266 Joty—On the Origin of the Canals of Mars. 
will be observed, accounted for on the supposition that these lines if pursued 
further towards the poles would be found to be curved out of the meridional 
direction, «nd so would cross the poles in the manner in which the rifts cross the 
polar cap in Lowell’s map, showing the progressive melting of this cap (‘‘ Mars,” 
plate 1., p. 84). These lines will also be found plotted upon the sphere in 
Plate xv. They correspond to the path of a satellite rotating at a very high angle 
to the equator. Upon Plate xv. will also be found projections on the sphere of 
many of the lines plotted upon the Mercator’s projection of Plate xvi. In the pro- 
jections the retrograde curves are distinguished by a minus sign, as the character 
of the curve is not in all cases apparent from inspection. 
To consider each curve inscribed according to the present hypothesis upon 
Plate xvi. would be needless. The agreement is apparent even to casual inspection. 
In a couple of cases it will be perceived that I have assumed a curve to be com- 
pound in nature. One instance is that of the chain of Boreas and Anapus, The 
latter I have assumed to form part of a curve drawn to the approximate velocity 
ratio of 4:9. The former I have suggested to represent a very early impression 
upon the planet’s crust. The equality ratio 1:1 will account for such a slightly 
curved line. But in such a case it is perhaps better to refer the curve to better 
observations than we at present possess, remarking that the curve is a possible 
curve even as it stands. It appears permissible to assume that the one other 
case (Erannoboas and Cephissus) is referable to the canals meeting by chance only. 
The following conditions and attributes of these curves will serve to complete 
the present reference to them. 
A satellite rotating at a distance of 60 miles from the surface of Mars will 
complete its month in one hour and forty minutes. At the present rate of axial 
rotation of Mars this involves a ratio of 1:13. From this it follows, assuming 
that Mars can never in the past have been rotating at a slower rate than 
at present, that spans possessing values between 166° and 194° are inadmis- 
sible. 
A direct span greater than 180° involves that the planet revolved faster than 
the satellite; a retrograde span greater than 360° also involves this assumption ; 
which may be considered precluded on dynamical grounds. 
At any particular ratio of velocities an indefinite number of curves are possible, 
according to inclination of orbit of the satellite, but only two spans can obtain, 
the direct and the retrograde. 
The closed curve is not necessarily that which might be marked out by a 
satellite. If the ratio of velocities is not represented by whole numbers, the 
satellite will describe a curve which does not enter into itself. The number of 
revolutions or months determining the repetition of the curve, in the case when 
the curve is a closed one, will depend upon the ratio of velocities. In certain 
