1897.] NEW YORK ACADEMY OF SCIENCES. 145 



They are now accomplished facts on many railroads using 

 rails of about the same type and stiffness, for which the esti- 

 mates were made, wliiie with the stifFer sections of my series, 

 still better results are obtained. 



The value of stiffness in rails in connection with sufficient 

 bearing surfaces for the wheel pressures, was shown to be so im- 

 portant by the first 80-pound rails in reducing the undulations 

 in the ti'ack — as I stated would be the case before they were 

 used — that in 1890, when designing my recent series of rail sec- 

 tions, I increased their stiffness per pound of metal, malving the 

 80-pound sections about eleven per cent, stiffer than the original 

 five-inch 80-pound rail of 1883. 



The rails of the series are stiffer than any sections of like 

 weight wliich have been rolled and have broad heads, which are 

 essential daring manufacture and subsequent service for smooth 

 tracks and a high degree of stability. 



For all of my sections, according to their stiffness and traffic 

 for which they are suited, I am now able to state definitely the 

 lower range of undulations per mile which will and which may 

 be maintained in the track as shown by my track indicator. 



The importance of this can not be over-estimated, for when 

 w^c know what to expect, the reason can be traced if it is not at- 

 tained. 



Each section of rail like a locomotive of a certain class can 

 only render a specific dut^^ or permit a certain standard of track. 

 On a branch line laid with four and five-eighth-inch 65-pound 

 rails and with supported joints, the undulations run down to 4 

 feet 6 inches per mile for the best track. This rail was not in- 

 tended for main line traffic, but it is frequently so used. 



The five-inch 75-pound rail was used to build a new road, and 

 with all its inequalities and with the settling of a new roadbed, it 

 is easily maintained, under heavy branch line traffic at .3 feet and 

 3 inches of undulations per mile, after five years' service, a rec- 

 ord never before equalled. 



For the five and one-eighth-inch 80-pound rails, three tie joints, 

 under the main line express trains running from 50 to 75 miles per 

 hour, the undulations range from 2 feet 6 inches to 2 feet 9 

 inches, per mile. This section has an exceptional stability for 

 the weight per yard. 



For the six-inch 100-pound rail, three tie joints, the undulations 

 per mile run down to 1 foot 6 inches to 2 feet per mile, as a 

 condition of track for summer heat and winter cold, a stability 

 of permanent way unequalled in the railway world. 



The figures given for the undulations per section are for rails 



Transactions N. Y. Acad. Sci., Vol. XVI., Sig. 10, March 30, 1897. 



