20 6 
Mr. Davies Gilbert on the 
this table taken at an hundred measures, and it has been 
found to be 400 of the former, each measure here must be 
4 times 4, or 16 feet ; consequently, each gradation of y will 
also be 16 feet, and the whole semi-span ^ or 25 measures. 
And since % will be given in the Table for each measure of 
y, the adjunct weights may readily be adapted to a strict 
preservation of the catenary form. 
At 21 measures of y . z = 21.1547 
20 measures of y . z = 20.1335 
1.0212 x 16 = 16.3392 feet. 
Consequently while the ordinate extends one measure, or 
16 feet from the 20th to the 21st measure, the length of the 
curve will increase 16 feet and very nearly, and the adjunct 
weight should be increased in the same proportion. 
At 21 the length of x is 2,2131 measures, or multiplied by 
16 = 35,4096 feet, the length of the suspension rods to the 
level of the apex. 
It appears from Table I. that the tension T for a given half 
span of 100 measures is very nearly at its minimum when 
x = 65,85 measures, almost one-third part of the whole 
span. In the example taken above 65.85 x4 = 263,4 feet, 
an height not to be attained in practice, nor strictly upplicable 
if it could be reached, because of the great length of suspen- 
sion. If the span and height (2 y and x) were given, the other 
quantities would be found in a similar manner. 
In the catenary of equal strength 
a . x .y . z remain as before ; but another symbol must now 
be introduced, J = the mass of the chain. Then will the 
