{"text_format":"1","workbook":"xlsx","n_sheets":4,"sheets":["Example Table 2","Classes as analyte","Example Table 5","Gys extended"],"not_rendered":{"charts":0,"images":3,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Example Table 2","index":0,"n_rows":51,"n_cols":27,"rows_kept":51,"cut":false,"hidden":false,"merged":[]}
["Gys_Extended_1.1",null,null,null,null,null,null,null,null,null,"Prediction of the Fundamental Sampling Error, FSE:",null,null,null,null,null,null,null,null,"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, ECP, PLEN, University of Copenhagen, 2021"]
[null,null,null,null,null,null,null,null,null,null,"s(FSE) % caused by the constiutional heterogeneity of a 0-dimensional lot"]
[null,"Table 1",{"$f":"IF(SUM(E5:E14)=1,\"\",\"ERROR:  Sum of x(k) must be 1\")","v":""},null,null,null,null,null,"Table 2",null,null,null,null,null,null,null,null,null,null,"ONLY ENTER values in the WHITE CELLS"]
[null,"Class k","Name","m(k), g","x(k)","s(FSE) %",null,"Mass factor",{"$f":"IF(I6=\"\",\"\",1/I6-1/I5)","v":7.0000000000000001E-3},null,"1) Enter parameters for the classes in Table 1"]
[null,1,"Sand",1E-4,0.05,{"$f":"IF(C5=\"\",\"\",100*SQRT($I$4*D30))","v":3.8309072032613898},null,"M(L), g",1000,null,"2) Enter mass of the lot and the sample in Table 2",null,null,null,null,null,null,null,null,"Grey cells are protected, to unprotect, click Review and Unprotect Sheet "]
[null,2,"Sesame",3.0000000000000001E-3,0.05,{"$f":"IF(C6=\"\",\"\",100*SQRT($I$4*F30))","v":4.2813374078668458},null,"M(S), g",125]
[null,3,"Barley",4.4999999999999998E-2,0.7,{"$f":"IF(C7=\"\",\"\",100*SQRT($I$4*H30))","v":3.5706932100083875},null,null,null,null,"For estimation of m(k) = fgd3r use Table 9 below (Cell B40+)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a(k):C oncentration of analyte k in the lot, g/g"]
[null,4,"Steel",0.88100000000000001,0.2,{"$f":"IF(C8=\"\",\"\",100*SQRT($I$4*J30))","v":14.126565399983113}]
[null,5,null,null,null,{"$f":"IF(C9=\"\",\"\",100*SQRT($I$4*L30))","v":""},null,null,null,null,"Each class is considered to be an analyte in this sheet",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Here a(k) = 1 for the class that is considered analyte."]
[null,6,null,null,null,{"$f":"IF(C10=\"\",\"\",100*SQRT($I$4*N30))","v":""},null,"Headings and comments:"]
[null,7,null,null,null,{"$f":"IF(C11=\"\",\"\",100*SQRT($I$4*P30))","v":""},null,"Data and results for mixture 4, Table 2 in the paper: https://doi.org/10.1016/j.aca.2021.339127"]
[null,8,null,null,null,{"$f":"IF(C12=\"\",\"\",100*SQRT($I$4*R30))","v":""},null,"m(k)'s are measured values and do not need to be estimated using Table 9",null,null,null,null,null,null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g"]
[null,9,null,null,null,{"$f":"IF(C13=\"\",\"\",100*SQRT($I$4*T30))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,"x(k):","Fraction of class k in the lot, M(k)/M(L)"]
[null,10,null,null,null,{"$f":"IF(C14=\"\",\"\",100*SQRT($I$4*V30))","v":""},null,"To make your own estimates use the sheet: Classes as analyte",null,null,null,null,null,null,null,null,null,null,null,"a(L):","Concentration of analyte i in the lot, g/g"]
[null,null,null,"Sum:",{"$f":"SUM(E5:E14)","v":1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"HI:","Heterogeneity Invariant for the class HI(k) or lot HI(L), g or %"]
[null,"Table 3"]
[null,null,"Analyte:",{"$f":"IF(C5=\"\",\"\",C5)","v":"Sand"},null,{"$f":"IF(C6=\"\",\"\",C6)","v":"Sesame"},null,{"$f":"IF(C7=\"\",\"\",C7)","v":"Barley"},null,{"$f":"IF(C8=\"\",\"\",C8)","v":"Steel"},null,{"$f":"IF(C9=\"\",\"\",C9)","v":""},null,{"$f":"IF(C10=\"\",\"\",C10)","v":""},null,{"$f":"IF(C11=\"\",\"\",C11)","v":""},null,{"$f":"IF(C12=\"\",\"\",C12)","v":""},null,{"$f":"IF(C13=\"\",\"\",C13)","v":""},null,{"$f":"IF(C14=\"\",\"\",C14)","v":""}]
[null,null,"a(L)",{"$f":"IF(E5=\"\",\"\",E5)","v":0.05},null,{"$f":"IF(E6=\"\",\"\",E6)","v":0.05},null,{"$f":"IF(E7=\"\",\"\",E7)","v":0.7},null,{"$f":"IF(E8=\"\",\"\",E8)","v":0.2},null,{"$f":"IF(E9=\"\",\"\",E9)","v":""},null,{"$f":"IF(E10=\"\",\"\",E10)","v":""},null,{"$f":"IF(E11=\"\",\"\",E11)","v":""},null,{"$f":"IF(E12=\"\",\"\",E12)","v":""},null,{"$f":"IF(E13=\"\",\"\",E13)","v":""},null,{"$f":"IF(E14=\"\",\"\",E14)","v":""}]
[null,"Class k","Name","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":"Sand"},{"$f":"IF($D5=\"\",\"\",$D5*(1/D$18-1)^2*$E5)","v":1.8050000000000002E-3},{"$f":"IF(D20<>\"\",100*D20/D$30,\"\")","v":0.86093820800839471},{"$f":"IF($D$6*$D5=0,\"\",$D5*$E5)","v":5.0000000000000004E-6},{"$f":"IF(F20<>\"\",100*F20/F$30,\"\")","v":1.9094537052949147E-3},{"$f":"IF($D$7*$D5=0,\"\",$D5*$E5)","v":5.0000000000000004E-6},{"$f":"IF(H20<>\"\",100*H20/H$30,\"\")","v":2.745130334866684E-3},{"$f":"IF($D$8*$D5=0,\"\",$D5*$E5)","v":5.0000000000000004E-6},{"$f":"IF(J20<>\"\",100*J20/J$30,\"\")","v":1.7538598069701894E-4},{"$f":"IF($D$9*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(L20<>\"\",100*L20/L$30,\"\")","v":""},{"$f":"IF($D$10*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(N20<>\"\",100*N20/N$30,\"\")","v":""},{"$f":"IF($D$11*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(P20<>\"\",100*P20/P$30,\"\")","v":""},{"$f":"IF($D$12*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(R20<>\"\",100*R20/R$30,\"\")","v":""},{"$f":"IF($D$13*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(T20<>\"\",100*T20/T$30,\"\")","v":""},{"$f":"IF($D$14*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(V20<>\"\",100*V20/V$30,\"\")","v":""}]
[null,2,{"$f":"IF(C6=\"\",\"\",C6)","v":"Sesame"},{"$f":"IF($D$5*$D6=0,\"\",$D6*$E6)","v":1.5000000000000001E-4},7.1546111468841656E-2,{"$f":"IF($D6=\"\",\"\",$D6*(1/F$18-1)^2*$E6)","v":5.4150000000000004E-2},20.679383628343928,1.5000000000000001E-4,8.2353910046000525E-2,1.5000000000000001E-4,5.2615794209105683E-3,"","","","","","","","","","",{"$f":"IF($D$14*$D6=0,\"\",$D6*$E6)","v":""},""]
[null,3,{"$f":"IF(C7=\"\",\"\",C7)","v":"Barley"},{"$f":"IF($D$5*$D7=0,\"\",$D7*$E7)","v":3.15E-2},15.024683408456747,{"$f":"IF($D$6*$D7=0,\"\",$D7*$E7)","v":3.15E-2},12.029558343357962,{"$f":"IF($D7=\"\",\"\",$D7*(1/H$18-1)^2*$E7)","v":5.7857142857142864E-3},3.1765079589171634,3.15E-2,1.1049316783912193,"","","","","","","","","","","",""]
[null,4,"Steel",0.17620000000000002,84.042832272066008,{"$f":"IF($D$6*$D8=0,\"\",$D8*$E8)","v":0.17620000000000002},67.289148574592801,{"$f":"IF($D$7*$D8=0,\"\",$D8*$E8)","v":0.17620000000000002},96.738393000701961,{"$f":"IF($D8=\"\",\"\",$D8*(1/J$18-1)^2*$E8)","v":2.8192000000000004},98.889631356207161,"","","","","","","","","","","",""]
[null,5,"","","","","",{"$f":"IF($D$7*$D9=0,\"\",$D9*$E9)","v":""},"",{"$f":"IF($D$8*$D9=0,\"\",$D9*$E9)","v":""},"",{"$f":"IF($D9=\"\",\"\",$D9*(1/L$18-1)^2*$E9)","v":""},"","","","","","","","","","",""]
