The Astronomical Register. No. 187. JULY. 1878. ROYAL OBSERVATORY, GREENWICH. The Annual Visitation of the Royal Observatory took place on Saturday, June 1, when the Astronomer-Royal presented his report to the Board of Visitors, and the rooms in which the various instruments are deposited, with the grounds, were thrown open to those members of scientific societies who had received cards of invitation from the President of the Royal Society, Chairman of the Board of Visitors. The company assembled was a select and brilliant one. Among those present we noticed the President and ex-President of the Royal Astronomical Society-Lord Lindsay and Dr. Huggins-also Dr. Lassell, Professors Pritchard and Adams, Messrs. Knott, Walker, Beck, and many other astronomical celebrities, including the Transit of Venus Observers— Capt. Tupman and Father Perry. While noting the presence of many astronomers who have comparatively but lately entered on their career, we missed the familiar faces of many whom we have often met during the last twenty or thirty years at similar gatherings. Death has done its work in thinning our numbers, but there is no lack of enthusiastic workers in our science to fall into their places, and carry on the noble and arduous work of practical astronomy. On looking over the report of the Astronomer-Royal there is nothing that strikes us of a novel character; nor should we expect much novelty, since the routine work is of such important interest as to allow only of unavoidable interruptions as may arise from unfavourable weather, unexpected derangement of instruments, and such like. Observations of the ordinary character, have proceeded with the same regularity as in former years. Among the VOL. XVI. principal magnetical results we find that the mean westerly declination for 1877 is 18° 57', the mean dip 67° 40', and the most important of the meteorological, the mean temperature, 49°4, the same as the average of the preceding 36 years. ROYAL ASTRONOMICAL SOCIETY. Session 1878-79. The Last Meeting before the Long Vacation was held at the Society's Rooms at Burlington House, on Friday, June 14th, 1878. Prof. Cayley, M.A., F.R.S., &c., Vice-President, in the Chair. Mr. John Frederick Main, B.A., D. Sc. of University were balloted for and duly elected Fellows of the Society. Mr. Glaisher announced that fifty presents had been received since the last meeting, and the thanks of the Society were voted to the donors. Prof. Adams, who was called upon by the President, said: The communication I have to make to the Society will be very short, and I am afraid it is not one that can be followed by all present in the room. It is a note On a remarkable property in the analytical expression for the constant term in the reciprocal of the moon's radius rector, or what is commonly called the constant term of the moon's horizontal parallax. This constant has been developed in the lunar theories of Plana, Pontécoulant, and the more recent one of Delaunay, in terms of certain constant quantities. These are the eccentricities of the orbits of the moon and earth, the inclination of the moon's orbit to the ecliptic, and the ratio of the mean motions of the sun and moon which is denoted by m. The constant part of the reciprocal of the radius vector contains terms depending on the powers and products of the squares of the eccentricity and inclination of the lunar orbit, each of these terms having a co-efficient which is a function of m and of the square of the eccentricity of the orbit of the earth. Plana found that the co-efficients B and C, of the terms of this expression, which respectively involve the square of the eccentricity and the square of the inclination, both vanished, as far as he carried the development, which was not very far, he only taking account of m2 and m3. Pontécoulant carried the development of B and C as far as m5 and found that the additional terms likewise vanished, but he did not take into account the portion of these co-efficients depending on the square of the eccentricity of the earth's orbit. The facts thus observed gave some probability to the presumption that the following terms in m would likewise be found to vanish. But Pontécoulant and Plana did not show at all why these different terms vanished, for the co-efficients were found in a number of different parts that did not vanish separately, but only when collected together into one sum. Therefore, of course, it was left doubtful how far this observed law might hold good, and it was evident that in order to find whether there is any such general law, one must adopt different methods from those of Plana or Pontécoulant. After reflecting on the subject for some time, I found a general proof of the property that these co-efficients B and C will identically vanish, no matter how far you carry the developments. That appeared to me a very remarkable property. After a considerable time, when I returned to the subject, I found a much simpler proof than had occurred to me at first, and it is that proof that I now beg to communicate to the Society. Much more recently I have considered the terms of the next higher order with respect to the eccentricity and inclination, and I have found two simple and remarkable relations between the coefficients of these terms and the co-efficients of some of the leading terms of the analytical expressions for the mean motions of the lunar perigee and node. Prof. Cayley: If I understand it rightly, the ordinary process gives these co-efficients in different parts, so that there is a verification in showing that these seem to exhibit these relations. Prof. Adams: Quite so. Mr. Neison: The communication of Prof. Adams has great interest for me. He has solved a problem which I have tried, but only with partial success. He shows that