roportion； suppose d to e； then the distance between the centres of the sun and of the satellite's orbit would be always greater than the distance between the centres of the sun and of Jupiter nearly in the subduplicate of that proportion： as by some computations I have found。 And if the satellite did gravitate towards the sun with a force； lesser in the proportion of e to d； the distance of the centre of the satellite's orb from the sun would be less than the distance of the centre of Jupiter from the sun in the subduplicate of the same proportion。 Therefore； if at equal distances from the sun； the accelerative gravity of any satellite towards the sun were greater or less than the accelerative gravity of Jupiter towards the sun by one…one…thousandth part of the whole gravity； the distance of the centre of the satellite's orbit from the sun would be greater or less than the distance of Jupiter from the sun by one one…two…thousandth part of the whole distancethat is； by a fifth part of the distance of the utmost satellite from the centre of Jupiter； an eccentricity of the orbit which would be very sensible。 But the orbits of the satellites are concentric to Jupiter； and therefore the accelerative gravities of Jupiter and of all its satellites towards the sun； at equal distances from the sun； are as their several quantities of matter； and the weights of the moon and of the earth towards the sun are either none； or accurately proportional to the masses of matter which they contain。 〃COR。 5。The power of gravity is of a different nature from the power of magnetism； for the magnetic attraction is not as the matter attracted。 Some bodies are attracted more by the magnet； others less； most bodies not at all。 The power of magnetism in one and the same body may be increased and diminished； and is sometimes far stronger； for the quantity of matter； than the power of gravity； and in receding from the magnet decreases not in the duplicate； but almost in the triplicate proportion of the distance； as nearly as I could judge from some rude observations。
〃PROPOSITION VII。； THEOREM VII。 〃That there is a power of gravity tending to all bodies； proportional to the several quantities of matter which they contain。
That all the planets mutually gravitate one towards another we have proved before； as well as that the force of gravity towards every one of them considered apart； is reciprocally as the square of the distance of places from the centre of the planet。 And thence it follows； that the gravity tending towards all the planets is proportional to the matter which they contain。 〃Moreover； since all the parts of any planet A gravitates towards any other planet B； and the gravity of every part is to the gravity of the whole as the matter of the part is to the matter of the whole； and to every action corresponds a reaction； therefore the planet B will； on the other hand； gravitate towards all the parts of planet A； and its gravity towards any one part will be to the gravity towards the whole as the matter of the part to the matter of the whole。 Q。E。D。
〃HENCE IT WOULD APPEAR THAT the force of the whole must arise from the force of the component parts。〃
Newton closes this remarkable Book iii。 with the following words： 〃Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity； but have not yet assigned the cause of this power。 This is certain； that it must proceed from a cause that penetrates to the very centre of the sun and planets； without suffering the least diminution of its force； that operates not according to the quantity of the surfaces of the particles upon which it acts （as mechanical causes used to do）； but according to the quantity of solid matter which they contain； and propagates its virtue on all sides to immense distances； decreasing always in the duplicate proportions of the distances。 Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed； and in receding from the sun decreases accurately in the duplicate proportion of the distances as far as the orb of Saturn； as evidently appears from the quiescence of the aphelions of the planets； nay； and even to the remotest aphelions of the comets； if those aphelions are also quiescent。 But hitherto I have not been able to discover the cause of those properties of gravity from phenomena； and I frame no hypothesis； for whatever is not deduced from the phenomena is to be called an hypothesis； and hypotheses； whether metaphysical or physical； whether of occult qualities or mechanical； have no place in experimental philosophy。 。 。 。 And to us it is enough that gravity does really exist； and act according to the laws which we have explained； and abundantly serves to account for all the motions of the celestial bodies and of our sea。〃＇2＇
The very magnitude of the importance of the theory of universal gravitation made its general acceptance a matter of considerable time after the actual discovery。 This opposition had of course been foreseen by Newton； and； much as be dreaded controversy； he was prepared to face it and combat it to the bitter end。 He knew that his theory was right； it remained for him to convince the world of its truth。 He knew that some of his contemporary philosophers would accept it at once； others would at first doubt； question； and dispute； but finally accept； while still others would doubt and dispute until the end of their days。 This had been the history of other great discoveries； and this will probably be the history of most great discoveries for all time。 But in this case the discoverer lived to see his theory accepted by practically all the great minds of his time。 Delambre is authority for the following estimate of Newton by Lagrange。 〃The celebrated Lagrange；〃 he says； 〃who frequently asserted that Newton was the greatest genius that ever existed； used to add'and the most fortunate； for we cannot find MORE THAN ONCE a system of the world to establish。' 〃 With pardonable exaggeration the admiring followers of the great generalizer pronounced this epitaph： 〃Nature and Nature's laws lay hid in night； God said ‘Let Newton be！' and all was light。〃
XIII。 INSTRUMENTS OF PRECISION IN THE AGE OF NEWTON During the Newtonian epoch there were numerous important inventions of scientific instruments； as well as many improvements made upon the older ones。 Some of these discoveries have been referred to briefly in other places； but their importance in promoting scientific investigation warrants a fuller treatment of some of the more significant。 Many of the errors that had arisen in various scientific calculations before the seventeenth century may be ascribed to the crudeness and inaccuracy in the construction of most scientific instruments。 Scientists had not as yet learned that an approach to absolute accuracy was necessary in every investigation in the field of science； and that such accuracy must be extended to the construction of the instruments used in these investigations and observations。 In astronomy it is obvious that instruments of delicate exactness are most essential； yet Tycho Brahe； who lived in the sixteenth century； is credited with being the first astronomer whose instruments show extreme care in construction。 It seems practically settled that the first telescope was invented in Holland in 1608； but three men； Hans Lippershey； James Metius； and Zacharias Jansen； have been given the credit of the invention at different times。 It would seem from certain papers； now in the library of the University of Leyden； and included in Huygens's papers； that Lippershey was probably the first to invent a telescope and to describe his invention。 The story is told that Lippershey； who was a spectacle…maker； stumbled by accident upon the discovery that when two lenses are held at a certain distance apart； objects at a distance appear nearer and larger。 Having made this discovery； be fitted two lenses with a tube so as to maintain them at the proper distance； and thus constructed the first telescope。 It was Galileo； however； as referred to in a preceding chapter； who first constructed a telescope based on his knowledge of the laws of refraction。 In 1609； having heard that an instrument had been invented； consisting of two lenses fixed in a tube； whereby objects were made to appear larger and nearer； he set about constructing such an instrument that should follow out the known effects of refraction。 His first telescope； made of two lenses fixed in a lead pipe； was soon followed by others of improved types； Galileo devoting much time and labor to perfecting lenses and correcting errors。 In fact； his work in developing the instrument was so important that the telescope came gradually to be known as the 〃Galilean telescope。〃 In the construction of his telescope Galileo made use of a convex and a concave lens； but shortly after this Kepler invented an instrument in which both the lenses used were convex。 This telescope gave a much larger field of view than the Galilean telescope； but did not give as clear an image； and in consequence did not come into general use until the middle of the seventeenth century。 The first powerful telescope of this type was made by