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XVIII. A Table for facilitating the Computations relative to Suspension Bridges. 
By Davies Gilbert, Esq. V.P.R.S. 
Read, May 19, 1831. 
The following Table is supplementary to those accompanying the paper 
On the Mathematical Theory of Suspension Bridges,” printed in the Philoso- 
phical Transactions for 1 826. It is deduced from the first Table there given, 
by the plain operations of common arithmetic ; but this admits of a far more 
ready application than the former, to all cases of practical investigation. 
The first column contains the deflections or versed sines of the curve, ex- 
pressed in fractional parts of the double ordinate or Span. It is therefore 2 y 
divided by x, and their reciprocals are added under each. 
The second column gives the lengths of the chain without alteration from 
the former Table, except that the double ordinate or span is taken as the unit. 
The third column has the tensions of the chain at the middle points or 
apices of the curve, when the tensions are least ; taking the weight of the 
chain, or that weight augmented by the adjunct weight, or with the adventitious 
weight also, as unity. The numbers are obtained by dividing a by 2 z. 
The fourth column gives the tensions in a similar manner for the extremi- 
ties of the chain, where they are greatest ; and it is made by dividing T by 2 z. 
The fifth column gives the angles made by the chains at their extremities 
with the plane of the horizon, being the complements of those in the former 
Table. 
As all these numbers are immediately derived from an existing Table, there 
would have been much additional trouble, and without any adequate advan- 
tage, in making the denominators of the fractions in the first column or their 
reciprocals (the decimal fractions), to succeed each other by equal differences. 
And I have thought it unnecessary to extend the Table further in either di- 
rection ; since no deflection is likely to be so great as a seventh of the span ; 
