[Bead before the Texas Academy of Science , December 31, 1896.~\ 
VERTICAL CURVES FOR RAILWAYS. 
BY J. C. NAGLE. 
Of late years the increasing speed at which passenger trains are run 
has necessitated snch improvements in the surface conditions and align- 
ment of track that the dangers and discomforts to which passengers are 
subjected shall he reduced to a minimum. Heavy steel rails laid on 
stone-ballasted tracks, kept always well surfaced, make the disagreeable 
effects of a speed of fifty miles an hour scarcely more noticable than the 
jolting of a buggy over a well paved street. Indeed, the year just ending 
has witnessed an attempt to even filter the air, so to speak, that the pas- 
sengers are to breathe within the car. Transition curves at the beginning 
and end of circular curves make the change from tangent to curve al- 
most imperceptible, the centrifugal force being balanced by the proper 
super-elevation of the outer rail — the elevation increasing inversely with 
the radius of transition curve. A study of the railway accidents will show 
that very few casualties result from the wreck of passenger trains, and 
these mostly from collisions with freights, so that the probability of in- 
jury per mile traveled is less than in any other form of locomotion, un- 
less, perhaps, it be ocean travel. 
Most of the serious train wrecks occur with freights, and in mountain- 
ous regions quite a large per cent of these are due to the train breaking 
in two and the wild section dashing forward into the front section at 
the bottom of an incline, or backward into the front of a following train. 
The causes of these accidents are many; but some, at least, are due to 
the absence of suitable vertical curves at the junction of two grade 
lines having a different rate. Transition curves are of prime importance 
for passenger service, but less so for freight traffic, while vertical curves 
are more necessary in the case of freights. The reason for this is seen in 
the short length and close coupling of passenger trains, particularly ves- 
tibuled trains, enabling them to pass readily from one grade line to the 
next. With freight trains, the case is different. They are generally long 
and not very closely coupled, so that when the rear cars crowd forward 
there may be considerable slack present. As the engine pulls out or slows 
up suddenly, a fearful jerking or jamming is the result, as can be seen in 
[ 21 ] 
