of Edinburgh , Session 1877-78. 
637 
action amounts to demonstration. How the actual performance of 
the receiving instrument is to be apportioned between these, it is, 
of course, difficult to say. Taking into account Professor Tait’s 
calculations as to the infinitesimal strength of a current that can 
make a telephone tick, and assuming that that tick is purely mole- 
cular, as we have done, molecular action must he there not the less 
considerable. 
2. Sketch of the Arrangement of Tables of Ballistic Curves in 
a medium resisting as the Square of the Velocity, and of 
the Application of these Tables to Gunnery. By Edward 
Sang. 
The motion of a body in a medium whose resistance is propor- 
tional to the square of the velocity, has been the subject of many 
inquiries. Its intimate connection with the theory and practice of 
gunnery has produced for it the attention of almost every cultivator 
of the higher analysis ; but, like several other seemingly elementary 
problems in mechanics, it has hitherto received no complete solution. 
If nothing else than the fluid’s resistance influence the motion 
the investigation is comparatively easy ; thus, taking the time as 
the primary variable, the 
speed has its own square 
for its derivative, and so 
must be proportional to 
the first inverse power of 
the time, and consequently 
the distance passed over 
must be proportional to 
the logarithm of that time. 
Hence, if the present posi- 
tion, the velocity and the 
coefficient of resistance be 
, , O B P A F 
given, we can compute, for- 
wards, the position and 
velocity at any future time; or backwards, what those had been 
at previous times. But since the velocities are inversely propor- 
tional to the times elapsed from some fixed epoch, it follows that, 
VOL. ix. 4 p 
