242 W. Harhiess — Magnitude of the Solar System. 



of the sun and moon, while the latter is affected in addition 

 by the action of the planets, and to ascertain what that is we 

 must determine their masses. The methods of doing so fall 

 into two great classes according as the planets dealt with have or 

 have not satellites. The most favorable case is that in which 

 one or more satellites are present, because the mass of the pri- 

 mary follows immediately from their distances and revolution 

 times, but even then there is a difficulty in the way of obtain- 

 ing very exact results. By extending the observations over 

 sufficiently long periods the revolution times can be ascertained 

 with any desired degree of accuracy, but all measurements of 

 the distance of a satellite from its primary are affected by per- 

 sonal equation, which we can not be sure of completely elimi- 

 nating, and thus a considerable margin of uncertainty is 

 brought into the masses. In the cases of Mercury and Yenus, 

 which have no satellites, and to a certain extent in the case of 

 the earth also, the only available way of ascertaining the masses 

 is from the perturbations produced by the action of the various 

 planets on each other. These perturbations are of two kinds, 

 periodic and secular. When sufficient data have been accumu- 

 lated for the exact determination of the secular perturbations, 

 they will give the best results, but as yet it remains advanta- 

 geous to employ the periodic perturbations also. 



Passing now to the photo-tachymetrical methods, we have 

 first to glance briefly at the mechanical appliances by which the 

 tremendous velocity of light has been successfully measured 

 They are of the simplest possible character, and are based 

 either upon a toothed wheel, or upon a revolving mirror. 



The toothed wheel method was first used by Fizeau in 1849. 

 To understand its operation, imagine a gun barrel with a 

 toothed wheel revolving at right angles to its muzzle in such a 

 way that the barrel is alternately closed and opened as the 

 teeth and the spaces between them pass before it. Then, with 

 the wheel in rapid motion, at the instant when a space is oppo- 

 site the muzzle let a ball be fired. It will pass out freely, and 

 after traversing a certain distance let it strike an elastic cushion 

 and be reflected back upon its own path. When it reaches the 

 wheel, if it hits a space it will return into the gun barrel, but 

 if it hits a tooth it will be stopped. Examining the matter a 

 little more closely, we see that as the ball requires a certain 

 time to go and return, if during that time the wheel moves 

 through an odd multiple of the angle between a space and a 

 tooth the ball will be stopped, while if it moves through an 

 even multiple of that angle the ball will return into the barrel. 

 Sow imagine the gun barrel, the ball and the elastic cushion to 

 be replaced respectively by a telescope, a light wave and a 

 mirror. Then if the wheel moved at such a speed that the 



