Joty—On the Origin of the Canais of Mars. 257 
impulses travelling along with the exciting cause of fresh disturbances. The final 
result will only be controlled by the damping effects of viscosity. Such a condition 
may obtain when the satellite’s motion is retrograded. It recalls Professor G. 
Darwin’s suggestion for the origin of our Moon. 
A rough geometrical examination of the conditions of summation of impulse 
waves at high velocities of the satellite relative to the crust appears to show that 
side lines, as in the static conditions, of maxima stress are formed, and this 
whether the satellite’s relative velocity is greater or less than that of sound. 
At the velocity of sound it appears that an apical spreading wave alone is 
formed. 
In eases of high relative velocity the question of the effects is complicated by 
the very different behaviour of materials under suddenly applied stresses. Many 
substances will break down under such conditions which would successfully resist 
greater stresses applied gradually. ‘The effects of very rapid motion will be, we 
may expect, like that of an earthquake shock, in a small way. This shock will be 
repeated over the same ground with each return of the satellite. Phobos, when he 
has lessened his distance to some 60 miles from the surface of Mars, will accomplish 
his month in one hour and forty minutes. 
Stability of the Satellite. 
It is necessary to raise the question of the effects of this close approximation 
upon the satellite itself. Here again a full determination of the stresses is a 
matter of much difficulty. It is easy to show, however, that the rigidity of the 
satellite will most probably be more than sufficient to secure it against the effects 
of the stresses set up in it. Even if its resistance to tensile stress is no more than 
that of basalt, there is a large coefficient of safety. This may be seen by con- 
sidering in a general way the stresses thrown upon the equatorial section of the 
satellite which is at any instant tangential to Mars’ surface, due to the centrifugal 
force outwards acting upon the inner hemisphere being necessarily less than the 
attraction of the primary requires. We may consider the extreme case of supposing 
the satellite 23 miles from Mars’ surface—that is with but 5 miles separating the 
surfaces. The velocity of Phobos is then 353,600 e.ms. per second. A mass of 
one gramme placed at the centre of gravity of the inner hemisphere is acted on by 
a force of 364°08 dynes. Assuming the acceleration of gravity upon the surface 
of Mars to be 981 x 38/100 dynes, Mars’ attraction on this mass is 366°15 dynes; 
there is therefore an inward acting force of 2°07 dynes per gramme. Considering 
this as the mean force per gramme of Phobos’ hemisphere, the stress per square 
centimetre on the equatorial section is 15 x 10° dynes; which is about 4th the 
TRANS. ROY. DUBL. SOC., N.8, VOL. VI., PART X. 210) 
