# Connexions

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• Preface to Physics
• Preface to College Physics

• #### 12. Modern Physics

• 13. Atomic Masses
• 14. Useful Information
• 15. Glossary of Key Symbols and Notation

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Textbook by: Oka Kurniawan. E-mail the author

# Useful Information

Module by: OpenStax College. E-mail the author

This appendix is broken into several tables.

Table 1: Important Constants1
Symbol Meaning Best Value Approximate Value
c c size 12{c} {} Speed of light in vacuum 2 . 99792458 × 10 8 m / s 2 . 99792458 × 10 8 m / s size 12{2 "." "99792458" times "10" rSup { size 8{8} }  {m} slash {s} } {} 3 . 00 × 10 8 m / s 3 . 00 × 10 8 m / s size 12{3 "." "00" times "10" rSup { size 8{8} }  {m} slash {s} } {}
G G size 12{G} {} Gravitational constant 6 . 67384 ( 80 ) × 10 11 N m 2 / kg 2 6 . 67384 ( 80 ) × 10 11 N m 2 / kg 2 size 12{6 "." "67384" $$"80"$$ times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {} 6 . 67 × 10 11 N m 2 / kg 2 6 . 67 × 10 11 N m 2 / kg 2 size 12{6 "." "67" times "10" rSup { size 8{ - "11"} }  {N cdot m rSup { size 8{2} } } slash {"kg" rSup { size 8{2} } } } {}
N A N A size 12{N rSub { size 8{A} } } {} Avogadro’s number 6 . 02214129 ( 27 ) × 10 23 6 . 02214129 ( 27 ) × 10 23 size 12{6 "." "02214129" $$"27"$$ times "10" rSup { size 8{"23"} } } {} 6 . 02 × 10 23 6 . 02 × 10 23 size 12{6 "." "02" times "10" rSup { size 8{"23"} } } {}
k k size 12{k} {} Boltzmann’s constant 1 . 3806488 ( 13 ) × 10 23 J / K 1 . 3806488 ( 13 ) × 10 23 J / K size 12{1 "." "3806488" $$"13"$$ times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {} 1 . 38 × 10 23 J / K 1 . 38 × 10 23 J / K size 12{1 "." "38" times "10" rSup { size 8{ - "23"} }  {J} slash {K} } {}
R R size 12{R} {} Gas constant 8 . 3144621 ( 75 ) J / mol K 8 . 3144621 ( 75 ) J / mol K size 12{8 "." "3144621" $$"75"$$  {J} slash {"mol" cdot K} } {} 8 . 31 J / mol K = 1 . 99 cal / mol K = 0 . 0821 atm L / mol K 8 . 31 J / mol K = 1 . 99 cal / mol K = 0 . 0821 atm L / mol K size 12{8 "." "31" {J} slash {"mol" cdot K=1 "." "99" {"cal"} slash {"mol" cdot K=0 "." "0821" {"atm" cdot L} slash {"mol" cdot K} } } } {}
σ σ size 12{σ} {} Stefan-Boltzmann constant 5 . 670373 ( 21 ) × 10 8 W / m 2 K 5 . 670373 ( 21 ) × 10 8 W / m 2 K size 12{5 "." "670373" $$"21"$$ times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {} 5 . 67 × 10 8 W / m 2 K 5 . 67 × 10 8 W / m 2 K size 12{5 "." "67" times "10" rSup { size 8{ - 8} }  {W} slash {m rSup { size 8{2} } cdot K} } {}
k k size 12{k} {} Coulomb force constant 8 . 987551788 . . . × 10 9 N m 2 / C 2 8 . 987551788 . . . × 10 9 N m 2 / C 2 size 12{8 "." "987551788" "." "." "."  times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {} 8.99 × 10 9 N m 2 / C 2 8.99 × 10 9 N m 2 / C 2 size 12{9 times "10" rSup { size 8{9} }  {N cdot m rSup { size 8{2} } } slash {C rSup { size 8{2} } } } {}
