16 Trans. Acad. Sci. of St. Louis. 



dently similar, and the average of observed values made in 

 this area was determined. Thus, in the row of squares 

 adjacent to the edge, the top line of squares constitutes such 

 an area. These squares are marked 1 to 12, a. The line of 

 squares 1 to 12, i, is another such area. The averages in the 

 vertical rows a to i, 7, and a to i, 12 were also separately 

 found. 



The average value for such areas was then entered in all 

 the squares of the areas, excepting that the values in the cor- 

 ner squares were smoothed a little, in order to make adjoin- 

 ing side rows unite with each other. Over these corner 

 squares the pressures diminish in two directions toward the 

 nearest edges of the board. In such cases the integrated 

 pressures must therefore be less than in squares removed 

 from the corners. 



In like manner the averages in the second row of squares 

 from the edges were determined. In this row the squares 

 2 to 11, b; 2 to 11, h; b to h, 2 ; and b to h, 11 were sepa- 

 rately treated. The data contained in the table may be used 

 by anyone to repeat these computations. The results for 

 each square on the board are entered in Figs. 3 and 4, where 

 the values have all been multiplied by 100. The values in 

 Fig. 4 are of course negative in sign. These values therefore 

 correspond to a spring balance reading of 100 lbs., when the 

 arm is three feet. The moments of the forces applied to 

 these four-inch squares with respect to the axis of rotation 

 have been summed. It was assumed as sufficiently exact, that 

 the center of pressure for each square of -^ square foot, was 

 at its center. The arm for the vertical row a to i, 1, is f ft., 

 the arm for vertical row a to i, 2, is one foot, etc. The sum 

 of the moments for the front and back sides of the board 

 was found to be, — 



Front 1 fi9 



Back 128 



Total 297 



By the spring balance 300 



Difference 3 



A difference of one per cent. 



