198 ANNUAL OF SCIENTIFIC DISCOVERY. 



transverse slopes, and with end heights whose sum does not exceed 100 feet. 

 Both sets of tables embrace directly all ordinary widths of roadbed, and are 

 extended by proper formulae to side hill work, or work of triangular cross 



sections. 



i 



The quantity S of formula 3 may be found by construction, and then 

 employed to enter the table of prisms. The operation and advantages of 

 this process were shown by the solution of practical examples. 



Mr. Warner further gave some rules for the computation by centre and 

 side heights. This part of the subject, he said, had been more fully discussed 

 than the method of transverse slopes, several American writers having 

 treated it with ability, especially Colonel Ellwood Morris. 



Under such circumstances, it was prudent to say little concerning the 

 value of one's own work. He would, however, remark, that he had exhibited 

 nothing which did not appear to him as original, at least in its whole scope ; 

 and that, as far as his rules were applicable, he had given practical proof of 

 their expedition and accuracy. In regard to the method of transverse slopes, 

 he would observe, that he had as yet met with no other treatment of it as 

 full and satisfactory to him as his own; but, independently of what belonged 

 to the theory, the labor of computation had been great, having engaged 

 his attention, at intervals, for several years. 



