80 



MARINE BOTTOM SAMPLES OF LAST CRUISE OF CARNEGIE 



Table 28. The magnitude of the errors owing to sieving and quartering in the mechanical analysis 



of sand grades 



Sample 19 divided into four parts, and each part sieved twice 

 Percentages in size grades 



Total 99.99 100.00 

 Total weight in 

 grams 1.633 



100.00 99.99 100.00 100.01 99.99 99.99 



1.502 1.394 1.368 



Deviations between duplicate determinations in each part 



> 1 0.00 



1 - .5 -0.35 



.5 - .25 +0.32 



.25 - .12 -1.03 



.12 - .07 +1.14 



<.07 -0.09 



Average deviation = 0.29 per cent; cri 

 able error owing to sieving. 



0.00 



+ 0.23 



-0.07 



-0.65 



+ 0.77 



-0.27 



= standard deviation 



0.00 ... . 0.00 



+ 0.01 -0.34 



+ 0.21 -0.06 



+ 0.18 +0.52 .. . 



-0.36 +0.05 



-0.05 -0.17 



0.33 per cent; P.E.i =0.22 per cent 



prob- 



Deviations from grand average of the averages of each part 



+ 0.09 

 + 0.10 

 -0.77 

 + 0.25 

 + 0.70 

 -0.41 



-0.02 

 -0.16 

 -0.62 

 + 0.37 

 + 0.35 

 + 0.06 



+ 0.07 

 -0.33 

 + 0.30 

 -0.96 

 -0.27 

 + 1.16 



-0.15 

 + 0.37 

 + 1.07 

 + 0.29 

 -0.78 

 -0.84 



Average deviation = 0.44 per cent; <r2 = 0.57 per cent; P. E.2 = 0.38 p^r cent = probable error owing to 

 quartering; a = standard deviation of a single determination =Vo'i2 + &2^ = 0.66 per cent; P. E. = prob- 

 able error of a single determination = 0.44 per cent. 



Sample 21 divided into two parts, and each part sieved twice 



Percentages in size grades 



4.20 4.30 



43.31 43.59 



35.96 35.53 



15.88 15.94 



<.07 0.70 0.82 0.76 0.65 0.66 0.66 



Total 100.00 100.00 100.01 100.01 



Total weight in 



grams 0.856 0.775 



3.99 

 42.92 

 35.02 

 17.36 



0.71 



Deviations between duplicate determinations in each part 



1 - 5 

 .5 - .25 

 .25 - .12 

 .12 - .07 

 < .07 



Average 

 sieving. 



1 - .5 

 .5 - .25 

 .25 - .12 

 .12 - .07 

 <.07 



+0.11 



-0.38 



+1.98 



-1.59 



-0.12 



deviation = 0.59 per cent; 



<^\ 



+ 0.19 



+ 0.56 



-0.86 



+ 0.12 



-0.01 



= 0.69 per cent; P. E.j = 0.46 per cent 



probable error owing to 



0.25 

 0.86 

 0.49 

 0.63 

 0.01 



0.36 

 0.48 

 1.49 

 2.22 

 0.11 



Deviations from grand average of each set of determinations 



0.40 0.21 



0.39 



0.94 



1.48 



0.05 



0.95 

 0.08 

 1.36 

 0.06 



Average deviation = 0.64 per cent; cr = standard deviation of a single d eterminati on = 0.90 per cent; 

 P. E. = probable error of a single determination = 0.60 per cent, a^ ='\/<t'^ - <y\^ = 0.57 per cent; P. E.2 

 = 0.38 per cent = probable error owing to quartering^ 



