10 

 therefore 



The Astronomer Royal on the Conditions 



!=..(..„ '"' 



T— a , 1 p dsf^ es ex\ 



Then, to find , we have merely to form ^^1 +~~~J> 



as given by one of the last equations of Article 9. 



16. By means of these formulae, the numbers in the follow- 

 ing Tables have been computed, on the supposition that the 

 ship's velocity is double the terminal velocity of the cable in 

 falling through water, or that e = 2. 



The first Table exhibits the ordiuates and tensions in a defi- 

 nite cable-curve. The unit of measure is the constant c, and 

 the unit of tension is the weight in water of a piece of the cable 

 whose length =c. 



On laying down a curve with these ordinates, it will be seen 

 to possess the qualifications that we have mentioned ; its lower 

 part resembling a catenary, and its upper part approaching to a 

 straight line. 



17. The second Table exhibits the elements of difi"erent cable- 

 curves corresponding to difi'erent amounts of stray length of the 

 cable, in water of a definite depth. The unit of measure here is 

 the depth of the sea or y. The numbers in the last line are 

 taken from the investigations in the next three articles. They 

 will be materially altered by the more practical considerations 

 in the third section. 



