SOLAR DYNAMICS— SOME NEW ASTRONOMY. 325 



equal times." Here we want definiteness of idea. To regard this as true of the 

 real movement of a line joining the Sun and planet is very far from the truth. 

 But, if we ignore the movement of the Sun, and ignore the real movement of the 

 planet, and take account of the apparent movement the law is true. That is, it is 

 true of the angular velocity of the planet. But its angular velocity is one thing, 

 and its real velocity is quite another. Its angular velocity is never the same as 

 the real. It is sometimes in a direction the very opposite of the direction of the 

 actual movement. As velocity in the prime sense it is all apparent, at certain 

 times, 



As to Kepler's third law, the theory of movement here presented enables us 

 to see why " the squares of the times are to each other as the cubes of the dis- 

 tances." We see at once how this law results from two others: the law of falling 

 bodies, and the law of attraction. First, in each quarter of a revolution a cer- 

 tain amount of gain is to be made, viz : the distance of the planet. This gain is 

 to be made by a constant increase, or diminution, of velocity, according to the 



2d d d' 



law of falling bodies — 1'*= g . From this we get t^ : t'^ \ * g : g\ But this gain 



is made according to the attracting force — gravity. And, g oc d^ From this 



1 1 



we get the proportion g : g^ [ ' d^ : d'^ Combining these two proportions we 

 have Kepler's third law. t^ : t'^ | ] d^ : d'\ 



I submit this simple exhibit of the why of this wonderful law in confirmation 

 of my position. And I submit in confirmation of my position that here we have 

 all we want in explanation of the cause producing and continuing the momentum 

 . — and the centrifugal force. Here it is all explained. I submit in conformation 

 of my position that as the satellites are not so much under law to the equators, 

 as to the paths, and to the orbits of their rulers, we are to expect such a general 

 forward movement as permits a degree of constancy with reference to the paths. 



The diagram gives us a new base of observation for studying the cause of 

 the precession of the equinox. Also for studying the causes for the revolution 

 of the perihelion and aphelion ; and for variations in apogeal advances and regres- 

 sions. It gives us a new base of observation for studying the plane of the ecliptic, 

 as a plane of relative position. And as all orbital planes are similar in this re- 

 spect, we may have a better understanding of orbits, and of forces determining 

 them. It is only where we distinguish the apparent from the real, in movement, 

 and in velocity, that we can rightly estimate the varying momentum which has so 

 much to do in all these matters. The momentum that determines .the elipticity of 

 orbits. That determines the direction of the major axis ; and that determines the 

 variations of orbital inclinations. And now we are in a better position to look 

 after the law which determines the axes of the planets, and so the equators, and 

 to get a clue to the secret cause of the diurnal revolutions. A careful study of 

 this whole subject, will reveal that none of the revolving bodies move in a plane ; 

 but that in addition to the deflection causing the revolution ; there is another de- 

 flection causing inclination of the orbit of the inferior, as referred to the orbit of 



