Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

Why Seven Steps?

The number seven meant a lot to Newton. He sensed its mythic resonance, for example, is his seven colours of the rainbow - where he added an extra colour, indigo, that no-one could see in order to make up a 'complete spectrum' of seven (Cohen, 1980. The Newtonian Revolution, p. 204). Likewise his Optics (1704) found seven steps of colouration in the 'Newton's rings', and was itself composed in seven sections (both these observations were made by D.Castillejo (1986. The Expanding Force in Newton's Cosmos, p. 97). His more esoteric writings concerning the decoding of the apocalypse also show much seven-fold symbolism.

The sevenfold structure became a distinctive hallmark of the various 'Newtonian' ephemerides that used TMM. To quote Craig Waff,

The theory had a symmetry about the Equation of Centre (the ellipse function) as the central, 4th equation, larger than any other step.

It would appear that Newton had found just about all of the lunar equations available to be found, at the level of accuracy available to him (see, Comparison with Modern Equations). For comparison, Mayer's lunar theory of 1754 was said to have 13 equation-steps.

Expressing the Newtonian sequence of lunar equations in their simplest possible form, without any amplitude-modulation or steps of equation, and with amplitudes expressed in arcminutes:

Thus, the second equation goes through two cycles per Sun-apse cycle, as the Variation has two cycles per lunar month. I found that the four new equations all worked, in that TMM worked better with each of them than without, as was not implied by earlier commentators (Baily, 1835, Whiteside,1976, Wilson 1989).When all this arrived in the Principia, of 1713 (Scholium to Propn. 39, Book III), it was formulated in seven paragraphs.

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998