Joty—On the Origin of the Canals of Mars. 265 
In a similar manner it will be found that the ratio of the angular velocities in 
the case of a retrograde satellite may be expressed by :— 
V, _ span — 180 
Ves ie RS Ohe aad 
— 
C9 
er 
From these we see that the span due to a direct satellite cannot exceed 180 
upon the equator, and that of a retrograde satellite cannot be less than 180°. 
The angular velocity of the satellite may be assumed invariable within the limits 
of distance at which it can effect the surface of the planet: any variations in the 
span of the curves must therefore be due to change in the rate of axial rotation of 
the planet. We have every reason to believe that this rate of axial rotation has 
continually been diminishing in the past, and hence expect to find such differ- 
ences in the spans as the probable variations of the planet’s velocity would 
account for, if at various periods in its history it picked up satellites. 
To apply Mr. Lowell’s map as a test of this hypothesis of the origin of the 
lines the mode of procedure will be readily understood (Plate xvt.). 
We look preferably to the most complete and definite curves. The chains of 
eanals of which Acheron and Erebus are members mark out such a fairly definite 
curve. We produce it by eye-judgment till it intersects the equator. Reading 
the span upon the equator, this is found to be 255°. In the first place, this 
curve is then due to a retrograde satellite. Inserting this number in (3), we find 
the ratio of the angular velocities to have been as 5 to 12. The point of highest 
latitude of the curve gives the inclination of the satellites’ orbit to the equator. 
These data enable the curve to be constructed upon the sphere as before. Trans- 
ferring this to a Mercator’s projection on the same scale as Mr. Lowell’s map of 
Mars, it is possible to apply a tracing of the curve to Lowell’s map, and examine 
the degree of similarity between the curves. 
In this process we are assuming three points from Lowell’s curve, and plotting 
a curve according to a particular law to pass through these three points. This 
law involves the hypothesis under consideration in this Paper. It is, of course, 
possible to draw an indefinite number of curves through three assigned points. 
But we find, as will be seen from the reproduction of Mr. Lowell’s map in 
Plate xv1., that the curve just determined, which is drawn as a dotted line, coincides 
closely with that observed by Mr. Lowell and his colleagues. Transferring our 
attention from one to another of the dotted curves drawn upon Lowell’s map, it 
will be seen that, in nearly all the cases dealt with—and the principal definite 
curves have been examined—the curve, determined according to the present hypothesis, 
lies closely along or upon the observed curve. I venture to think this agreement cannot 
be accidental. 
The curves upon Lowell’s map, which nearly lie along meridian lines, are, it 
TRANS. ROY. DUB. SOC., N.S. VOL. VI., PART. X. 2R 
