1897.] NEW YORK ACADEMY OF SCIENCES. 139 



H. Jacoby, " On two Trail-plates of Circumpolar Stars, made by 

 Anders Conner, at the Helsingfors Observatory." 



It was explained that these photographic negatives of circum- 

 polar stars were taken with the telescope stationary, so that each 

 star left a trail upon the plate, which, after necessary corrections, 

 would be an arc of a circle around the true North Pole of the 

 heavens. The exposures which were for a few moments at in- 

 tervals of half an hour, during a continuous period of over four- 

 teen hours, thus gave a series of short arcs extending over a little 

 more than a semicircle. This method, if no unforeseen difficul- 

 ties appear, should give the position of the pole to within a few 

 hundredths of a second of an arc, and a system of right ascen- 

 sions differing from the truth by a uniform correction. 



The paper was favorably discussed by the chairman and 

 others. 



The next paper was the following : 



INVESTIGATIONS OF THE UNDULATIONS IN RAIL- 

 WAY TRACKS BY THE AUTHOR'S TRACK IN- 

 DICATOR, AND THE REDUCTION OF TWO- 

 THIRDS OF THEIR AMOUNT IN THE 

 PAST FIFTEEN YEARS BY THE 

 USE OF THE AUTHOR'S STIFF 

 RAIL SECTIONS. 



By p. H. Dudley. 



If we stand by the side of a railway and notice the tracks as 

 a train passes over them, we see, first, a general depression of 

 the rails under the wheel base of the trucks or the locomotive, 

 the greatest depressions being directly under the wheels ; we 

 further notice that the rails under the wheels bear more firmly 

 on the ties, the latter depressing, and with instruments we find 

 that the ballast and roadbed are also depressed. 



We notice further that on either side of the wheels the surface 

 of the rails is slightly higher, and if the wheel base is four or five 

 feet long that the fibre stresses in the rails undergo a reversion 

 and are of opposite character from those directly under the 