[null,6,"","","","","","","",{"$f":"IF($D$8*$D10=0,\"\",$D10*$E10)","v":""},"",{"$f":"IF($D$9*$D10=0,\"\",$D10*$E10)","v":""},"",{"$f":"IF($D10=\"\",\"\",$D10*(1/N$18-1)^2*$E10)","v":""},"","","","","","","","",""]
[null,7,"","","","","","","","","",{"$f":"IF($D$9*$D11=0,\"\",$D11*$E11)","v":""},"",{"$f":"IF($D$10*$D11=0,\"\",$D11*$E11)","v":""},"",{"$f":"IF($D11=\"\",\"\",$D11*(1/P$18-1)^2*$E11)","v":""},"","","","","","",""]
[null,8,"","",{"$f":"IF(D27<>\"\",100*D27/D$30,\"\")","v":""},"",{"$f":"IF(F27<>\"\",100*F27/F$30,\"\")","v":""},"",{"$f":"IF(H27<>\"\",100*H27/H$30,\"\")","v":""},"",{"$f":"IF(J27<>\"\",100*J27/J$30,\"\")","v":""},"",{"$f":"IF(L27<>\"\",100*L27/L$30,\"\")","v":""},{"$f":"IF($D$10*$D12=0,\"\",$D12*$E12)","v":""},{"$f":"IF(N27<>\"\",100*N27/N$30,\"\")","v":""},{"$f":"IF($D$11*$D12=0,\"\",$D12*$E12)","v":""},{"$f":"IF(P27<>\"\",100*P27/P$30,\"\")","v":""},{"$f":"IF($D12=\"\",\"\",$D12*(1/R$18-1)^2*$E12)","v":""},{"$f":"IF(R27<>\"\",100*R27/R$30,\"\")","v":""},"",{"$f":"IF(T27<>\"\",100*T27/T$30,\"\")","v":""},"",{"$f":"IF(V27<>\"\",100*V27/V$30,\"\")","v":""}]
[null,9,"","",{"$f":"IF(D28<>\"\",100*D28/D$30,\"\")","v":""},"",{"$f":"IF(F28<>\"\",100*F28/F$30,\"\")","v":""},"",{"$f":"IF(H28<>\"\",100*H28/H$30,\"\")","v":""},"",{"$f":"IF(J28<>\"\",100*J28/J$30,\"\")","v":""},"",{"$f":"IF(L28<>\"\",100*L28/L$30,\"\")","v":""},"",{"$f":"IF(N28<>\"\",100*N28/N$30,\"\")","v":""},{"$f":"IF($D$11*$D13=0,\"\",$D13*$E13)","v":""},{"$f":"IF(P28<>\"\",100*P28/P$30,\"\")","v":""},{"$f":"IF($D$12*$D13=0,\"\",$D13*$E13)","v":""},{"$f":"IF(R28<>\"\",100*R28/R$30,\"\")","v":""},{"$f":"IF($D13=\"\",\"\",$D13*(1/T$18-1)^2*$E13)","v":""},{"$f":"IF(T28<>\"\",100*T28/T$30,\"\")","v":""},"",{"$f":"IF(V28<>\"\",100*V28/V$30,\"\")","v":""}]
[null,10,"","","","","","","","","","","","","","","",{"$f":"IF($D$12*$D14=0,\"\",$D14*$E14)","v":""},"",{"$f":"IF($D$13*$D14=0,\"\",$D14*$E14)","v":""},"",{"$f":"IF($D14=\"\",\"\",$D14*(1/V$18-1)^2*$E14)","v":""},""]
[null,"The lot","HI(L):",{"$f":"IF(D18=\"\",\"\",SUM(D20:D29))","v":0.20965500000000004},{"$f":"IF(D18=\"\",\"\",SUM(E20:E29))","v":99.999999999999986},{"$f":"IF(F18=\"\",\"\",SUM(F20:F29))","v":0.26185500000000006},{"$f":"IF(F18=\"\",\"\",SUM(G20:G29))","v":99.999999999999986},{"$f":"IF(H18=\"\",\"\",SUM(H20:H29))","v":0.18214071428571432},{"$f":"IF(H18=\"\",\"\",SUM(I20:I29))","v":99.999999999999986},{"$f":"IF(J18=\"\",\"\",SUM(J20:J29))","v":2.8508550000000006},{"$f":"IF(J18=\"\",\"\",SUM(K20:K29))","v":99.999999999999986},{"$f":"IF(L18=\"\",\"\",SUM(L20:L29))","v":""},{"$f":"IF(L18=\"\",\"\",SUM(M20:M29))","v":""},{"$f":"IF(N18=\"\",\"\",SUM(N20:N29))","v":""},{"$f":"IF(N18=\"\",\"\",SUM(O20:O29))","v":""},{"$f":"IF(P18=\"\",\"\",SUM(P20:P29))","v":""},{"$f":"IF(P18=\"\",\"\",SUM(Q20:Q29))","v":""},{"$f":"IF(R18=\"\",\"\",SUM(R20:R29))","v":""},{"$f":"IF(R18=\"\",\"\",SUM(S20:S29))","v":""},{"$f":"IF(T18=\"\",\"\",SUM(T20:T29))","v":""},{"$f":"IF(T18=\"\",\"\",SUM(U20:U29))","v":""},{"$f":"IF(V18=\"\",\"\",SUM(V20:V29))","v":""},{"$f":"IF(V18=\"\",\"\",SUM(W20:W29))","v":""}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Table 9"]
[null,"Class k","Name","f","r, g/cm","dl(k)","d(k)","dn(k)","g(k)","m(k)",null,"1) Enter parameters f, r, dl(k)and  d(k)",null,null,null,null,"f:","Shape factor"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":"Sand"},null,null,null,null,{"$f":"IF(F42=\"\",\"\",(((G42^4-F42^4)/(4*(G42-F42)))^(1/3)))","v":""},{"$f":"IF(F42=\"\",\"\",(1-(F42/G42)^4)/(4*(1-F42/G42)))","v":""},{"$f":"IF(D42=\"\",\"\",D42*E42*H42^3)","v":""},null,"2) Press the button to copy m(k)'s to Table 1",null,null,null,null,"r:","Density, g×cm-3"]
[null,2,{"$f":"IF(C6=\"\",\"\",C6)","v":"Sesame"},null,null,null,null,"",{"$f":"IF(F43=\"\",\"\",(1-(F43/G43)^4)/(4*(1-F43/G43)))","v":""},"",null,null,null,null,null,null,"dl(k):","Lower diameter, cm"]
[null,3,"Barley",null,null,null,null,"","","",null,null,null,null,null,null,"d(k):","Upper diameter, cm"]
[null,4,"Steel",null,null,null,null,"","","",null,null,null,null,null,null,"dn(k):","Nominel diameter of the class, cm"]
[null,5,"",null,null,null,null,"","","",null,null,null,null,null,null,"g(k):","The granulometric factor for class k"]
[null,6,"",null,null,null,null,"","","",null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g",null,null,null,"m(k) = f×g×dn3×r"]
[null,7,"",null,null,null,null,"","",""]
[null,8,"",null,null,null,null,"","","",null,null,null,null,null,null,"f is the ratio of a fragment of class k of diameter d(k) and a cube with sides d(k)"]
[null,9,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For a sphere  f = p/6 = 0.52"]
[null,10,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For 'average particles' f = 0.5 is often used"]

{"sheet":"Classes as analyte","index":1,"n_rows":51,"n_cols":27,"rows_kept":51,"cut":false,"hidden":false,"merged":[]}
[{"$f":"'Example Table 2'!A1","v":"Gys_Extended_1.1"},null,null,null,null,null,null,null,null,null,"Prediction of the Fundamental Sampling Error, FSE:",null,null,null,null,null,null,null,null,{"$f":"'Example Table 2'!V1","v":0}]
[null,null,null,null,null,null,null,null,null,null,"s(FSE) % caused by the constiutional heterogeneity of a 0-dimensional lot"]
[null,"Table 1",{"$f":"IF(SUM(E5:E14)=1,\"\",\"ERROR:  Sum of x(k) must be 1\")","v":"ERROR:  Sum of x(k) must be 1"},null,null,null,null,null,"Table 2",null,null,null,null,null,null,null,null,null,null,"ONLY ENTER values in the WHITE CELLS"]
[null,"Class k","Name","m(k), g","x(k)","s(FSE) %",null,"Mass factor",{"$f":"IF(I6=\"\",\"\",1/I6-1/I5)","v":""},null,"1) Enter parameters for the classes in Table 1"]
[null,1,null,null,null,{"$f":"IF(C5=\"\",\"\",100*SQRT($I$4*D30))","v":""},null,"M(L), g",null,null,"2) Enter mass of the lot and the sample in Table 2",null,null,null,null,null,null,null,null,"Grey cells are protected, to unprotect, click Review and Unprotect Sheet "]
[null,2,null,null,null,{"$f":"IF(C6=\"\",\"\",100*SQRT($I$4*F30))","v":""},null,"M(S), g"]
[null,3,null,null,null,{"$f":"IF(C7=\"\",\"\",100*SQRT($I$4*H30))","v":""},null,null,null,null,"For estimation of m(k) = fgd3r use Table 9 below (Cell B40+)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a(k): Concentration of analyte k in the lot, g/g"]
[null,4,null,null,null,{"$f":"IF(C8=\"\",\"\",100*SQRT($I$4*J30))","v":""}]
[null,5,null,null,null,{"$f":"IF(C9=\"\",\"\",100*SQRT($I$4*L30))","v":""},null,null,null,null,"Each class is considered to be an analyte in this sheet",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Here a(k) = 1 for the class that is considered analyte."]
