In November, 1878, Sir William Thomson suggested to Mr. IJ. H. Darwin that he should investigate, experimentally, the lunar disturbance of gravity and the question of the tidal yielding of the solid earth. This committee of the British Association was subsequently reappointed, and the authors' names were added to the list of its members. In May, 1879, the authors visited Sir William Thomson at Glasgow, and there saw an instrument which, although roughly put together, he believed to contain the principle by which success might perhaps be attained. The instrument was erected in the physical laboratory of the University of Glasgow. The following are the rough details: A solid lead cylinder, weighing perhaps a pound or two, was suspended by a fine brass wire, about five feet in length, from the center of the lintel or cross-heam of the solid stone gallows which is erected there for the purpose of pendulum experiments. A spike projected a little wa,),' out of the bottom of the cylindrical weight; a single silk fiber, several inches in length, was cemented to this spike, and the other end of the fiber was cemented to the edge of an ordinary galvanometer mirror. A second silk fiber, of equal length, was cemented to the edge of the mirror, at a point near to the attachment of the former fiber. The other end of this second fiber was then attached to a support, which was connected with the base of the stone gallows. The support was so placed that it stood very near to the spike at the bottom of the pendulum, and the mirror thus hung by the bifilar suspension of two silks, which stood exceedingly near to one another in their upper parts. . It is obvious that a small displacement of the pendulum, in a direction perpendicular to the two silks, will cause the mirror to turn about a vertical axis. A lamp and slit were arranged, as in a galvanometer, for exhibiting the movement, of the mirror by means of the beam of light reflected from the mirror. It was found to be in incessant movement, of so irregular a character that jt was hardly poMible to localize the mean position of the spot of light on the screen, within five or six inches. On returning to the instrument after several hours, the observer frequently found that the light had wandered to quite a different part of the room, and it was sometimes necessary to search through nearly a semicirde before finding it again. The cause of this extreme irregularity of the movement of the pendulum was obscure; and as Sir Willie Thomson was of opinion that the instrument was well worthy of careful study, the authors determined to undertake a series of experiments at the Cavendish Laboratory at Cambridge. Accordingly throughout 1880 they proceeded to make experiments with an instrument which involved the principle above explained. Several modifications of some importance were introduced. The pendulum was hung in fluid, in order to quickly destroy the oscillations generated by local tremors, and, being suspended by two wires, it was only free to OStJillate in one direction, namely, the meridian. There was also introduced an apparatus, which we have not space to explain, by which a known very small horizontal thrust might be applied to the pendulum. By means of this the actual displacements of the pendulum were determinable from the observed displacements of the spot of light on the screen. The image on the screen was found tobein a state of continual agitation of an irregular character, so that it was not posible to take a reading with very great accuracy. But as * Report of the Committee, consisting of Mr. G. H. Darwin, Prof. Sir William Thomson, Prof. Tait, Prof. Grant, Dr. Siemens, Prof. Purser, ^rol. G. Forbes, and Mr. Horace Darwin, appointed for the Measurement of the Lunar Disturbance of Gravity. Account of experfments by G. H. toiii and H. Darwin, read at the British Association, York, September, 1881. the pendulum was hung in fluid, the agitation was not nearly so great as it had been in the instrument at Glasgow. The observers also found that the pendulum was subject to a diurnal oscillation, and that it stood furthest north toward 6 P.M., and furthest south toward 6 A.M. Superposed on this motion was a gradual change of the mean diurnal position, for during two months the pendulum moved northward. The instrument was found to exhibit the flexure of the stone piers of the gallows, even when the force employed was only a slight pressure with one finger. Water poured on the ground round the basement of the stone gallows tilted tile whole structure over, and very small changes of temperature in the stone piers were found to give distinct effects. It was concluded that one foot of displacement in the spot of light on the scale corresponded with 1” of change in the direction of the plumb-line with reference to the base of the gallows. From these experiments the authors concluded that the instrumentwas susceptible of all the delicacy requisite, but that the mode of suspension was unsatisfactory. Accordingly in 1881 they proceeded to erect a new instrument in which the support for the pendulum was a copper tube, which itself formed the envelope for containing the fluid in which the pendulum was suspended. The whole apparatus was immersed in a large mass of water. and the observations were taken from outside of the room by means of a telescope. The unsteadiness of the image was diminished, probably on account ofthe precautions taken against inequalities of temperature in various parts of the instrument, and because the pendulum was hung in a very confined space. The accuracy with which readings could bc taken was thus increased. Similar diurnal oscillations of the pendulum were again observed, and a similar slow change in the mean diurnal position. The authors therefore concluded that these changes are