212 APPLIED SCIENCE 



of a length of the cable, hanging vertically from the ship to the 

 bottom of the sea. Cables of the old form, in which simple iron 

 wires were laid round its core, would support from 4,000 to 5,000 

 fathoms of themselves hanging vertically in water. They could, 

 therefore, be laid fairly taut in depths of 2,000 or 2,500 fathoms, 

 such as are met with in the Atlantic, but engineers are in the 

 habit of allowing a very much larger margin than the above. 

 They make all their structures from six to ten times stronger 

 than by exact calculation they need be. This figure ' six ' or ' ten ' 

 they call the co-efficient of safety. A co-efficient of safety of 

 ' two/ such as was given by these old cables, gave very little safety 

 indeed. When the cables are not laid taut, but with a certain 

 slack, the strain need not be quite so great. The friction of the 

 water tends to relieve the strain, but this relief with the old 

 smooth cables was small. 



Sir W. Thomson was again the first to give the true theory 

 of the strains which occur, and the curve assumed by the rope 

 during submersion. The first account of the theory appears in 

 the ' Engineer' newspaper of October 1857. 



A much more elaborate investigation was, independently of 

 Sir W. Thomson's theory, made by Messrs. Brook and Long- 

 ridge, whose able paper was published in the 'Proceedings of the 

 Institution of Civil Engineers ' for 1858. Dr. Siemens, of Berlin, 

 independently arrived at similar conclusions; the subject is 

 nevertheless not a very simple one, for the Astronomer Royal was 

 misled more than once in his investigations concerning it. 



When the ship and cable are both at rest, the latter hangs 

 in a simple catenary curve, the strains on which are easily com- 

 puted ; but when the cable is being paid out, it lies in an in- 

 clined straight line from a point a very little below the surface 

 of the sea to the bottom (provided, however, the cable as it lies 

 at the bottom is not strained) ; above the water the cable hangs 

 in a short catenary ; the angle at which the cable lies in the 

 water depends on the speed of the ship and the specific gravity 

 of the cable ; it is independent of the strain on the cable, and 

 is therefore unaltered whether the cable is being paid out slack 

 or taut. As the speed of the ship increases, the angle which 

 the cable makes with the horizon diminishes ; the same effect 

 is produced by diminishing the specific gravity of the cable 



