nile it 
TRANSACTIONS OF THE SECTIONS, ll 
the vibrations are parallel to the plane of reflexion, and perpendicular to the plane 
of incidence, and consequently to the plane of polarization, which for this ray Ii co- 
incides with the plane of incidence. According to M. Cauchy, also, the ray which 
is gradually extinguished in proportion as the incidence increases, is the ray Ip ; there- 
fore it is for this ray that the vibrations, always perpendicular to the direction of pro- 
pagation and to the intersection of the planes of incidence and reflexion, are in the 
plane of incidence, and consequently perpendicular to the plane of polarization, 
which is perpendicular to the plane of incidence. Therefore in all cases the luminous 
vibrations are perpendicular to the plane of polarization. 
My. Stokes has raised an objection to this demonstration, which appears to us 
to fail. He says that M. Cauchy has deduced his numbers from a theory which 
assumes as its starting-point, the hypothesis that the vibrations are perpendicular 
to the plane of polarization; but there is nothing to prove that in this case, as in 
many others, we do not arrive at the same result by starting from the opposite 
hypothesis. We do not deny that this may be the case; but in order that our rea- 
soning may subsist in its full extent, it is sufficient that the numbers of M. Cauchy 
should be considered as numbers obtained by photometric experiments. Now this 
is certainly the case, for these numbers undoubtedly agree with all the known results 
of photometric experiments. As soon as they are admitted as natural numbers, no 
objections can be raised to our mode of reasoning. 
Exvectricity, MAGNETISM. 
A Mathematical Investigation of the Proportion between the Length required 
for an Electric Telegraph Cable and its Specific Gravity. By Captain 
BLAKELY. 
The author showed, by the principles of the composition of motion, as a telegraph 
wire was paid out from a ship, the velocity which gravity would give it would soon 
become uniform by the resistance of the water as its parts descended ;-therefore, the 
descending part of the cable from the advancing ship to the part of the cable which 
had reached and was supported upon the bottom, and which he showed in very deep 
water, say two miles or more, might stretch back six or more miles from the ship. 
Now, unless a great strain were kept on the brake in the ship where the cable was 
_ paying out, a strain, which in the case of the Atlantic cable had caused it to part, it 
was obvious from this demonstration that there must always be what the sailor 
termed ‘‘ slack” in the cable when it reached and lay on the bottom, for the inclined 
length of the rope was always longer than the horizontal length of the bottom on 
which it was intended to lie. The author then proceeded to estimate, by mathema- 
tical formule, and numerically, the exact proportion of these in several supposed 
depths of soundings, rapidity of paying out, and specific gravity of the cable ; and 
came to the conclusion, that the only way of lessening an evil, which must never be 
expected to be entirely got rid of, was by increasing the speed of the vessel paying 
out the cable, and diminishing the specific gravity of the cable itself, so that it should 
sink gently to its final position. 
On the Electro-dynamic Induction Machine. 
By the Rev. Professor Carian, of Maynooth College. 
After stating that he had discovered the induction coil in 1836, that in 1837 he had 
devised an instrument for getting a rapid succession of electrical currents from the 
coil, and that thus he had completed the coil in 1837, as a machine by which a regular 
supply of electricity might be furnished, the author said that he would lay before 
the Association the results of a long series of experiments on the induction machine. 
_ The first of these results is a means of getting a shock directly from the armature of 
_ a magnet at the moment of its demagnetization, by using, not a solid piece of iron, 
