scheme, since his time, has been re-presented in other and perhaps visually clearer ways. Shown here is a vector presentation indicating, for two different positions, P1 and P2, of the Moon in its orbit around the Earth, the respective vectors LS1 and LS2 for the perturbing acceleration due to the Sun. The Moon's position at P1 is fairly close to what it was at P in Newton's diagram; corresponding perturbation LS1 is like Newton's LS in size and direction. At another position P2, the Moon is farther away from the Sun than the Earth is, the Sun's attraction LQ2 on the Moon is weaker than the Sun's attraction SQ=SQ2 on the Earth, and then the resulting perturbation LS2 points obliquely away from the Sun. Constructions like those in Newton's diagram can be repeated for many different positions of the Moon in its orbit. For each position, the result is a perturbation vector like LS1 or LS2 in the second diagram. Shown here is an often-presented form of the diagram that summarises sizes and directions of the perturbation vectors for many different positions of the Moon in its orbit. Each small arrow is a perturbation vector like LS, applicable to the Moon in the particular position around the orbit from which the arrow begins. The perturbations on the Moon when it is nearly in line along the Earth-Sun axis, i.e. near new or full moon, point outwards, away from the Earth. When the Moon-Earth line is 90° from the Earth-Sun axis they point inwards, towards the Earth, with a size that is only half the maximum size of the axial (outwards) perturbations. (Newton gave a rather good quantitative estimate for the size of the solar perturbing force: at quadrature where it adds to the Earth's attraction he put it at of the mean terrestrial attraction, and twice as much as that at the new and full moons where it opposes and diminishes the Earth's attraction.) Newton also showed that the same pattern of perturbation applies, not only to the Moon, in its relation to the Earth as disturbed by the Sun, but also to other particles more generally in their relation to the solid Earth as disturbed by the Sun (or by the Moon); for example different portions of the tidal waters at the Earth's surface. The study of the common pattern of these perturbing accelerations grew out of Newton's initial