately this 

 tide is verj' minute, and as is shown in a Report for 18S6 to the 

 British Association on the tides, it is entirely masked by 

 oscillations of sea-level produced by meteorological or other 

 causes. 



Thus it does not seem likely that it will ever be possible to 

 evaluate the effective rigidity of the earth's mass by means of 

 tidal observations 



December 9. — "Note on a New Form of Direct-Vision 

 Spectroscope." By G. D. Liveing, M.A., F.R.S., Professor 

 of Chemistry, and J. Dew.ar, M..\., F.R.S., University of 

 Cambridge. 



December 16, 1886. — " Preliminary Account of the Observa- 

 tions of the Eclipse of the Sun at Grenada in August 1886." 

 By Captain Darwin, R. E. Communicated by Lord Rayleigh, 

 Sec.R.S. 



The instruments allotted to me consiste;! of the coronagraph 

 and the prismatic camera ; the two instrunr ents being mounted 

 on the same equatorial stand. 



The photogr.iph obtained with the prismatic camera shows 



several images of the prominences, and it therefore gives every 

 promise of yielding good results when measured and examined. 



The five- and ten- second photographs of the corona show signs 

 of a slight vibration, but they will be useful for the inner part of 

 the corona. As my main object was to obtain instantaneous 

 photographs, these long-exposure plates had to be obtained by 

 working the automatic shutter by hand ; it was this probably that 

 caused the vibration. 



The instantaneous photographs of the corona when developed 

 were complete blanks, proving that the exposure was too short. 

 It should, however, be observed that this does not prove that the 

 light of the corona was insufficient to cauie an appreciable effect 

 on the plate if combined with other light. More light energy is 

 necessary to start photographic action than is required to produce 

 a visible difference of shade when once the action is started. 



Many of the photographs taken during partial eclipse show 

 what may be described as a false corona, that is, an increase of 

 density near the sun and between the cusps, rr in front of the 

 moon. In none of them can the moon be seen eclipsing the 

 corona. 



The results, therefore, are adverse to the jiossibility of obtain- 

 ing photographs of the corona in sunlight ; it is, however, I 

 consider, by no means proved that the method is impossible. But 

 at present I am inclined to consider that the result tends to show 

 that ?t practical method of obtaining photographic records of the 

 corona during sunlight is not likely to be ( btained. The trial 

 was not conclusive because the conditions were very unfavour- 

 able. In order to reduce the air-glare to a minimum, so that 

 the light of the corona shall not be overpowered, the following 

 points must be observed : — 



(i) The air should be clear and dry. 



(2) The sun should be near the zenith. 



(3) The station should be at a considerable elevation above 

 the sea. 



(4) The corona, if it does vary in intensity, should be at its 

 maximum brightness. 



Now every one of these conditions was unfavourable. The 

 air was saturated with moisture, the sky was of a hazy blue, the 

 sun was low, the station was near the sea-level, and the corona, 

 according to the genera! impression, was not so bright as on 

 other occasions. 



I hope, however, to deal more fully with these considerations 

 on another occasion. 



Mathematical Society, January 13. — Sir J. Cocl-le, F.R. S., 

 President, in the chair. — Prof. G. B, Mathews was elected a 

 Member. — The following communications were made : — Con- 

 jugate " Tuckei" circles, by R. Tucker. — On the incorrectness of 

 the rules for contracting the processes of finding the square and 

 cube roots of a number, by Prof. M. J. M. Hill. — On the com- 

 plex angle, by J. J. Walker, F.R.S. — Shorter communications 

 were also made by Messrs. Heppel, Macmahon, and S. Roberts, 

 F. R.S., in the discussion of which several members took part. 



Victoria Institute, Jan. 3. — Dr. Wright read a paper describ- 

 ing the Ilittite monuments which he had examined in the East, 

 and giving an account of the present position of the question as to 

 the age and extent of the country of the Hittites. Many after- 

 wards joined in the discussion. Thirty members and associates 

 weie elected, and it was announced that 100 had joined during 

 the past year, making l2O0 members the Institute's strength. 



Edinburgh 



Mathematical Society, January 14. — Mr. W. J. Mac- 

 donald, Vice-President, in the chair. — Prof. Chrystal gave a 

 paper on the generation of any curve as a roulette; and Mr. 

 William Renton contributed some mnemonics for plane and 

 spherical trigonometry. 



Paris 



Academy of Sciences, January 10. — M. Gosselin in the 

 chair. — Note on the works of the late M. Oppolzer, Correspond- 

 ing Member of the Section for Astronomy, by M. Tifserand. 

 In this obituary notice reference is made more especially to the 

 eminent astronomer's " Traite des Orbites," his determination 

 of the orbits of the planets and many comets, and his theory of 

 the movement of the moon. — On various phenomena presented 

 by the artesian wells recently sunk in Algeria, by M. de 

 Lesseps. The results are described of unusually successful 

 operations undertaken in 1885 and last year in the region of the 

 Shotts, where one well, yielding as much as 8000 litres per 



