INTRODUCTION 15 



bone of contention among mathematical astronomers, namely, the 

 secular acceleration of the moon's mean motion. It was found 

 by Halley, early in the last century, by a comparison of ancient 

 with modern eclipses, that the month is certainly shorter than it 

 was in the days of Ptolemy, and that the shortening has been pro- 

 gressive, apparently going on continuously ' In 100 

 years the moon, according to the results of Laplace, gets in ad- 

 vance of its mean place about 10", and the advance increases 

 with the square of the time! 



In passing, mark the highly significant fact that this 

 law of the moon's advance coincides with the law of 

 falling bodies. 



My next quotation is from the pen of Professor 

 Charles Lane Poor (The Solar System, p. 169) : 



Le Verrier discovered a slight irregularity in the motion of 

 Mercury, which for over a half a century has been a source of 

 trouble to astronomers and has led Newcomb to question the ex- 

 actitude of the law of gravitation. The perihelion of Mercury's 

 orbit has a secular perturbation, or regular forward movement, 

 amounting to 579." 16 per century. Taking into account the dis- 

 turbing action of all the known bodies in the solar system, New- 

 comb shows the law of gravitation will account for only 537/'62; 

 or the perihelion of Mercury moves forward along the plane of 

 the orbit by some 41. "54 per Century in a manner that cannot be 

 accounted for. In his Astronomical Constants Newcomb dis- 

 misses many possible explanations of this anomalous motion, and 

 after careful treatment discards them all as untenable. He 

 shows that this motion cannot be due to erroneous determination 

 of the masses of the various planets, nor to hitherto undiscovered 

 planets. For a readjustment of the masses,or the introduction in- 

 to the system of new bodies sufficiently large to explain the dis- 

 crepancy, will introduce serious discordances into the motions of 

 the other planets. He seems to accept as the most probable hy- 

 pothesis, first propounded by Hall, that the gravitation of the sun 

 is not exactly as the inverse square but that the exponent of the 

 distance is 2.0000001574, instead of 2. He provisionally accepts 

 this as a working theory and introduces it into the computation of 

 his tables of planetary motion. 



Here we are confronted with a statement that may 

 well give pause to those who harbor the belief that cur- 

 rent astronomy is an exact science. It is not the law of 

 the inverse square that our astronomers employ in their 

 computations, but that of the inverse 2.0000001574 



