222 Trans. Acad. Sci. of St. Louis. 



gauge within the car, is represented by the line O p'. The 

 rise in the curve passing through p' shows how the pressure 

 rises, as the collector carried on the car is thrust further out. 

 As the distance d increases the pressure approaches the limit- 

 ing value P, corresponding to the speed of the train. This 

 is re|)resented in the figure by the horizontal line at the top 

 of Fig. 3. ']'he curve approaches this line of limiting pres- 

 sure, as d increases. 



The distance from this line of limiiing pressure, down 

 to the curve at any distance cZ, represents the pressure 

 against an object standing on the ground. The way in which 

 this curve drops from this horizontal line as the vertical axis 

 is approached, shows how the train-draught increases as one 

 approaches the train. Measured from the ground, the pres- 

 sure on the windward side of an object due to train-draught 

 at the distance d from the train is P — /), while measured from 

 the train the pressure in the opposite direction is p. 



This curve as determined by the observations satisfies the 

 equation of an hyperbola. The vertical asymptote is within 

 the car a distance d'. The equation of this hyperbola is 

 evidently 



(P^p)(d'+d)=c. (1) 



In this equation P. d' and c are constants to be determined 

 from the observations. The value of P is of special impor- 

 tance. Its relation to the vel tcity of the train is represented 

 by the well-known equation of Newton 



h 

 P=T^v^ (2) 



where 5 is the density of the air. When v is expressed in 

 centimeters per second and P in dynes per square centimeter, 



the value of — at ordinary temperature and pressure is 



0.0006. When v is in miles per hour and P is in pounds per 

 square foot the equation becomes 



(3) 



