36 



BULLETIN 854, IT. S. DEPARTMENT OF AGRICULTURE. 



Let C v , A v , B v , and O s , A s , B s , be the V and s coordinates, respec- 

 tively, of the above centers of gravity. The calculations for these 

 coordinates are as follows: 



417 



423 

 429 

 435 



442 

 448 

 461 

 467 



0.5041 

 .7847 

 .9884 



1.204 



1.697 

 2. 1676 

 2-7711 

 3.0558 



0.0005 

 .0010 

 .0020 

 .0030 



.005 

 -0075 

 .0125 

 .0150 



Log V. 



9:894704fe=39.672744 



(yuQo^Mecin=9.9181Sb=.B„ 



iaoSj Antil °s^=°- 82s3 



lHo?ff7olSum=41.493438 



jj?)fiSI Meall = 10.373359= A v 

 W 4S5lll Antil0 ^"= 2 - 3624 



Sum= 81. 166182 

 Mean= 10.1457727= C v 

 Antilog C»=1.398S5 



Log s. 



7 oo&™= 2S - 47712 i 

 7"Sm7 M eaii= 7.119280= B s 



7 477121 I Antil °g S s= 0.0013181 



7.698970) 

 7.875061 1 



l'l7009lj Antilog ^«= 0-0091571 



Sum= 31. 847032 

 Mean= 7.961758= .4, 



Sum= 60.324153 

 Mean= 7.540519= Cs 

 Antilog Cs=0.0034715 



Since 



A v - C v = 10.373359 -10.1457727=0.227586 

 C„ -£,,=10.1457727— 9.918186 = .227587 

 A,- C s = 7.961758 — 7.540519 = .421239 

 C-B s = 7.540519 — 7.119280 = .421239 



A v — C V _ A S — C s 

 O v — B v C s — B s 



the three points, A, O, and B are in a straight line, which checks the 

 accuracy of the work (see American Civil Engineers' Pocketbook, 

 second edition, p. 848). 



The exponent, z, of V in formula 14, is the inclination of the line 

 ACB, and is equal to the tangent of the angle formed by the line and 

 the unit}- axis of V. 



A s -B s _ 0.842478 

 A v -B„ 0.455173 



= 1.8509=2 



The intercept, m, is determined as follows from equation 15, using 

 the coordinates of the center of gravity, C: 



Log m = log s — z log V 



= C s — z C v 



= 7.540519 - 1.8509 X 10.1457727 = 7.270709 

 and m = 0.0018651. 



(19) 



The exponent of V and the value of m are found in the same man- 

 ner for the other sizes of both concrete and clay tile, running nearly 

 full. These values are shown in column 7 of Table 6. This table 

 gives the formula derived as explained above for each size of tile as 

 well as the range of velocities used in the derivation. 



