222 Tables and Rules for the Chains [April* 



Geological Society of Pennsylvania, in which is a most interesting 

 " Critical notice of various organic remains discovered in North 

 America," by Dr. Harlan. At p. 89, is the following : 



" The bones of one species of shark, upwards of forty feet in length, 

 allied to the Carcharias, have occasionally been found in several loca- 

 lities. In Cuvikr's Theory of the Earth, by S. L. Mitchell, p. 400, 

 it is stated, ' The skeleton of a huge animal was found on the bank of 

 the Meherrin river, near Murfreesborough, N. C. It was dugout of a 

 hill distant sixty miles from the ocean. Captain Neville and Dr. Fow- 

 ler, who visited the spot, gathered the scattered vertebrse and laid 

 them in a row thirty-six feet in length. If to this the head and tail 

 be added, the animal must have been fifty feet or more in length, &c. 

 We have recognized them as the remains of a gigantic species of 

 shark.' " 



He refers to other specimens, indicating sharks of forty feet or more 

 in length ; but this will, I doubt not, be sufficient to show that it is quite 

 probable the fish seen by Lieut. Foley and the chacon of the Bay 

 of Manilla may be individuals of the same family as those only known 

 to us as yet by their fossil remains. 



IX. — Rules for Calculating the Lengths of the Drop-bars of Suspension 

 Bridges, the Length and Defection of the Chain, Rise of the Roadway, 

 8<c. By Captain J. Thomson, Engineers. 



The application of the following problem in statistics, to find the 

 length of the drop-bars and links of a suspension bridge, has, I be- 

 lieve, the merit of originality ; while it will be found extremely con- 

 venient in practice, in determining at once the requisite proportions, 

 and obviating the necessity of after adjustment, which will always occur 

 where the curve of such a bridge is assumed as a true catenarian. 

 If a be the angle of suspension, 

 b the length in feet of one of the links of the chain, 

 d the number of drop-bars in each chain ; then the tangent of the 



angle a, divided by one-half d. = n = ^ — is the constant dif- 



d 



ference between the tangents of the angles formed by the links of the 



chain with the horizon. These tangents will be as follows : upper link 



= Tan. a, 2nd = Tan. a — n, 3rd = Tan. a — 2»&c. and the lowest 



d 

 —Tan. a — n. The sines to radius b, corresponding to these 



angles, are the differences of the lengths of the drop-bars ; and the 

 cosines of these angles are the horizontal distances between the drop- 





