52 



PROCEEDINGS OF THE AMERICAN ACADEMY 



curve, the heavy line of Figure 2, ordinates representing tempera- 

 ture in excess of 100° C, and abscissas representing phases of the 



ns-J- 



stroke in terms of the angular distance of the crank pin from its zero 

 position, the position occupied at the end of the out stroke. The 

 left end of the base line indicates — tt, or — 180°, the beginning of 

 forward stroke ; the middle of the line represents 0° ; the right 

 end represents +7r, or +180°, the end of backstroke. Thus the 



134"4C 



IOO"C 



cycle of a complete forward and back stroke is compassed, and the 

 length of the base line is called 2 tt. 



My task now was to find a mathematical expression for any ordi- 

 nate, y, of the given curve in terms of the corresponding abscissa, x\ 

 that is, to write y = 0(a'), and find the form of the function <f>. 