Ii real phenomenon, and do not depend upou changes of temperature in tile instrument itself. Tbey also noted that there are periods lasting for several days in which the pendulum is in a state of continual agitation, so that the readings taken at a few seconds apart do not agree inter Be, and that there are other periods of abnormal quiescence. These periods do not seem intimately connected with the external meteorological conditions, at least as far as the experiments have been hitherto carried. The pendulum was found to be practically insensible to the effect of local tremors, such as are produced by hitting the stone support or stamping on the ground in the immediate neighborhood of the instrument. But it was extraordinarily sensitive to steady forces. If a force be applied at a point on the floor a dimple is produced in consequence of the elastic yielding of the soil, and any object on the floor is slightly tilted toward the point where the force is applied. Now when a persou stood in the room at sixteen feet away from the instrument, and again at seventeen feet, the difference was rendered distinctly evident between the amounts of inclination toward the point of pressure of the stone basement supporting the pendulum in the two cases. Although no great pains had been taken to render the instrument as sensitive as possible, it was found that an alteration of the pl^mb- line through one one-hundredth of a second of arc was distinctly measurable. The second part of the paper contains an account of the work of some of the previous observers on the same subject. M. ZSllncr's instrument, the “ horizontal pendulum,” is described. It does not appear that any extensive series of observations have been made with it. An account of M. d'Abbadie's work is next given. He made his observations by means of reflections from a pool of mercury, and the site of his experiments was at Abbadia, near Hendaye, in the south of France. He found that there were periods of agitation and of quiescence in the mercury, apparently without reference to any perceptible external causes. There were also gradual changes of level extending over several months, ana the experience . of several year showed that there was-something like an annual inequality of level. There were sometimes changes through 2” or Zr which took place in a few hours. At Geneva M. Plantamour has been making observations concerning variations of the plumb-line, by means of delicate levels, and has arrived at results in general accordance with those of M. d'Abbadie. The experiments of the authors present a general con firmation of these conclusions, and show tbat the earth's sur face is in a state of continual movement. With reference to this continual oscillation the authors adduce an experiment which was commenced about three and a half years ago by Mr. Horace Darwin at Down, in Kent. The experiment was undertaken in connection with Mr. Darwin's investigation of the geological activity of earthworms. There are two stout metal rods, one of iron and the other of copper. The ends were sharpened, and they were hammered down vertically about eight feet deep into the soil, and they are in contact with one another, or nearly so. The ends were then cut off about three inches above the ground. A stone was obtained like a small grindstone, with a circular hole in the middle. This stone was laid on the ground with tbe two metal rods appearing through the hole. An arrangement with a micrometer screw enables the observer to take contact measurements of the position of the upper surface of the stone with regard to the rods. The stone has, on the whole, always continued to fall, but the general descent can only be gathered from observations taken at many months apart, for it is found to be in a state of continual vertical oscillation. The measurements are so delicate that the raising of the stone produced by one or two cans full of water poured on the ground can easily be perceived. The effect of frost and the wet season combined is strongly marked, for on January 23, 1881, the stone was 4 12 mm. higher than it had been on September 7, 1880. The prolonged drought of the present summer has had a great effect, for between May 8 and June 29 the stone sank through 5'79 mm. The changes produced in the height of the stone are, of course, entirely due to superficial causes; but the amounts of the oscillations are certainly surprising, and although the basements of astronomical instruments may be very deep, they cannot entirely escape from similar oscillations. The last part of the paper contains a discussion of the present aspects of the question, and iI. criticism of the various forms of instrument which have been used hitherto for the detection of small variations in the position of the plumb-line. The authors suggest that greater precautions should be taken in the protection of the piers of transit instruments from changes of temperature, and in the drainage of the soil round the basements of the piers; tbey also draw attention to the disturbing effect of the weight of the observer's body. They express a hope that systematic observations of changes of level may be undertaken at a number of observatories by some instrument analogous to that with which they are working. They are still prosecuting their experiments, and they are in hopes of being able to reduce their instrument to a convenient form, so that it may not be difficult to transport or to erect. In conclusion they state that they have no hope of being able to observe the lunar attraction in the present site of observation, but they think it posssible that they may devise a portable instrument which shall be amply sensitive enough for such a purpose, if the bottom of a deep mine should be found to give a sufficiently invariable support for the instrument.