[null,6,null,null,null,{"$f":"IF(C10=\"\",\"\",100*SQRT($I$4*N30))","v":""},null,"Headings and comments:"]
[null,7,null,null,null,{"$f":"IF(C11=\"\",\"\",100*SQRT($I$4*P30))","v":""}]
[null,8,null,null,null,{"$f":"IF(C12=\"\",\"\",100*SQRT($I$4*R30))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g"]
[null,9,null,null,null,{"$f":"IF(C13=\"\",\"\",100*SQRT($I$4*T30))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,"x(k):","Fraction of class k in the lot, M(k)/M(L)"]
[null,10,null,null,null,{"$f":"IF(C14=\"\",\"\",100*SQRT($I$4*V30))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,"a(L):","Concentration of analyte i in the lot, g/g"]
[null,null,null,"Sum:",{"$f":"SUM(E5:E14)","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"HI:","Heterogeneity Invariant for the class HI(k) or lot HI(L), g or %"]
[null,"Table 3"]
[null,null,"Analyte:",{"$f":"IF(C5=\"\",\"\",C5)","v":""},null,{"$f":"IF(C6=\"\",\"\",C6)","v":""},null,{"$f":"IF(C7=\"\",\"\",C7)","v":""},null,{"$f":"IF(C8=\"\",\"\",C8)","v":""},null,{"$f":"IF(C9=\"\",\"\",C9)","v":""},null,{"$f":"IF(C10=\"\",\"\",C10)","v":""},null,{"$f":"IF(C11=\"\",\"\",C11)","v":""},null,{"$f":"IF(C12=\"\",\"\",C12)","v":""},null,{"$f":"IF(C13=\"\",\"\",C13)","v":""},null,{"$f":"IF(C14=\"\",\"\",C14)","v":""}]
[null,null,"a(L)",{"$f":"IF(E5=\"\",\"\",E5)","v":""},null,{"$f":"IF(E6=\"\",\"\",E6)","v":""},null,{"$f":"IF(E7=\"\",\"\",E7)","v":""},null,{"$f":"IF(E8=\"\",\"\",E8)","v":""},null,{"$f":"IF(E9=\"\",\"\",E9)","v":""},null,{"$f":"IF(E10=\"\",\"\",E10)","v":""},null,{"$f":"IF(E11=\"\",\"\",E11)","v":""},null,{"$f":"IF(E12=\"\",\"\",E12)","v":""},null,{"$f":"IF(E13=\"\",\"\",E13)","v":""},null,{"$f":"IF(E14=\"\",\"\",E14)","v":""}]
[null,"Class k","Name","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %","HI(k), g","HI(k), %"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":""},{"$f":"IF($D5=\"\",\"\",$D5*(1/D$18-1)^2*$E5)","v":""},{"$f":"IF(D20<>\"\",100*D20/D$30,\"\")","v":""},{"$f":"IF($D$6*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(F20<>\"\",100*F20/F$30,\"\")","v":""},{"$f":"IF($D$7*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(H20<>\"\",100*H20/H$30,\"\")","v":""},{"$f":"IF($D$8*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(J20<>\"\",100*J20/J$30,\"\")","v":""},{"$f":"IF($D$9*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(L20<>\"\",100*L20/L$30,\"\")","v":""},{"$f":"IF($D$10*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(N20<>\"\",100*N20/N$30,\"\")","v":""},{"$f":"IF($D$11*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(P20<>\"\",100*P20/P$30,\"\")","v":""},{"$f":"IF($D$12*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(R20<>\"\",100*R20/R$30,\"\")","v":""},{"$f":"IF($D$13*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(T20<>\"\",100*T20/T$30,\"\")","v":""},{"$f":"IF($D$14*$D5=0,\"\",$D5*$E5)","v":""},{"$f":"IF(V20<>\"\",100*V20/V$30,\"\")","v":""}]
[null,2,{"$f":"IF(C6=\"\",\"\",C6)","v":""},{"$f":"IF($D$5*$D6=0,\"\",$D6*$E6)","v":""},"",{"$f":"IF($D6=\"\",\"\",$D6*(1/F$18-1)^2*$E6)","v":""},{"$f":"IF(F21<>\"\",100*F21/F$30,\"\")","v":""},{"$f":"IF($D$7*$D6=0,\"\",$D6*$E6)","v":""},{"$f":"IF(H21<>\"\",100*H21/H$30,\"\")","v":""},"",{"$f":"IF(J21<>\"\",100*J21/J$30,\"\")","v":""},"",{"$f":"IF(L21<>\"\",100*L21/L$30,\"\")","v":""},"",{"$f":"IF(N21<>\"\",100*N21/N$30,\"\")","v":""},"",{"$f":"IF(P21<>\"\",100*P21/P$30,\"\")","v":""},"",{"$f":"IF(R21<>\"\",100*R21/R$30,\"\")","v":""},"",{"$f":"IF(T21<>\"\",100*T21/T$30,\"\")","v":""},{"$f":"IF($D$14*$D6=0,\"\",$D6*$E6)","v":""},{"$f":"IF(V21<>\"\",100*V21/V$30,\"\")","v":""}]
[null,3,{"$f":"IF(C7=\"\",\"\",C7)","v":""},{"$f":"IF($D$5*$D7=0,\"\",$D7*$E7)","v":""},"",{"$f":"IF($D$6*$D7=0,\"\",$D7*$E7)","v":""},{"$f":"IF(F22<>\"\",100*F22/F$30,\"\")","v":""},{"$f":"IF($D7=\"\",\"\",$D7*(1/H$18-1)^2*$E7)","v":""},{"$f":"IF(H22<>\"\",100*H22/H$30,\"\")","v":""},"",{"$f":"IF(J22<>\"\",100*J22/J$30,\"\")","v":""},"",{"$f":"IF(L22<>\"\",100*L22/L$30,\"\")","v":""},"",{"$f":"IF(N22<>\"\",100*N22/N$30,\"\")","v":""},"",{"$f":"IF(P22<>\"\",100*P22/P$30,\"\")","v":""},"",{"$f":"IF(R22<>\"\",100*R22/R$30,\"\")","v":""},"",{"$f":"IF(T22<>\"\",100*T22/T$30,\"\")","v":""},"",{"$f":"IF(V22<>\"\",100*V22/V$30,\"\")","v":""}]
[null,4,"","","",{"$f":"IF($D$6*$D8=0,\"\",$D8*$E8)","v":""},{"$f":"IF(F23<>\"\",100*F23/F$30,\"\")","v":""},{"$f":"IF($D$7*$D8=0,\"\",$D8*$E8)","v":""},{"$f":"IF(H23<>\"\",100*H23/H$30,\"\")","v":""},{"$f":"IF($D8=\"\",\"\",$D8*(1/J$18-1)^2*$E8)","v":""},{"$f":"IF(J23<>\"\",100*J23/J$30,\"\")","v":""},"",{"$f":"IF(L23<>\"\",100*L23/L$30,\"\")","v":""},"",{"$f":"IF(N23<>\"\",100*N23/N$30,\"\")","v":""},"",{"$f":"IF(P23<>\"\",100*P23/P$30,\"\")","v":""},"",{"$f":"IF(R23<>\"\",100*R23/R$30,\"\")","v":""},"",{"$f":"IF(T23<>\"\",100*T23/T$30,\"\")","v":""},"",{"$f":"IF(V23<>\"\",100*V23/V$30,\"\")","v":""}]
[null,5,"","","","",{"$f":"IF(F24<>\"\",100*F24/F$30,\"\")","v":""},{"$f":"IF($D$7*$D9=0,\"\",$D9*$E9)","v":""},{"$f":"IF(H24<>\"\",100*H24/H$30,\"\")","v":""},{"$f":"IF($D$8*$D9=0,\"\",$D9*$E9)","v":""},{"$f":"IF(J24<>\"\",100*J24/J$30,\"\")","v":""},{"$f":"IF($D9=\"\",\"\",$D9*(1/L$18-1)^2*$E9)","v":""},{"$f":"IF(L24<>\"\",100*L24/L$30,\"\")","v":""},"",{"$f":"IF(N24<>\"\",100*N24/N$30,\"\")","v":""},"",{"$f":"IF(P24<>\"\",100*P24/P$30,\"\")","v":""},"",{"$f":"IF(R24<>\"\",100*R24/R$30,\"\")","v":""},"",{"$f":"IF(T24<>\"\",100*T24/T$30,\"\")","v":""},"",{"$f":"IF(V24<>\"\",100*V24/V$30,\"\")","v":""}]
