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Hence, referring events to the time at which light leaves O (or more generally the line XOY), we see that in case (a) the apparent eclipse is retarded and in case (b) it is accelerated by an equal amount. What happens in case (c) when the bodies are equal?
It is suggested that there is neither retardation nor acceleration, i.e. that the apparent eclipse takes place at the same time as the true eclipse, and this is actually the case. It was Professor Dyson who called attention to this case after reading Father Stein's paper at my request.
(c) When the masses are equal, they both revolve round O, their common C.G. The position for true eclipse is, bright body at A and dark at B; but the light which then leaves the bright body does not suffer eclipse, since when it reaches B the dark body will have moved away. Let aA, Aa, bB, Bẞ be four equal
small arcs described by either body in time T which light takes to cross the semi-orbit. Then the sequence of events is as follows:
The eclipsed light must start before the bright body has reached A, and is eclipsed by the dark body after it has left B, so that the position for apparent eclipse is displaced from AB to aß. But we have no means of noting this displacement in space in the case of Algol variables. All we could note would be a change in epoch, and this is zero; for we see that the eclipsed light leaves XOY at the moment of true eclipse, when the bodies are at AB.
Hence, whatever the size of the orbit, when the masses are equal there will be no change in epoch of eclipse due to lightequation.
In other cases there will be a change of epoch,-a retardation if the dark body is larger, an acceleration if it is smaller. But the change will be small unless the masses are very unequal; and it will depend not only upon the size of the orbit, but on the ratio of the masses, which cannot be separately determined.
In Professor Barnard's paper, page 357, line 27,
for Struve read Struve's.
In Mr. Baldwin's paper, page 369 (Table I.), the headings of the last four columns should be, respectively,
d log sin2 I; Zenith dist.; Extinction corr.; AM;
and the bracket over these columns omitted.
H. F. NEWALL, Esq., M.A., F.R.S., PRESIDENT, in the Chair. Captain Richard Algernon Craigie Daunt, D.S.O., Lynalta, Newtownards, Co. Down, Ireland,
Edgar Odell Lovett, Ph.D., Professor of Astronomy, Princeton University, New Jersey, U.S.A.,
were balloted for and duly elected Fellows of the Society.
The following candidates were proposed for election as Fellows of the Society, the names of the proposers from personal knowledge being appended:
Warin Foster Bushell, The Hermitage, Harrow (proposed by Col. G. L. Tupman);
Charles P. Butler, A.R.C.Sc., F.R.P.S., Solar Physics Obser-
William Doberck, Ph.D., late Director, Hong Kong Observatory,
James Nangle, Technical College, Sydney, N.S. Wales, Aus-
Charles W. Raffety, Wynnstay, Woodcote Valley Road, Purley,
Rev. T. J. Williams-Fisher, M. A., Rector of Norton, Atherstone
Seventy-one presents were announced as having been received since the last meeting, including amongst others :-Lieut. A. ff.
Garrett, The Jaipur Observatory and its builder, presented by the author; Greenwich Astrographic Catalogue, vol. ii., 16 charts of the Astrographic Chart of the heavens, and Observations of the planet Eros, 1900-1901, presented by the Royal Observatory, Greenwich; Professor E. S. Holden, Galileo, and other tracts, presented by the author; Oxford Astrographic Catalogue, vol. iv., presented by the University Observatory, Oxford; Pennsylvania University Publications, Catalogue of 648 double stars discovered by Professor Hough, presented by the University; three lantern slides of the Corona of 1908 January 3, taken by Professor Campbell, presented by the Lick Observatory.
An Empirical Law of Astronomical Refraction.
1. The following investigation was originally undertaken with the view of substituting a simple proof of the law of refraction for students who could not follow the more elaborate proof involving the differential equation. But it was a surprise to find how closely the observed refraction could be represented with so rough a supposition as that of three, or even two, homogeneous shells of atmosphere; and the question was suggested whether, in the present state of our knowledge, more elaborate hypotheses were really justified. If a rough supposition fits the facts, clearly it is no proof of the correctness of a more elaborate one that it also fits the facts.
2. Moreover, suspicion of the correctness of existing hypotheses was suggested from another direction. Meteorologists are finding that the temperature of the atmosphere does not follow a smooth gradient, as is generally assumed in refraction hypotheses: at a certain height a wholly unexpected state of things has been found to exist. According to M. Teisserenc de Bort there is above 10 or 12 km., an "isothermal layer" in which the temperature ceases to fall as we ascend; and the conditions are similar over parts of the world where the temperatures close to the surface differ widely. It is difficult to reconcile these results of observation with the hypotheses usually adopted in constructing tables of refraction.* It is, however, not intended to examine at present the consequences of taking M. Teisserenc de Bort's work into account;-merely to show that it may not be difficult to do so when we have fuller information, without, perhaps, dislocating existing refraction tables.
3. First let us consider an atmosphere of one homogeneous spherical layer. Let C be the Earth's centre; OM a section of its surface through C and the star; LB the section of the boundary of
* I am indebted to Mr. Saunder for a reference to a paper by Professor Bakhuyzen in Konink. Akad. van Weten. te Amsterdam, 1907 January 26; see Nature, 1907 April 4, p. 538; in which the discordance between observation and the assumption usually made is demonstrated by a concrete example.
the atmosphere; ABO the direction of the star's light, refracted once only at the boundary B. The star is thus seen in the direction OBD, instead of in the direction BA.
if z be the ratio of the height of the atmosphere to the
4. The similarity of equations (2) and (3) suggests a geometrical construction for the refraction which is obvious enough, but which I do not remember to have seen in print.
Hence OGC = 4, just as OBC = 4, and the refraction is - GCB. 5. If now we take the case of two homogeneous shells of atmosphere, we see that the refraction will be represented by the sum