144 FROM NEBULA TO NEBULA 



As said before, given the length of arc in seconds and 

 the curvature in miles, it is easily possible to ascertain 

 the radius of the circle. The rule, stated in the form of 

 an equation with the initial letters of the things referred 

 to (See Young's Genl. Astr., Art. 420), is: 



c : a : : a : 2 r 



Now the length of the radius in terms of degrees of 

 circumference is called a radian, and is known to be 

 57 17' 44".8, or 206,264.8". Substituting this and our 

 other values in the equation given, we have, 



22,625 (miles) : arc (in miles) : : 50".2 : 412,530" 

 which, being reduced, yields 



arc=185,977,500 miles, 



the meaning of which is, that in one year the center of 

 mass of our solar system travels exactly the width of the 

 earth's orbit, as measured along the equinoctial colure, 



AND THAT THIS COLUKE MARKS THE LINE OF THE SUN ^S PATH. 



Choosing round numbers, we ascertain by simple compu- 

 tation the length of the sun's orbit, considering it as a 

 closed curve, to be 25,810 x 186,000,000 miles, or 4,800,- 

 000,000,000 miles, its diameter 1,530,000,000,000; the axis 

 of the cone from Centrum to Vertex 1,760,000,000,000 and 

 from the Vertex to our sun (that is to say, the stem of the 

 Prime Resultant) 1,918,000,000,000 miles. Finally, there 

 being 31,557,000 seconds in a year, the sun's velocity is 

 found to be just a trifle short of six miles per second. 



' ' But six miles ' ', you will say, ' ( is only about half 

 the actual velocity of the sun as found by the direct 

 methods, how do you account for the balance ? " I will 

 answer you. Hitherto in this discussion I have, for the 

 sake of simplicity, ignored the very material feature that 

 all this while the plane of the ecliptic, though remaining 

 sensibly parallel with itself, is falling, keeping pace with 

 the fall of the system. In other words, the sun is falling 

 vertically just as fast as it is "gyroscoping" laterally; 

 or, to borrow the parlance of the astrophysicists, he has 

 both a "proper" motion and a " radial" motion. You 

 may retort, that in such case he is travelling along the 