[null,6,"","","","",{"$f":"IF(F25<>\"\",100*F25/F$30,\"\")","v":""},"",{"$f":"IF(H25<>\"\",100*H25/H$30,\"\")","v":""},{"$f":"IF($D$8*$D10=0,\"\",$D10*$E10)","v":""},{"$f":"IF(J25<>\"\",100*J25/J$30,\"\")","v":""},{"$f":"IF($D$9*$D10=0,\"\",$D10*$E10)","v":""},{"$f":"IF(L25<>\"\",100*L25/L$30,\"\")","v":""},{"$f":"IF($D10=\"\",\"\",$D10*(1/N$18-1)^2*$E10)","v":""},{"$f":"IF(N25<>\"\",100*N25/N$30,\"\")","v":""},"",{"$f":"IF(P25<>\"\",100*P25/P$30,\"\")","v":""},"",{"$f":"IF(R25<>\"\",100*R25/R$30,\"\")","v":""},"",{"$f":"IF(T25<>\"\",100*T25/T$30,\"\")","v":""},"",{"$f":"IF(V25<>\"\",100*V25/V$30,\"\")","v":""}]
[null,7,"","","","",{"$f":"IF(F26<>\"\",100*F26/F$30,\"\")","v":""},"",{"$f":"IF(H26<>\"\",100*H26/H$30,\"\")","v":""},"",{"$f":"IF(J26<>\"\",100*J26/J$30,\"\")","v":""},{"$f":"IF($D$9*$D11=0,\"\",$D11*$E11)","v":""},{"$f":"IF(L26<>\"\",100*L26/L$30,\"\")","v":""},{"$f":"IF($D$10*$D11=0,\"\",$D11*$E11)","v":""},{"$f":"IF(N26<>\"\",100*N26/N$30,\"\")","v":""},{"$f":"IF($D11=\"\",\"\",$D11*(1/P$18-1)^2*$E11)","v":""},{"$f":"IF(P26<>\"\",100*P26/P$30,\"\")","v":""},"",{"$f":"IF(R26<>\"\",100*R26/R$30,\"\")","v":""},"",{"$f":"IF(T26<>\"\",100*T26/T$30,\"\")","v":""},"",{"$f":"IF(V26<>\"\",100*V26/V$30,\"\")","v":""}]
[null,8,"","",{"$f":"IF(D27<>\"\",100*D27/D$30,\"\")","v":""},"",{"$f":"IF(F27<>\"\",100*F27/F$30,\"\")","v":""},"",{"$f":"IF(H27<>\"\",100*H27/H$30,\"\")","v":""},"",{"$f":"IF(J27<>\"\",100*J27/J$30,\"\")","v":""},"",{"$f":"IF(L27<>\"\",100*L27/L$30,\"\")","v":""},{"$f":"IF($D$10*$D12=0,\"\",$D12*$E12)","v":""},{"$f":"IF(N27<>\"\",100*N27/N$30,\"\")","v":""},{"$f":"IF($D$11*$D12=0,\"\",$D12*$E12)","v":""},{"$f":"IF(P27<>\"\",100*P27/P$30,\"\")","v":""},{"$f":"IF($D12=\"\",\"\",$D12*(1/R$18-1)^2*$E12)","v":""},{"$f":"IF(R27<>\"\",100*R27/R$30,\"\")","v":""},"",{"$f":"IF(T27<>\"\",100*T27/T$30,\"\")","v":""},"",{"$f":"IF(V27<>\"\",100*V27/V$30,\"\")","v":""}]
[null,9,"","",{"$f":"IF(D28<>\"\",100*D28/D$30,\"\")","v":""},"",{"$f":"IF(F28<>\"\",100*F28/F$30,\"\")","v":""},"",{"$f":"IF(H28<>\"\",100*H28/H$30,\"\")","v":""},"",{"$f":"IF(J28<>\"\",100*J28/J$30,\"\")","v":""},"",{"$f":"IF(L28<>\"\",100*L28/L$30,\"\")","v":""},"",{"$f":"IF(N28<>\"\",100*N28/N$30,\"\")","v":""},{"$f":"IF($D$11*$D13=0,\"\",$D13*$E13)","v":""},{"$f":"IF(P28<>\"\",100*P28/P$30,\"\")","v":""},{"$f":"IF($D$12*$D13=0,\"\",$D13*$E13)","v":""},{"$f":"IF(R28<>\"\",100*R28/R$30,\"\")","v":""},{"$f":"IF($D13=\"\",\"\",$D13*(1/T$18-1)^2*$E13)","v":""},{"$f":"IF(T28<>\"\",100*T28/T$30,\"\")","v":""},"",{"$f":"IF(V28<>\"\",100*V28/V$30,\"\")","v":""}]
[null,10,"","","","",{"$f":"IF(F29<>\"\",100*F29/F$30,\"\")","v":""},"",{"$f":"IF(H29<>\"\",100*H29/H$30,\"\")","v":""},"",{"$f":"IF(J29<>\"\",100*J29/J$30,\"\")","v":""},"",{"$f":"IF(L29<>\"\",100*L29/L$30,\"\")","v":""},"",{"$f":"IF(N29<>\"\",100*N29/N$30,\"\")","v":""},"",{"$f":"IF(P29<>\"\",100*P29/P$30,\"\")","v":""},{"$f":"IF($D$12*$D14=0,\"\",$D14*$E14)","v":""},{"$f":"IF(R29<>\"\",100*R29/R$30,\"\")","v":""},{"$f":"IF($D$13*$D14=0,\"\",$D14*$E14)","v":""},{"$f":"IF(T29<>\"\",100*T29/T$30,\"\")","v":""},{"$f":"IF($D14=\"\",\"\",$D14*(1/V$18-1)^2*$E14)","v":""},{"$f":"IF(V29<>\"\",100*V29/V$30,\"\")","v":""}]
[null,"The lot","HI(L):",{"$f":"IF(D18=\"\",\"\",SUM(D20:D29))","v":""},{"$f":"IF(D18=\"\",\"\",SUM(E20:E29))","v":""},{"$f":"IF(F18=\"\",\"\",SUM(F20:F29))","v":""},{"$f":"IF(F18=\"\",\"\",SUM(G20:G29))","v":""},{"$f":"IF(H18=\"\",\"\",SUM(H20:H29))","v":""},{"$f":"IF(H18=\"\",\"\",SUM(I20:I29))","v":""},{"$f":"IF(J18=\"\",\"\",SUM(J20:J29))","v":""},{"$f":"IF(J18=\"\",\"\",SUM(K20:K29))","v":""},{"$f":"IF(L18=\"\",\"\",SUM(L20:L29))","v":""},{"$f":"IF(L18=\"\",\"\",SUM(M20:M29))","v":""},{"$f":"IF(N18=\"\",\"\",SUM(N20:N29))","v":""},{"$f":"IF(N18=\"\",\"\",SUM(O20:O29))","v":""},{"$f":"IF(P18=\"\",\"\",SUM(P20:P29))","v":""},{"$f":"IF(P18=\"\",\"\",SUM(Q20:Q29))","v":""},{"$f":"IF(R18=\"\",\"\",SUM(R20:R29))","v":""},{"$f":"IF(R18=\"\",\"\",SUM(S20:S29))","v":""},{"$f":"IF(T18=\"\",\"\",SUM(T20:T29))","v":""},{"$f":"IF(T18=\"\",\"\",SUM(U20:U29))","v":""},{"$f":"IF(V18=\"\",\"\",SUM(V20:V29))","v":""},{"$f":"IF(V18=\"\",\"\",SUM(W20:W29))","v":""}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Table 9"]
[null,"Class k","Name","f","r, g/cm","dl(k)","d(k)","dn(k)","g(k)","m(k)",null,"1) Enter parameters f, r, dl(k)and  d(k)",null,null,null,null,"f:","Shape factor"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":""},null,null,null,null,{"$f":"IF(F42=\"\",\"\",(((G42^4-F42^4)/(4*(G42-F42)))^(1/3)))","v":""},{"$f":"IF(F42=\"\",\"\",(1-(F42/G42)^4)/(4*(1-F42/G42)))","v":""},{"$f":"IF(D42=\"\",\"\",D42*E42*H42^3)","v":""},null,"2) Press the button to copy m(k)'s to Table 1",null,null,null,null,"r:","Density, g×cm-3"]
[null,2,{"$f":"IF(C6=\"\",\"\",C6)","v":""},null,null,null,null,"",{"$f":"IF(F43=\"\",\"\",(1-(F43/G43)^4)/(4*(1-F43/G43)))","v":""},"",null,null,null,null,null,null,"dl(k):","Lower diameter, cm"]
[null,3,"",null,null,null,null,"","","",null,null,null,null,null,null,"d(k):","Upper diameter, cm"]
[null,4,"",null,null,null,null,"","","",null,null,null,null,null,null,"dn(k):","Nominel diameter of the class, cm"]
[null,5,"",null,null,null,null,"","","",null,null,null,null,null,null,"g(k):","The granulometric factor for class k"]
[null,6,"",null,null,null,null,"","","",null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g",null,null,null,"m(k) = f×g×dn3×r"]
[null,7,"",null,null,null,null,"","",""]
[null,8,"",null,null,null,null,"","","",null,null,null,null,null,null,"f is the ratio of a fragment of class k of diameter d(k) and a cube with sides d(k)"]
[null,9,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For a sphere  f = p/6 = 0.52"]
[null,10,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For 'average particles' f = 0.5 is often used"]

{"sheet":"Example Table 5","index":2,"n_rows":81,"n_cols":22,"rows_kept":81,"cut":false,"hidden":false,"merged":[]}