q e q e size 12{q rSub { size 8{e} } } {} Charge on electron 1 . 602176565 ( 35 ) × 10 19 C 1 . 602176565 ( 35 ) × 10 19 C size 12{ - 1 "." "602176565" $$"35"$$ times "10" rSup { size 8{ - "19"} } C} {} 1 . 60 × 10 19 C 1 . 60 × 10 19 C size 12{ - 1 "." "60" times "10" rSup { size 8{ - "19"} } C} {}
ε 0 ε 0 size 12{ε rSub { size 8{0} } } {} Permittivity of free space 8 . 854187817 . . . × 10 12 C 2 / N m 2 8 . 854187817 . . . × 10 12 C 2 / N m 2 size 12{8 "." "854187817" "." "." "."  times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {} 8 . 85 × 10 12 C 2 / N m 2 8 . 85 × 10 12 C 2 / N m 2 size 12{8 "." "85" times "10" rSup { size 8{ - "12"} }  {C rSup { size 8{2} } } slash {N cdot m rSup { size 8{2} } } } {}
μ 0 μ 0 size 12{μ rSub { size 8{0} } } {} Permeability of free space × 10 7 T m / A × 10 7 T m / A size 12{4π times "10" rSup { size 8{ - 7} }  {T cdot m} slash {A} } {} 1 . 26 × 10 6 T m / A 1 . 26 × 10 6 T m / A size 12{1 "." "26" times "10" rSup { size 8{ - 6} }  {T cdot m} slash {A} } {}
h h size 12{h} {} Planck’s constant 6 . 62606957 ( 29 ) × 10 34 J s 6 . 62606957 ( 29 ) × 10 34 J s size 12{6 "." "62606957" $$"29"$$ times "10" rSup { size 8{ - "34"} } J cdot s} {} 6 . 63 × 10 34 J s 6 . 63 × 10 34 J s size 12{6 "." "63" times "10" rSup { size 8{ - "34"} } J cdot s} {}
Table 2: Submicroscopic Masses2
Symbol Meaning Best Value Approximate Value
m e m e size 12{m rSub { size 8{e} } } {} Electron mass 9 . 10938291 ( 40 ) × 10 31 kg 9 . 10938291 ( 40 ) × 10 31 kg size 12{9 "." "10938291" $$"40"$$ times "10" rSup { size 8{ - "31"} } "kg"} {} 9 . 11 × 10 31 kg 9 . 11 × 10 31 kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } "kg"} {}
m p m p size 12{m rSub { size 8{p} } } {} Proton mass 1 . 672621777 ( 74 ) × 10 27 kg 1 . 672621777 ( 74 ) × 10 27 kg size 12{1 "." "672621777" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {} 1 . 6726 × 10 27 kg 1 . 6726 × 10 27 kg size 12{1 "." "6726" times "10" rSup { size 8{ - "27"} } "kg"} {}
m n m n size 12{m rSub { size 8{n} } } {} Neutron mass 1 . 674927351 ( 74 ) × 10 27 kg 1 . 674927351 ( 74 ) × 10 27 kg size 12{1 "." "674927351" $$"74"$$ times "10" rSup { size 8{ - "27"} } "kg"} {} 1 . 6749 × 10 27 kg 1 . 6749 × 10 27 kg size 12{1 "." "6749" times "10" rSup { size 8{ - "27"} } "kg"} {}
u u size 12{u} {} Atomic mass unit 1 . 660538921 ( 73 ) × 10 27 kg 1 . 660538921 ( 73 ) × 10 27 kg size 12{1 "." "660538921" $$"73"$$ times "10" rSup { size 8{ - "27"} } "kg"} {} 1 . 6605 × 10 27 kg 1 . 6605 × 10 27 kg size 12{1 "." "6605" times "10" rSup { size 8{ - "27"} } "kg"} {}
