VOL. LXIX.J PHILOSOPHICAL TRANSACTIONS. 385 



error makes only a very small alteration in the result. It is impossible for any 

 one to form a complete judgment of his method without going through the 

 whole of his calculations, which pre-supposes that the mean motion of the lunar 

 nodes is computed. This motion may be concisely determined, and exactly 

 enough for the purpose, from prop. 30 of the Principia, and thence is inferred 

 the motion of the nodes of a satellite revolving in the plane of the equator at 

 the surface of the earth, with a velocity equal to that of the earth round its axis. 

 We are then to suppose, that the mean motion of the nodes of a satellite, re- 

 volving with such a velocity, is the same with the motion of the nodes of a ring 

 of rigid matter surrounding the earth at its equator, and revolving with the same 

 velocity. This last hypothesis is admitted by Simpson, who thinks that his own 

 2d lemma contains a full demonstration of the point. Foi' my own part, I be- 

 lieve with Frisius, that we are to look here for the material error in Newton's 

 solution of the problem. It is evident, that the true motion of the nodes of 

 the satellite, and the ring of matter, are not the same : and it is by no means 

 obvious that their mean motions are so. The mean motion of the nodes of a 

 ring of hard matter cohering together is very easily computed by the method in 

 art. 4th to the 9th, and turns out nearly double the mean motion of a moon re- 

 volving at the surface of the earth with the same velocity. 



It is a very interesting inquiry to find out the real cause of the mistake in the 

 Principia, lib. 3, prop. SQ ; and therefore at a future opportunity I may perhaps 

 consider this particular part of the subject more attentively. I have long been 

 satisfied with the account already given, and should probably have remained so, 

 if M. D'Aleinbert,* in his Opusc. vol. 5, had not persisted to affirm, that the 

 mean motion of the nodes of the ring of matter and of the satellite were the 

 same. This opinion of so celebrated a mathematician raises scruples in one's 

 mind ; and shows, that when we venture to differ from Sir Isaac Newton in 

 these matters, it is with the utmost difficulty that we can arrive at certainty. 



XXXIII. An Examination of Various Ores in the Museum of Dr. JFilliam 

 Hunter. By George Fordyce, M. D., F. R. S., and Mr. S. Alckorne. p. 527. 

 The first ore here examined is called gold pyrites. Pyrites is an ore of iron, 

 containing sometimes copper, sometimes arsenic, sometimes other metals ; 

 generally, if not always combined with sulphur. This ore, from its yellow co- 

 lour, has at first sight been often taken for an ore of gold. It is the most 



* II n'y a de paiite que dans le mouvement moyen de ces deux anneaux, ou de lanneau solide et 

 de la lune ; les mouvemens instantancs sont trrs difterens de part et d' autre j ainsi la comparaison du 

 mouvement de lanneau avec celui de la lune, serviroit tout au plus a trouver le mouvement moyen 

 de I'anneau, ou de la precession des equinoxes, mais nullement a determiner la nutation de I'axe et 

 r equation de la precession. — Orig. 



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