52 BULLETIN 835, U. S. DEPARTMENT OF AGRICULTURE. 



The remaining 22 sets of observations were divided into two groups, 

 and the equation of this parabola was derived as follows : 



log x S 11= 13.751 log (y a -f-5.5)S 13l =10.4:8i 



2^= 17.124 S u = 14.061 



A == 3,374 A = 3.579 



„ ._^79_ 1 0fi log (y 2 +5.5) 2 22 =24.542 



~ 3.374 — 30.875X1.06=32.666 



log x 2 22 =30.875 A = 1.876-10 



1.876— 10-f-22 =9.631— 10=log a 

 log (y a +5.5) =9.631— 10+1.06 log x 



y 2 =0.43 a? 1 ; 06 — 5.5 

 Since y 2 =y 1 — y, y—y-L—yz 

 then ?/=21.39 a; -*— (0.43a? 1 : 06 — 5.5) 



The values calculated from this equation are tabulated and the 

 differences from the values of y as obtained in the experiment are 

 noted. 



When the curve resulting from the plotting x or y against log x 

 or log y is straight, the exponential curve is derived in the same man- 

 ner as for a parabola. The data are divided into two groups and the 

 value of n and log a found. 



log ?/=log a — nx log s represents the equation for both groups, so 

 that log a can be eliminated by subtracting one from the other. 



_jo g yi -iogy, . whidh g±=a4343 



logs (logo?,— logajj 



log ft=log y — nx log e 



In several cases it was found that for high values of x and y the 

 curves were straight lines and the equations for these straight lines 

 found. 



Subtracting the values of y 1 in the equation y 1 =mo+& from the y 

 values of the data gave values of y 2 . 



The log y 2 plotted against x gave straight lines, so that the curve 

 for these low values of x and y were exponential curves which were 

 derived as explained above. 



The formulae for the curves representing moisture movement in 

 the flumes held at different angles when filled with Riverside heavy- 

 decomposed granite loam (Placentia loam) were as follows: 

 Flume No. 42 (45° up) : 



y=33.7+0.12ai— (18.5s-°- 2fl 