[{"$f":"'Example Table 2'!A1","v":"Gys_Extended_1.1"},null,null,null,null,null,null,null,null,"Prediction of the Fundamental Sampling Error, FSE:",null,null,null,null,null,null,null,{"$f":"'Example Table 2'!T1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, ECP, PLEN, University of Copenhagen, 2021"}]
[null,null,null,null,null,null,null,null,null,"s(FSE) % caused by the constiutional heterogeneity of a 0-dimensional lot"]
[null,"Table 1",{"$f":"IF(SUM(E5:E14)=1,\"\",\"ERROR:  Sum of x(k) must be 1\")","v":""},null,null,null,"Table 2",null,null,null,null,null,null,null,null,null,null,"ONLY ENTER values in the WHITE CELLS"]
[null,"Class k","Name","m(k), g","x(k)",null,"Lot mass:",null,null,"1) Enter parameters for the classes in Table 1"]
[null,1,"Silt and clay",8.2828068750000123E-8,0.26800000000000002,null,"M(L), g",1000000,null,"2) Enter mass of the lot in Table 2",null,null,null,null,null,null,null,"This sheet is protected, to unprotect, click Review and Unprotect Sheet "]
[null,2,"Sand fine",3.8305243187499989E-6,0.27800000000000002,null,null,null,null,"3) Enter concentrations, a(i,k),for up to 6 analytes in Table 3-8 "]
[null,3,"Sand medium",1.0600000000000004E-4,0.23200000000000001,null,null,null,null,"4) Enter sample mass, M(S), and/or s(FSE) % in Table 3 "]
[null,4,"Sand coarse",3.7550500000000041E-3,6.7000000000000004E-2]
[null,5,"Organic Matter",2.3437500000000014E-5,0.155,null,null,null,null,"For estimation of m(k) = fgd3r use Table 9 below (Cell B70+)"]
[null,6,null,null,null,null,"Headings and comments:"]
[null,7,null,null,null,null,"The data and results for Table 5 in the paper: https://doi.org/10.1016/j.aca.2021.339127",null,null,null,null,null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g"]
[null,8,null,null,null,null,"Results for predicted uncertainty in Table 5 is highlighted in yellow",null,null,null,null,null,null,null,null,null,null,"x(k):","Fraction of class k in the lot, M(k)/M(L)"]
[null,9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a(i,k):","Concentration of analyte i in class k, g/g"]
[null,10,null,null,null,null,"To make your own estimates use the sheet: Gys extended",null,null,null,null,null,null,null,null,null,null,"a(L):","Concentration of analyte i in the lot, g/g"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"HI:","Heterogeneity Invariant for the class, HI(k),and the lot, HI(L)"]
[null,"Table 3",null,null,null,null,null,null,null,"Table 4"]
[null,"Analyte 1:","Silt and clay",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g ",null,"Analyte 2:","Sand fine",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g ",null,null,"OBS: A class can be an analyte."]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,null,"For the class as analyte: ",null,null,"a(i,k) = any number <> 0"]
[null,{"$f":"SUM($E$5:E$14*B21:B30)","v":2.6800000000000001E-4},{"$f":"SUM(C21:C30)","v":2.8104365000356017E-4},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J21:J30)","v":2.7800000000000004E-4},{"$f":"SUM(K21:K30)","v":2.8701806200147307E-4},null,null,null,null,null,null,null,"For all other classes:",null,null,"a(i,k) =  0"]
[null,"a(1,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(2,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null," "]
[null,1E-3,{"$f":"IF(B21=\"\",\"\",D5*(B21/B$19-1)^2*E5)","v":1.6560174294738832E-7},{"$f":"IF(C21=\"\",\"\",100*C21/$C$19)","v":5.8923851489009103E-2},1,{"$f":"IF(E21=\"\",\"\",100*SQRT((1/E21-1/$H$5)*$C$19))","v":1.6764348151953605},1,{"$f":"IF(G21=\"\",\"\",1/(((G21/100)^2)/$C$19+1/$H$5))","v":2.8104286015044795},null,0,{"$f":"IF(J21=\"\",\"\",D5*(J21/J$19-1)^2*E5)","v":2.2197922425000035E-8},{"$f":"IF(K21=\"\",\"\",100*K21/K$19)","v":7.7339810150645182E-3},{"$f":"IF($E21=\"\",\"\",IF(J$19=0,\"\",$E21))","v":1},{"$f":"IF(M21=\"\",\"\",100*SQRT((1/M21-1/$H$5)*K$19))","v":1.6941598950022725},{"$f":"IF($G21=\"\",\"\",IF(J$19=0,\"\",$G21))","v":1},{"$f":"IF(O21=\"\",\"\",1/(((O21/100)^2)/$K$19+1/H$5))","v":2.8701723821015834},null,null,"In this example the concentrations are set equal to 0.001"]
[null,0,{"$f":"IF(B22=\"\",\"\",D6*(B22/B$19-1)^2*E6)","v":1.0648857606124999E-6},0.3789040459014143,0.1,5.3013547504312069,2,0.70260863134966467,null,1E-3,{"$f":"IF(J22=\"\",\"\",D6*(J22/J$19-1)^2*E6)","v":7.1827015790477504E-6},{"$f":"IF(K22=\"\",\"\",100*K22/K$19)","v":2.5025259835427662},{"$f":"IF($E22=\"\",\"\",IF(J$19=0,\"\",$E22))","v":0.1},{"$f":"IF(M22=\"\",\"\",100*SQRT((1/M22-1/$H$5)*K$19))","v":5.3574063995525574},{"$f":"IF($G22=\"\",\"\",IF(J$19=0,\"\",$G22))","v":2},{"$f":"IF(O22=\"\",\"\",1/(((O22/100)^2)/$K$19+1/H$5))","v":0.71754464013300268},null,null,"but, any number <> 0 will give the same result"]
[null,0,2.4592000000000011E-5,8.7502421775722343,2.5000000000000001E-2,10.602709898464051,5,0.11241744736374017,null,0,2.4592000000000011E-5,8.5681018917456839,2.5000000000000001E-2,10.714813200910626,5,0.11480721161989185]
[null,0,2.515883500000003E-4,89.519314881091688,0.01,16.764356450312182,10,2.8104364210500703E-2,null,0,2.515883500000003E-4,87.655929472030593,0.01,16.941607336120516,10,2.8701805376353647E-2]
[null,0,3.6328125000000023E-6,1.2926150439456585,null,"",20,7.0260912007230449E-3,null,0,3.6328125000000023E-6,1.2657086716658819,"","",20,7.1754514985497208E-3]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,"Table 5",null,null,null,null,null,null,null,"Table 6"]
[null,"Analyte 3:","Sand medium",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g ",null,"Analyte 4:","Sand coarse",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g "]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)"]