 Sun mass 1 . 99 × 10 30 kg 1 . 99 × 10 30 kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } "kg"} {} average radius 6 . 96 × 10 8 m 6 . 96 × 10 8 m size 12{6 "." "96" times "10" rSup { size 8{8} } m} {} Earth-sun distance (average) 1 . 496 × 10 11 m 1 . 496 × 10 11 m size 12{1 "." "496" times "10" rSup { size 8{"11"} } " m"} {} Earth mass 5 . 9736 × 10 24 kg 5 . 9736 × 10 24 kg size 12{5 "." "9736" times "10" rSup { size 8{"24"} } "kg"} {} average radius 6 . 376 × 10 6 m 6 . 376 × 10 6 m size 12{6 "." "376" times "10" rSup { size 8{6} } m} {} {} orbital period 3 . 16 × 10 7 s 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } " s "} {} Moon mass 7 . 35 × 10 22 kg 7 . 35 × 10 22 kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } "kg"} {} average radius 1 . 74 × 10 6 m 1 . 74 × 10 6 m size 12{1 "." "74" times "10" rSup { size 8{6} } m} {} orbital period (average) 2 . 36 × 10 6 s 2 . 36 × 10 6 s size 12{2 "." "36" times "10" rSup { size 8{6} } " s"} {} Earth-moon distance (average) 3 . 84 × 10 8 m 3 . 84 × 10 8 m size 12{3 "." "84" times "10" rSup { size 8{8} } " m"} {}
Table 4: Metric Prefixes for Powers of Ten and Their Symbols
Prefix Symbol Value Prefix Symbol Value
tera T 10 12 10 12 size 12{"10" rSup { size 8{"12"} } } {} deci d 10 1 10 1 size 12{"10" rSup { size 8{ - 1} } } {}
giga G 10 9 10 9 size 12{"10" rSup { size 8{9} } } {} centi c 10 2 10 2 size 12{"10" rSup { size 8{ - 2} } } {}
mega M 10 6 10 6 size 12{"10" rSup { size 8{6} } } {} milli m 10 3 10 3 size 12{"10" rSup { size 8{ - 3} } } {}
kilo k 10 3 10 3 size 12{"10" rSup { size 8{3} } } {} micro μ μ size 12{μ} {} 10 6 10 6 size 12{"10" rSup { size 8{ - 6} } } {}
hecto h 10 2 10 2 size 12{"10" rSup { size 8{2} } } {} nano n 10 9 10 9 size 12{"10" rSup { size 8{ - 9} } } {}
deka da 10 1 10 1 size 12{"10" rSup { size 8{1} } } {} pico p 10 12 10 12 size 12{"10" rSup { size 8{ - "12"} } } {}
10 0 ( = 1 ) 10 0 ( = 1 ) size 12{"10" rSup { size 8{0} } $$=1$$ } {} femto f 10 15 10 15 size 12{"10" rSup { size 8{ - "15"} } } {}
 Alpha Α Α size 12{Α} {} α α size 12{α} {} Eta Η Η size 12{Η} {} η η size 12{η} {} Nu Ν Ν size 12{Ν} {} ν ν size 12{ν} {} Tau Τ Τ size 12{Τ} {} τ τ size 12{τ} {} Beta Β Β size 12{Β} {} β β size 12{β} {} Theta Θ Θ size 12{Θ} {} θ θ size 12{θ} {} Xi Ξ Ξ size 12{Ξ} {} ξ ξ size 12{ξ} {} Upsilon Υ Υ size 12{Υ} {} υ υ size 12{υ} {} Gamma Γ Γ size 12{Γ} {} γ γ size 12{γ} {} Iota Ι Ι size 12{Ι} {} ι ι size 12{ι} {} Omicron Ο Ο size 12{Ο} {} ο ο size 12{ο} {} Phi Φ Φ size 12{Φ} {} ϕ ϕ size 12{ϕ} {} Delta Δ Δ size 12{Δ} {} δ δ size 12{δ} {} Kappa Κ Κ size 12{Κ} {} κ κ size 12{κ} {} Pi Π Π size 12{Π} {} π π size 12{π} {} Chi Χ Χ size 12{Χ} {} χ χ size 12{χ} {} Epsilon Ε Ε size 12{Ε} {} ε ε size 12{ε} {} Lambda Λ Λ size 12{Λ} {} λ λ size 12{λ} {} Rho Ρ Ρ size 12{Ρ} {} ρ ρ size 12{ρ} {} Psi Ψ Ψ size 12{Ψ} {} ψ ψ size 12{ψ} {} Zeta Ζ Ζ size 12{Ζ} {} ζ ζ size 12{ζ} {} Mu Μ Μ size 12{Μ} {} μ μ size 12{μ} {} Sigma Σ Σ size 12{Σ} {} σ σ size 12{σ} {} Omega Ω Ω size 12{ %OMEGA } {} ω ω size 12{ω} {}