these co-efficients completely vanish, whereas I have only gone so far as to show that they vanish as far as m3. Prof. Adams: Pontécoulant did the same. Mr. Neison: These terms depend on the square and higher powers of the disturbing forces. I show that, as far as the second power of the disturbing force, these terms are multiplied by the co-efficient of the term in their argument, and as this co-efficient must be zero to give this constant portion of the parallax, these terms must vanish. These terms. B and C, therefore, as far as the second power of the disturbing force or to the order m3, must disappear. I have not yet extended it to the higher power of the disturbing force. Prof. Adams: I do not take the powers of m. I prove that the co-efficients identically vanish without assuming any form of development in m, which simplifies the matter very much. My investigation takes into account all powers of the disturbing force. I prove the property in question by showing that the function which gives rise to the terms in B and C is an exact differential of a certain function of the moon's co-ordinate, and therefore cannot have a constant part, such as these terms are. They must, therefore, identically vanish. Captain Tupman read a paper On the measurements of the Transit of Venus photographs. He said that the photographs which had been measured were taken with the five photoheliographs made by Mr. Dallmeyer for the transit of Venus expeditions, on "patent plates," six inches square, the images of the sun being very nearly 39 inches in diameter. The dry process of Captain Abney was used throughout. The measuring instrument, the determination of the errors of its glass millimetre scale, and the method of obtaining the optical distortion of the photoheliographs, had already been described in the Society's proceedings. It had been found by an elaborate investigation that the lines of equal distortion were sensibly circles concentric with the centre of the field. The actual correction for distortion for that zone of the field in which the points to be measured generally fell, was exhibited on the board, and was almost identical for all five instruments. Before commencing the measures of a negative, the position of the line of centres was marked upon the film by a simple mechanical process. This operation had been performed independently by Mr. Burton and himself, with no sensible difference. He had paid no attention to the marks left by Mr. Burton on the plates, and found that his own coincided with them in direction. In placing the negative in the instrument, the circular carrier was turned about until the line of centres was truly parallel to the direction of the sliding motion of the microscopes. When the negatives are placed under the microscope, with an amplification of only five or six diameters, the limbs of both planet and sun, even those which are pretty sharp to the unaided eye, become extremely indistinct, and the act of bisecting a limb with the wire or cross of the micrometer is mere guess work. The deposit of silver fades off gradually to nothing, and the denser the film the broader generally is the zone of fading off, and the more uncertain the measures. In many cases the difficulty is aggravated by ruggedness due to atmospheric disturbances, but the smooth and gradual fading off is the chief cause of uncertainty of measurements. There is only one really sharp picture in the whole collection, including the Indian and Australian contingents, and that is one of Captain Waterhouse's wet plates taken at Roorkee, with a Dallmeyer instrument precisely similar to the others. It should be remarked that in these instruments the artist has attempted to unite the photographic and visual foci on the collodion film. No doubt some sharpness of the photographic image was thus sacrificed, but this has little or nothing to do with the unfortunate failure of the photography generally. Each photograph had been measured six times by Mr. Burton, and six times by himself. He was not able to include in his series of measures all the photographs measured by Mr. Burton, for the reason that when some of them were viewed through the microscope he could see nothing to bisect, either from the extreme faintness of the film, or from its too gradual fading off. Mr. Burton generally employed a cross of webs, but he had preferred a single very fine web, the breadth of which was eliminated in the mean by the mode of bisecting. It had been suggested that the measuring instrument should possess the power of rotating the sun's image about a mechanical centre. This would be useful in some cases of rugged limbs, when the sun's image was not rendered elliptical by refraction, but in his opinion would make no material difference in the accuracy of measurement. The rotation could only be applied to the limbs of the sun, whereas, perhaps, the greatest difficulty had been at the limbs of the planet. From the measures corrected for distortion were obtained the photographic diameters of the sun and of Venus, the former presumably enlarged, the latter diminished, by irradiation, in a sensibly equal degree. The sum of the measured diameters in millimetres was compared with the sum of the tabular diameters, subject to errors, for the scale value, and thus every photograph furnished its own scale. The paper then gave the formulæ by which the measured distance of centres affected by errors of semi-diameters was compared with the tabular distance affected by errors of parallax, right ascension, and north polar distance. From each photograph was formed an equation involving all the unknown quantities, of which the errors of parallax and of semi-diameters were the more important. The rigorous solution of the equations resulting from Mr. Burton's measures was |