[null,{"$f":"SUM(E$5:E$14*B36:B45)","v":2.3200000000000003E-4},{"$f":"SUM(C36:C45)","v":5.257967979071758E-4},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J36:J45)","v":6.7000000000000002E-5},{"$f":"SUM(K36:K45)","v":4.8816322634242806E-2}]
[null,"a(3,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(4,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g"]
[null,0,{"$f":"IF(B36=\"\",\"\",D5*(B36/B$34-1)^2*E5)","v":2.2197922425000035E-8},{"$f":"IF(C36=\"\",\"\",100*C36/C$34)","v":4.2217682788016631E-3},{"$f":"IF($E21=\"\",\"\",IF(B$34=0,\"\",$E21))","v":1},{"$f":"IF(E36=\"\",\"\",100*SQRT((1/E36-1/$H$5)*C$34))","v":2.2930247973154976},{"$f":"IF($G21=\"\",\"\",IF(B$34=0,\"\",$G21))","v":1},{"$f":"IF(G36=\"\",\"\",1/(((G36/100)^2)/$C$34+1/H$5))","v":5.2579403329898504},null,0,{"$f":"IF(J36=\"\",\"\",D5*(J36/J$34-1)^2*E5)","v":2.2197922425000035E-8},{"$f":"IF(K36=\"\",\"\",100*K36/K$34)","v":4.5472336356260133E-5},{"$f":"IF($E21=\"\",\"\",IF(J$34=0,\"\",$E21))","v":1},{"$f":"IF(M36=\"\",\"\",100*SQRT((1/M36-1/$H$5)*K$34))","v":22.094405132956211},{"$f":"IF($G21=\"\",\"\",IF(J$34=0,\"\",$G21))","v":1},{"$f":"IF(O36=\"\",\"\",1/(((O36/100)^2)/$K$34+1/H$5))","v":487.92503928103929}]
[null,0,{"$f":"IF(B37=\"\",\"\",D6*(B37/B$34-1)^2*E6)","v":1.0648857606124999E-6},0.20252800413601887,{"$f":"IF($E22=\"\",\"\",IF(B$34=0,\"\",$E22))","v":0.1},7.251184353796944,{"$f":"IF($G22=\"\",\"\",IF(B$34=0,\"\",$G22))","v":2},1.3144902668810063,null,0,{"$f":"IF(J37=\"\",\"\",D6*(J37/J$34-1)^2*E6)","v":1.0648857606124999E-6},{"$f":"IF(K37=\"\",\"\",100*K37/K$34)","v":2.1814133124921677E-3},{"$f":"IF($E22=\"\",\"\",IF(J$34=0,\"\",$E22))","v":0.1},{"$f":"IF(M37=\"\",\"\",100*SQRT((1/M37-1/$H$5)*K$34))","v":69.868675207571044},{"$f":"IF($G22=\"\",\"\",IF(J$34=0,\"\",$G22))","v":2},{"$f":"IF(O37=\"\",\"\",1/(((O37/100)^2)/$K$34+1/H$5))","v":122.02591444458385}]
[null,1E-3,2.6948855172413797E-4,51.253364949497751,2.5000000000000001E-2,14.502369251432759,5,0.21031867492891593,null,0,2.4592000000000011E-5,5.0376592649667658E-2,2.5000000000000001E-2,139.73735565529319,5,19.526147775805267]
[null,0,2.515883500000003E-4,47.848969602210417,0.01,22.930259323636264,10,5.2579677026094986E-2,null,1E-3,4.8787010738059765E-2,99.939954722926061,0.01,220.94416069694981,10,4.8816084332070542]
[null,0,3.6328125000000023E-6,0.69091567587700276,"","",20,1.3144919774890474E-2,null,0,3.6328125000000023E-6,7.4417987754196819E-3,"","",20,1.2204065764620402]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,"Table 7",null,null,null,null,null,null,null,"Table 8"]
[null,"Analyte 5: ","Organic Matter",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g ",null,"Analyte 6:","All surfaces",null,"Sampling from a lot of ",null,{"$f":"$H$5","v":1000000},"g "]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)"]
[null,{"$f":"SUM(E$5:E$14*B51:B60)","v":1.55E-4},{"$f":"SUM(C51:C60)","v":3.8523492360239273E-4},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J51:J60)","v":0.26025010155316131},{"$f":"SUM(K51:K60)","v":2.6005593218160467E-4}]
[null,"a(5,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(6,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g"]
[null,0,{"$f":"IF(B51=\"\",\"\",D5*(B51/B$49-1)^2*E5)","v":2.2197922425000035E-8},{"$f":"IF(C51=\"\",\"\",100*C51/C$49)","v":5.7621781061342383E-3},{"$f":"IF($E21=\"\",\"\",IF(B$49=0,\"\",$E21))","v":1},{"$f":"IF(E51=\"\",\"\",100*SQRT((1/E51-1/$H$5)*C$49))","v":1.9627392551418261},{"$f":"IF($G21=\"\",\"\",IF(B$49=0,\"\",$G21))","v":1},{"$f":"IF(G51=\"\",\"\",1/(((G51/100)^2)/$C$49+1/H$5))","v":3.8523343954864626},null,0.68313912279674727,{"$f":"IF(J51=\"\",\"\",D5*(J51/J$49-1)^2*E5)","v":5.8611567318467163E-8},{"$f":"IF(K51=\"\",\"\",100*K51/K$49)","v":2.2538062034107718E-2},{"$f":"IF($E21=\"\",\"\",IF(J$49=0,\"\",$E21))","v":1},{"$f":"IF(M51=\"\",\"\",100*SQRT((1/M51-1/$H$5)*K$49))","v":1.6126241723528532},{"$f":"IF($G21=\"\",\"\",IF(J$49=0,\"\",$G21))","v":1},{"$f":"IF(O51=\"\",\"\",1/(((O51/100)^2)/$K$49+1/$H$5))","v":2.6005525589248477}]
[null,0,{"$f":"IF(B52=\"\",\"\",D6*(B52/B$49-1)^2*E6)","v":1.0648857606124999E-6},{"$f":"IF(C52=\"\",\"\",100*C52/C$49)","v":0.27642503194014306},{"$f":"IF($E22=\"\",\"\",IF(B$49=0,\"\",$E22))","v":0.1},{"$f":"IF(E52=\"\",\"\",100*SQRT((1/E52-1/$H$5)*C$49))","v":6.2067292922996122},{"$f":"IF($G22=\"\",\"\",IF(B$49=0,\"\",$G22))","v":2},{"$f":"IF(G52=\"\",\"\",1/(((G52/100)^2)/$C$49+1/H$5))","v":0.96308638146971048},null,0.19742050723925889,{"$f":"IF(J52=\"\",\"\",D6*(J52/J$49-1)^2*E6)","v":6.2065422415295373E-8},{"$f":"IF(K52=\"\",\"\",100*K52/K$49)","v":2.3866182130370811E-2},{"$f":"IF($E22=\"\",\"\",IF(J$49=0,\"\",$E22))","v":0.1},{"$f":"IF(M52=\"\",\"\",100*SQRT((1/M52-1/$H$5)*K$49))","v":5.0995676892851556},{"$f":"IF($G22=\"\",\"\",IF(J$49=0,\"\",$G22))","v":2},{"$f":"IF(O52=\"\",\"\",1/(((O52/100)^2)/$K$49+1/$H$5))","v":0.65013940777248724}]
[null,0,2.4592000000000011E-5,6.3836372284309864,2.5000000000000001E-2,12.41345905010396,5,0.15409394569600929,null,5.4469439366393063E-2,1.5375213520901617E-5,5.9122717916562104,2.5000000000000001E-2,10.199135761037919,5,0.10402236205198892]
[null,0,2.515883500000003E-4,65.307773149785547,0.01,19.627402266984888,10,3.8523490876179858E-2,null,4.7896425512759374E-3,2.424131014057705E-4,93.21575530777983,0.01,16.126249706024193,10,2.6005592541869602E-2]
[null,1E-3,1.0796748991935491E-4,28.026402411737187,"","",20,9.6308729973061009E-3,null,6.0181288046324999E-2,2.1469402651987897E-6,0.82556865639946975,"","",20,6.5013982622719353E-3]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Table 9"]
