312 KANSAS CITY REVIEW OF SCIENCE. 



And now let us consider some things preparatory to making diagrams. We 

 have the celestial heavens, with the North and South Poles, the celestial equator, 

 and the ecliptic. These give us our points of the compass, and enable us to 

 locate planes. In the diagrams the following things are to be observed : 



1. Parallelism of axis. The planets must keep their equatorial planes in 

 position. 



2. A direct line from the Sun to the center of the earth must never strike 

 the earth more than 23^^° north or south of the Equator, but must reach that 

 latitude, once north, and once south, during each. revolution. 



3. In each case we have a hypothesis as to the rate of the Sun's motion; 

 hence we know how far it would move during the revolution of each planet. 

 This distance, and the distance of each planet are to be carefully observed in the 

 scale adopted in the diagram. 



4. During the revolution of each planet, the Sun must pass over nearly 

 equal distances in equal times. 



5. The relative position of each planet and the Sun during a revolution 

 must be such as to form an ellipse. 



Observing the above conditions we present a few diagrams. Each shows 

 what the path of the earth would be, did the Sun move in a given direction and 

 at a given rate. These diagrams have reference not only to a particular latitude, 

 but to a particular point in the heavens : for not only the latitude, but the longi- 

 tude of the movement, affects the diagrams. These few diagrams, among the 

 many that might be given, serve to illustrate general principles. 



In the expanse of the universe, you may, if you please, regard the solar sys- 

 tem as small as a train of cars. If it were as small as a compass, or as the instru- 

 ments which the astronomer uses, its pointings would still be exact. We want 

 to use the system itself, as though it were an instrument, for certain mathematical 

 demonstrations. Our figures are made on a plane either of longitude, or of lati- 

 tude, in which the Sun is assumed to be moving. 



Plates III, IV, and V are on the plane of the solstitial colure. In the dia- 

 grams on Plate III the movement is toward 47° north declination. In Fig. 6, 

 the rate of the Sun's motion is twenty-seven miles per second. At this rate, the 

 Sun moves in one year nine times the distance from the Earth to the Sun. We 

 draw our lines accordingly. The line S C represents the Sun's line of passage in 

 one year. And S E represents the earth's distance from the Sun, which, during 

 the year, is to vary so as to form an ellipse. Next we divide S C into four equal 

 parts. The Sun passes over one of these during a quarter of a revolution. We 

 propose to start at the winter solstice. And we know just where to locate the 

 Earth. There is but one place possible. At the winter solstice the earth is in 

 this plane, the plane of the solstitial colure. And then, a direct line from the 

 Sun to the earth's center makes an angle of 23^° to the plane of the earth's 

 equator. Then the earth can only be at E. In six months the Sun will be at H. 

 And the Earth is again in this plane, the plane of the solstitial colure. And now 



