98 ON THE MAGNITUDE OF THE SOLAR SYSTEM. 



rical measurements of the solar parallax might be supplemented by 

 deteruiiaations based on the theory of gravitation, and the tirst attempts 

 ill that direction were made by Machin in 1729 and T. Mayer in 1753. 

 The measurement of the velocity of lightbetween points on the earth's 

 surface, first effected by Fizeau in 1849, opened up still other possibili- 

 ties, and thus for determining the solar parallax we have at our com- 

 mand no less than three entirely distinct classes of methods, which are 

 known resi>ectively as the trigonometrical, the gravitational, and the 

 photo-tachymetrical. We have already given a summary sketch of 

 the trigonometrical methods as applied by the ancient astronomers 

 to the dichotomy and shadow cone of the moon, and by the moderns to 

 Venus, Mars, and the asteroids, and we shall next glance briefly at the 

 giavitational and i)hoto-tachymetrical methods. 



The gravitational results which enter directly or indirectly into the 

 solar parallax are six in number, to wit: First, the relation of the moon's 

 mass to the tides; second, the relation of the moon's mass and parallax 

 to the force of gravity at the earth's surface; third, the relation of the 

 solar parallax to the masses of the earth and moon; fourth, the rela- 

 tion of the solar and lunar parallaxes to the moon's mass and parallac- 

 tic inequality; fifth, the relation of the solar and lunar parallaxes to 

 the moon's mass and the earth's lunar inequality; sixth, the relation of 

 the constants of nutation and precession to the moon's parallax. 



Respecting the first of these relations it is to be remarked that the 

 tide-producing forces are the attractions of the sun and moon upon the 

 w^aters of the ocean, and from the ratio of these attractions the moon's 

 mass can readily be determined. But unfortunately the ratio of the 

 solar tides to the lunar tides is affected both by the dei)th of the sea 

 and by the character of the channels through which the water flows, 

 and for that reason the observed ratio of these tides requires multipli- 

 cation by a correcting factor in order to convert it into the ratio of the 

 forces. The matter is further complicated by this correcting factor 

 varying from port to port, and in order to get satisfactory results long- 

 series of observations are necessary. The labor of deriving the moon's 

 mass in this way was formerly so great that for more than half a cen 

 tury Laplace's determination from the tides at Brest remained unique; 

 but the recent a]»plication of harmonic analysis to tlie data sup]dicd 

 by self-registering tide gauges is likely to yield abundant results in 

 the near future. 



Our second gravitational relation, viz, that connecting the moon's 

 mass and parallax with the force of gravity at the earth's surface, 

 aftbrds an indirect method of determining the moon's parallax witli 

 very great accuracy if the computation is carefully made, and with a 

 fair approximation to the truth even when the data are exceedingly 

 crude. To illustrate this, let us see what could be done with a railroad 

 transit such as is commonly used by surveyors, a steel tape, and a fairly 

 good watch. Neglecting small corrections due to the flattening of the 