[null,"Class k","Name","f","r, g×cm-3","dl(k), cm","d(k), cm","dn(k), cm","g(k)","m(k), g",null,"1) Enter parameters f, r, dl(k)and  d(k)",null,null,null,null,"f:","Shape factor"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":"Silt and clay"},0.5,2.65,0,6.3E-3,{"$f":"IF(F72=\"\",\"\",(((G72^4-F72^4)/(4*(G72-F72)))^(1/3)))","v":3.9687513071688524E-3},{"$f":"IF(F72=\"\",\"\",(1-(F72/G72)^4)/(4*(1-F72/G72)))","v":0.25},{"$f":"IF(D72=\"\",\"\",D72*E72*H72^3)","v":8.2828068750000123E-8},null,"2) Press the button to copy m(k)'s to Table 1",null,null,null,null,"r:","Density, g×cm-3"]
[null,2,"Sand fine",0.5,2.65,6.3E-3,0.02,{"$f":"IF(F73=\"\",\"\",(((G73^4-F73^4)/(4*(G73-F73)))^(1/3)))","v":1.4245601186648563E-2},{"$f":"IF(F73=\"\",\"\",(1-(F73/G73)^4)/(4*(1-F73/G73)))","v":0.36137021874999997},3.8305243187499989E-6,null,null,null,null,null,null,"dl(k):","Lower diameter, cm"]
[null,3,"Sand medium",0.5,2.65,0.02,0.06,4.3088693800637679E-2,0.37037037037037035,1.0600000000000004E-4,null,null,null,null,null,null,"d(k):","Upper diameter, cm"]
[null,4,"Sand coarse",0.5,2.65,0.06,0.2,0.14151417655663689,0.35425000000000001,3.7550500000000041E-3,null,null,null,null,null,null,"dn(k):","Nominel diameter of the class, cm"]
[null,5,"Organic Matter",0.5,1.5,0,0.05,3.1498026247371837E-2,0.25,2.3437500000000014E-5,null,null,null,null,null,null,"g(k):","The granulometric factor for class k"]
[null,6,null,null,null,null,null,"","","",null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g",null,null,null,"m(k) = f×g×dn3×r"]
[null,7,"",null,null,null,null,"","",""]
[null,8,"",null,null,null,null,"","","",null,null,null,null,null,null,"f is the ratio of a fragment of class k of diameter d(k) and a cube with sides d(k)"]
[null,9,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For a sphere  f = p/6 = 0.52"]
[null,10,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For 'average particles' f = 0.5 is often used"]

{"sheet":"Gys extended","index":3,"n_rows":81,"n_cols":22,"rows_kept":81,"cut":false,"hidden":false,"merged":[]}
[{"$f":"'Example Table 2'!A1","v":"Gys_Extended_1.1"},null,null,null,null,null,null,null,null,"Prediction of the Fundamental Sampling Error, FSE:",null,null,null,null,null,null,null,{"$f":"'Example Table 2'!T1","v":"Author: Bo Svensmark, svensmark@plen.ku.dk, Analytical Chemistry, ECP, PLEN, University of Copenhagen, 2021"}]
[null,null,null,null,null,null,null,null,null,"s(FSE) % caused by the constiutional heterogeneity of a 0-dimensional lot"]
[null,"Table 1",{"$f":"IF(SUM(E5:E14)=1,\"\",\"ERROR:  Sum of x(k) must be 1\")","v":"ERROR:  Sum of x(k) must be 1"},null,null,"nS","Table 2",null,null,null,null,null,null,null,null,null,null,"ONLY ENTER values in the WHITE CELLS"]
[null,"Class k","Name","m(k), g","x(k)",null,"Lot mass:",null,null,"1) Enter parameters for the classes in Table 1"]
[null,1,null,null,null,null,"M(L), g",null,null,"2) Enter mass of the lot in Table 2",null,null,null,null,null,null,null,"This sheet is protected, to unprotect, click Review and Unprotect Sheet "]
[null,2,null,null,null,null,null,null,null,"3) Enter concentrations, a(i,k),for up to 6 analytes in Table 3-8 "]
[null,3,null,null,null,null,null,null,null,"4) Enter sample mass, M(S), and/or s(FSE) % in Table 3 "]
[null,4]
[null,5,null,null,null,null,null,null,null,"For estimation of m(k) = fgd3r use Table 9 below (Cell B70+)"]
[null,6,null,null,null,null,"Headings and comments:"]
[null,7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g"]
[null,8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x(k):","Fraction of class k in the lot, M(k)/M(L)"]
[null,9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a(i,k):","Concentration of analyte i in class k, g/g"]
[null,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a(L):","Concentration of analyte i in the lot, g/g"]
[null,null,null,"Sum:",{"$f":"SUM(E5:E14)","v":0},null,null,null,null,null,null,null,null,null,null,null,null,"HI:","Heterogeneity Invariant for the class, HI(k),and the lot, HI(L)"]
[null,"Table 3",null,null,null,null,null,null,null,"Table 4"]
[null,"Analyte 1:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g ",null,"Analyte 2:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g ",null,null,"OBS: A class can be an analyte."]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,null,"For the class as analyte: ",null,"a(i,k) = any number <> 0"]
[null,{"$f":"SUM($E$5:E$14*B21:B30)","v":0},{"$f":"SUM(C21:C30)","v":0},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J21:J30)","v":0},{"$f":"SUM(K21:K30)","v":0},null,null,null,null,null,null,null,"For all other classes:",null,"a(i,k) =  0"]
[null,"a(1,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(2,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g"]
[null,null,{"$f":"IF(B21=\"\",\"\",D5*(B21/B$19-1)^2*E5)","v":""},{"$f":"IF(C21=\"\",\"\",100*C21/$C$19)","v":""},null,{"$f":"IF(E21=\"\",\"\",100*SQRT((1/E21-1/$H$5)*$C$19))","v":""},null,{"$f":"IF(G21=\"\",\"\",1/(((G21/100)^2)/$C$19+1/$H$5))","v":""},null,null,{"$f":"IF(J21=\"\",\"\",D5*(J21/J$19-1)^2*E5)","v":""},{"$f":"IF(K21=\"\",\"\",100*K21/K$19)","v":""},{"$f":"IF($E21=\"\",\"\",IF(J$19=0,\"\",$E21))","v":""},{"$f":"IF(M21=\"\",\"\",100*SQRT((1/M21-1/$H$5)*K$19))","v":""},{"$f":"IF($G21=\"\",\"\",IF(J$19=0,\"\",$G21))","v":""},{"$f":"IF(O21=\"\",\"\",1/(((O21/100)^2)/$K$19+1/H$5))","v":""}]
[null,null,{"$f":"IF(B22=\"\",\"\",D6*(B22/B$19-1)^2*E6)","v":""},"",null,"",null,"",null,null,{"$f":"IF(J22=\"\",\"\",D6*(J22/J$19-1)^2*E6)","v":""},{"$f":"IF(K22=\"\",\"\",100*K22/K$19)","v":""},{"$f":"IF($E22=\"\",\"\",IF(J$19=0,\"\",$E22))","v":""},{"$f":"IF(M22=\"\",\"\",100*SQRT((1/M22-1/$H$5)*K$19))","v":""},{"$f":"IF($G22=\"\",\"\",IF(J$19=0,\"\",$G22))","v":""},{"$f":"IF(O22=\"\",\"\",1/(((O22/100)^2)/$K$19+1/H$5))","v":""}]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,null,"","",null,"",null,"",null,null,"","","","","",""]
