586 Dr WHEWELL, ON PLATO'S SURVEY OF THE SCIENCES. 



Kepler's speculations on the subject just mentioned were given to the world in the 

 Mysterium Cosmographicum published in 1596. In his Preface, he says " In the beginning 

 of the year 1595 I brooded with the whole energy of my mind on the subject of the Copernican 

 system. There were three things in particular of which I pertinaciously sought the causes ; 

 why they are not other than they are : the number, the size, and the motion of the orbits." 

 We see how strongly he had his mind impressed with the same thought which Plato had so 

 confidently uttered : that there must be some reason for those proportions in the scheme of the 

 Universe which appear casual and vague. He was confident at this period that he had solved 

 two of the three questions which haunted him ; — that he could account for the number and 

 the size of the planetary orbits. His account was given in this way. — " The orbit of the 

 Earth is a circle ; round the sphere to which this circle belongs describe a dodecahedron ; the 

 sphere including this will give the orbit of Mars. Round Mars inscribe a tetrahedron ; the 

 circle including this will be the orbit of Jupiter. Describe a cube round Jupiter's orbit ; 

 the circle including this will be the orbit of Saturn. Now inscribe in the Earth's orbit an 

 icosahedron : the circle inscribed in it will be the orbit of Venus. Inscribe an octahedron in 

 the orbit of Venus ; the circle inscribed in it will be Mercury's orbit. This is the reason of 

 the number of the planets ;" and also of the magnitudes of their orbits. 



These proportions were only approximations ; and the Rule thus asserted has been shewn 

 to be unfounded, by the discovery of new Planets. This Law of Kepler has been repudiated 

 by succeeding Astronomers. So far, then, the Astronomy which Plato requires as a part of 

 true philosophy has not been brought into being. But are we thence to conclude that 

 the demand for such a kind of Astronomy was a mere Platonic imagination ? — was a mistake 

 which more recent and sounder views have corrected ? We can hardly venture to say that. 

 For the questions which Kepler thus asked, and which he answered by the assertion of this 

 erroneous Law, are questions of exactly the same kind as those which he asked and answered 

 by means of the true Laws which still fasten his name upon one of the epochs of astronomical 

 history. If he was wrong in assigning reasons for the number and size of the planetary 

 orbits, he was right in assigning a reason for the proportion of the motions. " This he did 

 in the Harmonice Mundi, published in 1619 : where he established that the squares of the 

 periodic times of the different Planets are as the cubes of their mean distances from the central 

 Sun. Of this discovery he speaks with a natural exultation, which succeeding astronomers 

 have thought well founded. He says: "What I prophesied two and twenty years ago as soon 

 as I had discovered the five solids among the heavenly bodies ; what I firmly believed before 

 I had seen the Harmonics of Ptolemy ; what I promised my friends in the title of this book 

 (On the perfect Harmony of the celestial motions), which I named before I was sure of my 

 discovery ; what sixteen years ago I regarded as a thing to be sought ; that for which I 

 joined Tycho Brahe, for which I settled in Prague, for which I devoted the best part of my 

 life to astronomical contemplations ; at length I have brought to light, and have recognized 

 its truth beyond my most sanguine expectations." (Harm. Mundi, Lib. V.) 



Thus the Platonic notion, of an Astronomy which deals with doctrines of a more exact 

 and determinate kind than the obvious relations of phenomena, may be found to tend either 

 to error or to truth. Such aspirations point equally to the five regular solids which Kepler 

 imagined as determining the planetary orbits, and to the Laws of Kepler in which Newton 



