English: All terms are expressed in the same unit if mass 1.1 Single Comparison 1.1.1 Absolute Mass (1.1.1.1) mt = [ mR (1 - (at/R)) + Dt ] / ( 1 - (at/t)) (1.1.1.2) u2 (mt) ≈ u2(mR) + (mt/t-mR/R)2u2(at) + at2(-mt/t2)2u2(t) + u2(Dt) 1.1.2 Conventional Mass (1.1.2.1 A) mct = ((t - ac) / (t - at)) { (mcR (R - at)/(R - ac)) + (Dt c / ( c - ac)) } (1.1.2.1 B) mct = [(c (t - ac)) / ((c - ac) (t - at)) ] {mR (1 - (at /R)) + Dt } (1.1.2.2 A) u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [(mct2 u2(t))/t2(t - ac)2] (1.1.2.2 B) u2(mct) ≈ (1-(ac/c))-2 {u2(mR) + (mR/R - mt/t)2u2(at) + (ac -at)2 mt2 u2(t)/t4 + u2(Dt)}  1.2 Series of Intercomparisons 1.2.1 Absolute Mass (1.2.1.1) Mt = [ Σ C ijP m i + CM’P M’(1 - (at/M’)) ] / ( 1 - (at/t)) (1.2.1.1_1990) Mt = [ CM’ M’(1 - (at/M’)) + CStSt ] / ( 1 - (at/t)) (1.2.1.2) u2(Mt) ≈ u2(Dt) + CM’Q u2(M’) + (Mt/t - CM’P M’/M’)2 u2(at) + at2 (Mt2/t4) u2(t) (1.2.1.2_1990) u2(Mt) ≈ u2(Dt) + CσM’ u2(M’) + (Mt/t - CM’ M’/M’)2u2(at) + at2 [(Mt2/t4)u2(t)] 1.2.2 Conventional Mass (1.2.2.1) Mct = (t-ac)/(t-at) { (c/(c-ac)) Σ C ijP m i + CM’P M’c (M’-at) /(M’-ac) }  (1.2.2.1_1990) Mct = ((t - ac) / (t - at)) { (CM’ M’c (M’ - at)/(M’ - ac)) + (CSt St c / ( c - ac)) } (1.2.2.2) u2(Mct) = [(t-ac)/(t-at)] 2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)] 2 u2(M’c)  + [Mct (at-ac)/(t-ac)2] 2 u2(t) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } (1.2.2.2_app.) approximate equation, if at ≈ ac u2 (Mct) ≈ [c/(c-ac)]2 u2(Dt) + CM’Q u2(M’c) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) (1.2.2.2_app rel.) approximate equation (relative terms) ▪ u2rel (Mct) ≈ [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at)  ▪ mt , Mt = absolute mass of object t ▪ mR , M’ = absolute mass of reference (or lead weight) R ▪ mct , Mct = conventional mass of unknown mass t ▪ mcR , M’c = conventional mass of reference (or lead weight) R ▪ Dt = calculated difference between unknown mass t and reference (or lead weight) R ▪ t = density of the unknown mass t (kg/m3) - usually provided by manufacturer ▪ R, M’ = density of the reference (or lead weight) R (kg/m3) - usually found on calibration certificate for the reference (or lead weight) ▪ at = air density at the time of the calibration (kg/m3) - the formula provided in section 3.2 can be used ▪ ac = conventional air density; equal by definition to 1.2 kg/m3.
French: Tous les termes sont exprimés dans la même unité de masse 1.1 Comparaison unique 1.1.1 Masse absolue (1.1.1.1) mt = [ mR (1 - (at/R)) + Dt ] / ( 1 - (at/t)) (1.1.1.2) u2 (mt) ≈ u2(mR) + (mt/t-mR/R)2u2(at) + at2(-mt/t2)2u2(t) + u2(Dt) 1.1.2 Masse conventionnelle (1.1.2.1 A) mct = ((t - ac) / (t - at)) { (mcR (R - at)/(R - ac)) + (Dt c / ( c - ac)) } (1.1.2.1 B) mct = [(c (t - ac)) / ((c - ac) (t - at)) ] {mR (1 - (at /R)) + Dt } (1.1.2.2 A) u2(mct) ≈ u2(mcR)+ c2/(c - ac)2 u2(Dt)+ [mcR/(R - ac) - mct/(t - ac)] 2u2(at) + (ac -at)2 [(mct2 u2(t))/t2(t - ac)2] (1.1.2.2 B) u2(mct) ≈ (1-(ac/c))-2 {u2(mR) + (mR/R - mt/t)2u2(at) + (ac -at)2 mt2 u2(t)/t4 + u2(Dt)}  1.2 Séries d'intercomparaison 1.2.1 Masse absolue (1.2.1.1) Mt = [ Σ C ijP m i + CM’P M’(1 - (at/M’)) ] / ( 1 - (at/t)) (1.2.1.1_1990) Mt = [ CM’ M’(1 - (at/M’)) + CStSt ] / ( 1 - (at/t)) (1.2.1.2) u2(Mt) ≈ u2(Dt) + CM’Q u2(M’) + (Mt/t - CM’P M’/M’)2 u2(at) + at2 (Mt2/t4) u2(t) (1.2.1.2_1990) u2(Mt) ≈ u2(Dt) + CσM’ u2(M’) + (Mt/t - CM’ M’/M’)2u2(at) + at2 [(Mt2/t4)u2(t)] 1.2.2 Masse conventionnelle (1.2.2.1) Mct = (t-ac)/(t-at) { (c/(c-ac)) Σ C ijP m i + CM’P M’c (M’-at) /(M’-ac) }  (1.2.2.1_1990) Mct = ((t - ac) / (t - at)) { (CM’ M’c (M’ - at)/(M’ - ac)) + (CSt St c / ( c - ac)) } (1.2.2.2) u2(Mct) = [(t-ac)/(t-at)] 2 { [c/(c-ac)]2 u2(Dt) + CM’Q [(M’-at)/(M’-ac)] 2 u2(M’c)  + [Mct (at-ac)/(t-ac)2] 2 u2(t) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) } (1.2.2.2_app.) équation d'approximation, si at ≈ ac u2 (Mct) ≈ [c/(c-ac)]2 u2(Dt) + CM’Q u2(M’c) + [(Mct /(t-ac)) - (CM’P M’c /(M’-ac))] 2 u2(at) (1.2.2.2_app rel.) équation d'approximation (termes relatifs) ▪ u2rel (Mct) ≈ [c/(c-ac)]2(1/Nt)2u2(Dt) + (CM’P/Nt)2 u2(M’c) +[(1/(t-ac))-(1/(M’-ac))]2u2(at)  ▪ ▪ mt , Mt = masse absolue de l’objet t ▪ mR , M’ = masse absolue de la référence (ou poids connu) R ▪ mct , Mct = masse conventionnelle de la masse inconnue t ▪ mcR , M’c = masse conventionnelle de la référence (ou poids connu) R ▪ Dt = différence calculée entre la masse inconnue t et la référence (ou poids connu) R ▪ t = masse volumique de la masse inconnue t (kg/m3) - habituellement fournie par le fabricant ▪ R, M’ = masse volumique de la référence (ou poids connu) R (kg/m3) - se trouve habituellement sur le certificat d’étalonnage de la référence (ou poids connu) ▪ at = masse volumique de l’air au moment de l’étalonnage (kg/m3) - la formule en 3.2 peut être utilisée ▪ ac = masse volumique conventionnelle de l’air, égale par définition à 1.2 kg/m3.