[null,"Table 5",null,null,null,null,null,null,null,"Table 6"]
[null,"Analyte 3:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g ",null,"Analyte 4:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g "]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)"]
[null,{"$f":"SUM(E$5:E$14*B36:B45)","v":0},{"$f":"SUM(C36:C45)","v":0},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J36:J45)","v":0},{"$f":"SUM(K36:K45)","v":0}]
[null,"a(3,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(4,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g"]
[null,null,{"$f":"IF(B36=\"\",\"\",D5*(B36/B$34-1)^2*E5)","v":""},{"$f":"IF(C36=\"\",\"\",100*C36/C$34)","v":""},{"$f":"IF($E21=\"\",\"\",IF(B$34=0,\"\",$E21))","v":""},{"$f":"IF(E36=\"\",\"\",100*SQRT((1/E36-1/$H$5)*C$34))","v":""},{"$f":"IF($G21=\"\",\"\",IF(B$34=0,\"\",$G21))","v":""},{"$f":"IF(G36=\"\",\"\",1/(((G36/100)^2)/$C$34+1/H$5))","v":""},null,null,{"$f":"IF(J36=\"\",\"\",D5*(J36/J$34-1)^2*E5)","v":""},{"$f":"IF(K36=\"\",\"\",100*K36/K$34)","v":""},{"$f":"IF($E21=\"\",\"\",IF(J$34=0,\"\",$E21))","v":""},{"$f":"IF(M36=\"\",\"\",100*SQRT((1/M36-1/$H$5)*K$34))","v":""},{"$f":"IF($G21=\"\",\"\",IF(J$34=0,\"\",$G21))","v":""},{"$f":"IF(O36=\"\",\"\",1/(((O36/100)^2)/$K$34+1/H$5))","v":""}]
[null,null,{"$f":"IF(B37=\"\",\"\",D6*(B37/B$34-1)^2*E6)","v":""},"",{"$f":"IF($E22=\"\",\"\",IF(B$34=0,\"\",$E22))","v":""},"",{"$f":"IF($G22=\"\",\"\",IF(B$34=0,\"\",$G22))","v":""},"",null,null,{"$f":"IF(J37=\"\",\"\",D6*(J37/J$34-1)^2*E6)","v":""},{"$f":"IF(K37=\"\",\"\",100*K37/K$34)","v":""},{"$f":"IF($E22=\"\",\"\",IF(J$34=0,\"\",$E22))","v":""},{"$f":"IF(M37=\"\",\"\",100*SQRT((1/M37-1/$H$5)*K$34))","v":""},{"$f":"IF($G22=\"\",\"\",IF(J$34=0,\"\",$G22))","v":""},{"$f":"IF(O37=\"\",\"\",1/(((O37/100)^2)/$K$34+1/H$5))","v":""}]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,"Table 7",null,null,null,null,null,null,null,"Table 8"]
[null,"Analyte 5:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g ",null,"Analyte 6:",null,null,"Sampling from a lot of ",null,{"$f":"$H$5","v":0},"g "]
[null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)",null,null,"a(L)","HI(L), g",null,"Predict s(FSE) %",null,"Predict M(S)"]
[null,{"$f":"SUM(E$5:E$14*B51:B60)","v":0},{"$f":"SUM(C51:C60)","v":0},null,null,null,null,null,null,{"$f":"SUM(E$5:E$14*J51:J60)","v":0},{"$f":"SUM(K51:K60)","v":0}]
[null,"a(5,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g",null,"a(6,k) ","HI(k), g","HI(k), %","M(S), g","s(FSE) %","s(FSE) %","M(S), g"]
[null,null,{"$f":"IF(B51=\"\",\"\",D5*(B51/B$49-1)^2*E5)","v":""},{"$f":"IF(C51=\"\",\"\",100*C51/C$49)","v":""},{"$f":"IF($E21=\"\",\"\",IF(B$49=0,\"\",$E21))","v":""},{"$f":"IF(E51=\"\",\"\",100*SQRT((1/E51-1/$H$5)*C$49))","v":""},{"$f":"IF($G21=\"\",\"\",IF(B$49=0,\"\",$G21))","v":""},{"$f":"IF(G51=\"\",\"\",1/(((G51/100)^2)/$C$49+1/H$5))","v":""},null,null,{"$f":"IF(J51=\"\",\"\",D5*(J51/J$49-1)^2*E5)","v":""},{"$f":"IF(K51=\"\",\"\",100*K51/K$49)","v":""},{"$f":"IF($E21=\"\",\"\",IF(J$49=0,\"\",$E21))","v":""},{"$f":"IF(M51=\"\",\"\",100*SQRT((1/M51-1/$H$5)*K$49))","v":""},{"$f":"IF($G21=\"\",\"\",IF(J$49=0,\"\",$G21))","v":""},{"$f":"IF(O51=\"\",\"\",1/(((O51/100)^2)/$K$49+1/$H$5))","v":""}]
[null,null,{"$f":"IF(B52=\"\",\"\",D6*(B52/B$49-1)^2*E6)","v":""},{"$f":"IF(C52=\"\",\"\",100*C52/C$49)","v":""},{"$f":"IF($E22=\"\",\"\",IF(B$49=0,\"\",$E22))","v":""},{"$f":"IF(E52=\"\",\"\",100*SQRT((1/E52-1/$H$5)*C$49))","v":""},{"$f":"IF($G22=\"\",\"\",IF(B$49=0,\"\",$G22))","v":""},{"$f":"IF(G52=\"\",\"\",1/(((G52/100)^2)/$C$49+1/H$5))","v":""},null,null,{"$f":"IF(J52=\"\",\"\",D6*(J52/J$49-1)^2*E6)","v":""},{"$f":"IF(K52=\"\",\"\",100*K52/K$49)","v":""},{"$f":"IF($E22=\"\",\"\",IF(J$49=0,\"\",$E22))","v":""},{"$f":"IF(M52=\"\",\"\",100*SQRT((1/M52-1/$H$5)*K$49))","v":""},{"$f":"IF($G22=\"\",\"\",IF(J$49=0,\"\",$G22))","v":""},{"$f":"IF(O52=\"\",\"\",1/(((O52/100)^2)/$K$49+1/$H$5))","v":""}]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[null,null,"","","","","","",null,null,"","","","","",""]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Table 9"]
[null,"Class k","Name","f","r, g×cm-3","dl(k), cm","d(k), cm","dn(k), cm","g(k)","m(k), g",null,"1) Enter parameters f, r, dl(k)and  d(k)",null,null,null,null,"f:","Shape factor"]
[null,1,{"$f":"IF(C5=\"\",\"\",C5)","v":""},null,null,null,null,{"$f":"IF(F72=\"\",\"\",(((G72^4-F72^4)/(4*(G72-F72)))^(1/3)))","v":""},{"$f":"IF(F72=\"\",\"\",(1-(F72/G72)^4)/(4*(1-F72/G72)))","v":""},{"$f":"IF(D72=\"\",\"\",D72*E72*H72^3)","v":""},null,"2) Press the button to copy m(k)'s to Table 1",null,null,null,null,"r:","Density, g×cm-3"]
[null,2,"",null,null,null,null,"",{"$f":"IF(F73=\"\",\"\",(1-(F73/G73)^4)/(4*(1-F73/G73)))","v":""},"",null,null,null,null,null,null,"dl(k):","Lower diameter, cm"]
[null,3,"",null,null,null,null,"","","",null,null,null,null,null,null,"d(k):","Upper diameter, cm"]
[null,4,"",null,null,null,null,"","","",null,null,null,null,null,null,"dn(k):","Nominel diameter of the class, cm"]
[null,5,"",null,null,null,null,"","","",null,null,null,null,null,null,"g(k):","The granulometric factor for class k"]
[null,6,"",null,null,null,null,"","","",null,null,null,null,null,null,"m(k):","Average mass of a fragment of class k, g",null,null,null,"m(k) = f×g×dn3×r"]
[null,7,"",null,null,null,null,"","",""]
[null,8,"",null,null,null,null,"","","",null,null,null,null,null,null,"f is the ratio of a fragment of class k of diameter d(k) and a cube with sides d(k)"]
[null,9,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For a sphere  f = p/6 = 0.52"]
[null,10,"",null,null,null,null,"","","",null,null,null,null,null,null,null,"For 'average particles' f = 0.5 is often used"]