440 Miscellaneous Intelligence. 
scarcely a moment’s delay. The importance of this subject is so pass 
that numbers will, doubtless, immediately have recourse to it, so that 
of the British Aemeiakite and at other meetings, and notw conan 
the Astronomer Royal’s two papers on the subject, I feel that my original 
conclusions are unshaken 
The subject is of great importance, hae I will (if you will allow me) 
give you as brief an “abstract 0 my i as I possibly can. 
I have demonstrated (but without a P aaete it is almost impossible 
to give the demonstration) that if a vessel be running in a straight course 
at any uniform speed whatever, and the cable is being paid out over the 
stern at the same velocity, then, in the case where the strain tending to 
break the cable as it leaves the stern is just equal to the weight in water 
of a poriicn of a same cable, whose length is the depth of the sea, the 
cable will be at any instant in the same condition as to tensio 
prongare as if it were simply lying straight on an inclined plane surface 
immersed in water; there will be no strain whatever on the parsicis which 
happens at any instant to be the bottom particle of the cable, and the 
cable will therefore sink down in a vertical plane with uniform relote. 
and be Ss d Koo} stretched) straight along the bottom of the sea without 
wey 
ee 
oa—the angle the cable forms with the horizon. 
t=the terminal normal velocity in feet per second, or the velocity 
of the cable at right angles to its i 
V=the velocity of the ship in feet per sec 
w==the weight in pounds of one foot of ie cable, i in water. 
d=diameter of the cable in feet. 
D=the depth of the sea in fathom 
L=length in fathoms, from the acs of the ship to where it touches 
a. 
Now the resistance expressed in pounds to each foot in length of a 
rough cylinder moving sideways in sea water is ‘8dv? pretty nearly (4 
being the diameter in feet, and w the velocity in feet — — 
We must have therefore w cosa—°8di?=0, 
We tenksles hive ¥=<> 3 —|2, oe ot coset &. 
sina sin & 
tes, taking as an example w=="32 and d="05, as is pretty nearly the 
case in the present Atlantic cable, we get 
log t=} (log 8-+log cos «), 
log V=} (log 8-+log cos «)—log sin «. 
whence, Bats wha events Sat 20°, cova tghl ge immediately 
