Mr. Woolhouse on the Deposit of Submarine Cables. 368 
that the due amounts of tension shall be continually maintained 
at its extremities. 
The cable being traced 
nie @ y 
upwards from the lowest al naa ri 
point soon assimilates to a (le! ice heady 
straight line, and when the 
c A a Ze me v.%4 
stray length is gradually in- 
creased the modifications of the curve will be as in the annexed 
diagram, where B’ D! is the direction of the ship’s motion, and 
AB, ac, a'd successive representations of the suspended cable. 
The curves being similar, A B will be a prototype of the rapidly 
decreasing portions a4, a'l', and the diminished scale of mea- 
surement bringing in an increased proportion of the upper part 
of the curve, it will evidently approximate to the right line mn 
as a limit, where py becomes evanescent. 
In each position of the curve we have by (3) Ty>=a+ po, and 
at the limit T,=«a, which we have observed is the minimum ten- 
sion at the lowest point. The Astronomer Royal, from con- 
founding T —a with the tension T, has presumed the non-existence 
of tension at this pomt; and subsequently Mr. Homersham Cox, 
in a paper read before the British Association, after advancing 
the same assumption as an original principle, has adduced a some- 
what ingenious and elaborate proof of the dynamical necessity of 
the descending cable taking the form of a straight line; but, it 
will appear, both the premises and conclusion are equally inad- 
missible. 
2. When @ is greater than the limiting angle A, cos »—« will 
be negative, and by (11), if T—a be positive at one point, it will 
be positive at all points. Also the value of cos »—e? sin? is 
negative, and by (3) p is negative, and hence the curve is always 
convex upwards. JBut as the direction of the curve at the lowest 
point (A’) is not continuous with the line of cable previously de- 
posited, there cannot: be any stay or reaction to support the re- 
quisite tension at that point, and the consequence will be a 
distorted movement in this locality accompanied by an irregular 
displacement and a useless and extravagant waste of a portion of 
the cable. Such will be the inevitable result of a profuse pay- 
ing out of the cable; and other injurious consequences may 
ensue from the friction occasioned by the cable being dragged to a 
certain distance along the bed of the ocean before the tension 
due to a steady movement can be reinstated. 
If, therefore, a Table be made out showing the weight, in water, 
of any number of fathoms of cable, it will be an important and 
valuable rule for practical guidance, always to moderate the paying 
out so as to keep the tension a certain proportion, say one-third 
or one-fourth, im excess of the weight corresponding to the 
