NOTES. CXV11 



orbia terrestrie, quam Mars Terrre in quantitate orbis Martis. Vcrum 

 hoc pacto nequo nuius pianette interpositio sufficiebat ingeiiti hiatu. 

 Jovem inter et Martem : manebat enim major Jovis ad ilium novum 

 proportio, quam est Saturni ad Jovem. Rursus alio modo explo- 



ravi " Kepler was twenty-five years old when he wrote this. We see 



how his mobile spirit set up hypotheses, and quickly abandoned and exchanged 

 them for others. Through all such changes he preserved a hopeful confidence 

 of discovering numerical laws, even where, amongst the most varied pertur- 

 bations of attracting forces (perturbations of which our ignorance of the 

 accompanying conditions forbids all attempt at calculating the combined 

 action), the matter of which the planetary orbs were formed has been con- 

 solidated into bodies revolving in some instances singly in simple orbits, 

 almost parallel to each other ; in others in groups, and in wonderfully inter- 

 secting and intertwining orbits. 



( 62 ) p. 318. Newtoni, Opuscula mathematica, philosophica et philologica, 

 1744, T. ii. Opusc. xviii. p. 246 : " Chordam musice divisam potius adhibui, 

 non tantum quod cum phacnomenis (lucis) optime convenit, scd quod fortasse, 

 aliquid circa colorum harmonias (quarum pictorcs non penitus ignari sunt), 

 sonorum concordantiis fortasse analogas, involvat. Quemadmodum vcrisimi- 

 lius videbitur animadvertenti ailiiiitatem, quce est inter extimam Purpuram 

 (Violarum colorcm) ac Rubcdinern, colorum extremitates, qualis inter octavro 



terminos (,qui pro unisonis quoiiammodo haberi possunt) rcperitur " 



Compare also Prevost, in the Mem. de 1'Acad. de Berlin pour 1802, p. 77 

 and 93. 



( 6ai ) p. 318. Seneca, Nat. Qurest. vii. 13: "Non has tantum stellas 

 quinque discurrcre, sed solas observatas esse : ceterum innumerabiles ferri 

 per occultum." 



( 622 ) p. 319. As I could not feel satisfied with the explanations which 

 Heyne had given (Dc Arcadibus luna autiquioribus, in Opusc. acnd. Vol. ii. 

 p. 332), of the origin of the widely prevalent astronomical myth of the Pro- 

 selenes, I was much rejoiced at receiving a new and very happy solution of 

 the problem fiorn my ingenious philological friend, Professor Johannes Franz. 

 This solution is not connected cither with the construction of the calendar by 

 the Arcadians, or with their worship of the Moon. I confine myself to an 

 extract from an inedited and more comprehensive discussion. " In a work 

 in which I have imposed on myself the obligation of frequently connecting 

 our complcter knowledge with the knowledge of the ancients, and even with 



