258 FROM NEBULA TO NEBULA 



strange star might have been with reference to the string 

 of planets, just how large it might have been, and just 

 how far from the sun, in order to bring about the present 

 planetary scheme. Had our author succeeded in figuring 

 out any such combination, he would doubtless have men- 

 tioned the fact in his book; but he doesn't. Nor shall I 

 consume the reader's time by mathematically demon- 

 strating the impossibility of any such combination exist- 

 ing. This much, at least, should be plain, that inasmuch 

 as Mercury travels faster than any other planet, the star 

 would have to be predicated as quite close to the sun and 

 certainly not as far aivay as Venus, else the latter should 

 possess the higher velocity; which it doesn't. 



Inasmuch as only terrestrial tides have come within 

 our daily experience, the question has never specifically 

 arisen as to what effect, if any, the mass of the body af- 

 fected has on the heights of its tides. For example, sup- 

 pose the sun were an exact duplicate of the earth, save in 

 the one respect of mass, and that the two were equi-dis- 

 tant from each other and from the moon, would the lunar 

 tides on the sun be then exactly as high as those on the 

 earth, or would they be directly proportional to their 

 mass, or would they be inversely proportional, or just 

 what rule would obtain? In the absence of any surer 

 guide, let us assume the tidal heights to be, inversely, 

 functions of the masses of the bodies affected, and that 

 the star, in order to raise upon the sun tides commensu- 

 rate with our terrestrial tides, had to exceed the size of the 

 sun as much as the latter outweighs the earth. Suppos- 

 ing, then, the star to have come to within 46,000,000 miles 

 of the sun (i. e. one-half the earth's mean distance, and 

 one-third way between Mercury and Venus) it must, un- 

 der Newton's rule of cubes, have possessed a mass some 

 40,000 times the solar mass and a diameter of 18,000,000 

 miles! It goes without saying that a body of such im- 

 mensity would have swallowed up our pygmy sun in short 

 order, nor left a vestige behind. Moving the star out 

 farther does not mend matters ; if to the earth's distance, 

 its diameter would have to be increased to 36,000,000 



