EW OBSERVATIONS OF THE PLANET MERCURY. -137 
Or taken in rows, there is between the extremes of row 1 an interval of 5''. 7 ; of row ?, an iDteiral of ft^'.i ; 
of row 3, an interval, of 22''.9. 
"We have then in these drawings nearly nil manner of intervals, from OH of:ui 
hour to several days; and all without the slightest efl'cct npon the p()-ition>^. cx<"pl 
for a slight recession from the terminator presently to be explained. 
That more marking 
ply a quo 
of the steadiness of our own air. For example, the air happened to be much steadier 
in Figs. 5 to 9 of Plate XXXT. than it was in Figs. 1 to 4. 
The October and November drawings are among the FlngstnfT ono«, the JaniiMry 
among the Mexican, and as Flagstaff time is 7 h. west of Greenwich, jiiid T icub.iya, 
Mexico, 6''.6 west, it will be seen that these drawings were mnde all the way from 
about nine o'clock in the morning to four in the afternoon. From fhem I( is evident 
that any short period of rotation is negatived ; while if the posilions of tlie mark- 
ings be measured, it will be found that they all harmonize with a period synchronous 
with the orbital revolution. 
10. Libration. — To prove now that such is the rotation-period: ifwc take all 
the drawings and measure in them the distance of any given marking from the 
terminator, we find, on reduction, this distance to be invariable, and invariability is 
a corollary of such synchronousness. To show this result, we must first consider an 
interesting detail of the planet's rotation disclosed by the markings simultaneously 
with that rotation itself, — the libration in longitude due to the eccentricity of the 
planet's orbit, since this enters as a correction into the reduction. 
As the rotation of the planet must be uniform, due to the great moment of its 
rotary momentum, while the angular velocity of revolution of a body moving m an 
ellii 
be produced, in the case of 
of 
bital periods for such an orbit, a libration of the markings in longitud 
To d 
the 
D 
ty of revolution in the 
ellipse is the angular velocity of a body supposed to be describing a circle m the 
occupied by the planet in the ellipse. For the area of the ellipse being tt ab, and 
period T, the areal velocity in tlie ellipse, which is constant, is -y-. i m^ 
velocity in a circle of radius V~^b supposed described in the same time. 
To find, therefore, the point on the ellipse where the radius has the value co 
spondincr to the mean angular velocity, we must take the expression for r o 
ellipse referred to its focus as a pole, 
^ (1 - e'^) 
r = - — ^ — > 
1 4- « cos V 