Table 6: SI Units
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Derived units Force N = kg m / s 2 N = kg m / s 2 size 12{N="kg" cdot {m} slash {s rSup { size 8{2} } } } {} newton
Energy J = kg m 2 / s 2 J = kg m 2 / s 2 size 12{J="kg" cdot {m rSup { size 8{2} } } slash {s rSup { size 8{2} } } } {} joule
Power W = J / s W = J / s size 12{W= {J} slash {s} } {} watt
Pressure Pa = N / m 2 Pa = N / m 2 size 12{"Pa"= {N} slash {m rSup { size 8{2} } } } {} pascal
Frequency Hz = 1 / s Hz = 1 / s size 12{"Hz"= {1} slash {s} } {} hertz
Electronic potential V = J / C V = J / C size 12{V= {J} slash {C} } {} volt
Capacitance F = C / V F = C / V size 12{F= {C} slash {V} } {} farad
Charge C = s A C = s A size 12{C=s cdot A} {} coulomb
Resistance Ω = V / A Ω = V / A size 12{ %OMEGA = {V} slash {A} } {} ohm
Magnetic field T = N / A m T = N / A m size 12{T= {N} slash { left (A cdot m right )} } {} tesla
Nuclear decay rate Bq = 1 / s Bq = 1 / s size 12{"Bq"= {1} slash {s} } {} becquerel
 Length 1 inch ( in . ) = 2 . 54 cm ( exactly ) 1 inch ( in . ) = 2 . 54 cm ( exactly ) size 12{1" inch " $$"in" "."$$ =2 "." "54"" cm " $$"exactly"$$ } {} 1 foot ( ft ) = 0 . 3048 m 1 foot ( ft ) = 0 . 3048 m size 12{1" foot " $$"ft"$$ =0 "." "3048"" m"} {} 1 mile ( mi ) = 1 . 609 km 1 mile ( mi ) = 1 . 609 km size 12{1" mile " $$"mi"$$ =1 "." "609"" km"} {} Force 1 pound ( lb ) = 4 . 448 N 1 pound ( lb ) = 4 . 448 N size 12{1" pound " $$"lb"$$ =4 "." "448"" N"} {} Energy 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J 1 British thermal unit ( Btu ) = 1 . 055 × 10 3 J size 12{1" British thermal unit " $$"Btu"$$ =1 "." "055" times "10" rSup { size 8{3} } " J"} {} Power 1 horsepower ( hp ) = 746 W 1 horsepower ( hp ) = 746 W size 12{1" horsepower " $$"hp"$$ ="746"" W"} {} Pressure 1 lb / in 2 = 6 . 895 × 10 3 Pa 1 lb / in 2 = 6 . 895 × 10 3 Pa size 12{1 {"lb"} slash {"in" rSup { size 8{2} } } =6 "." "895" times "10" rSup { size 8{3} } " Pa"} {}
 Length 1 light year ( ly ) = 9 . 46 × 10 15 m 1 light year ( ly ) = 9 . 46 × 10 15 m size 12{1" light"" year" $$"ly"$$  =9 "." "46" times "10" rSup { size 8{"15"} } " m"} {} 1 astronomical unit ( au ) = 1 . 50 × 10 11 m 1 astronomical unit ( au ) = 1 . 50 × 10 11 m size 12{1" astronomical"" unit" $$"au"$$  =1 "." "50" times "10" rSup { size 8{"11"} } " m"} {} 1 nautical mile = 1 . 852 km 1 nautical mile = 1 . 852 km size 12{1" nautical"" mile" =1 "." "852"" km"} {} 1 angstrom ( Å ) = 10 − 10 m 1 angstrom ( Å ) = 10 − 10 m size 12{1" angstrom" $$Å$$  ="10" rSup { size 8{ - "10"} } " m"} {} Area 1 acre ( ac ) = 4 . 05 × 10 3 m 2 1 acre ( ac ) = 4 . 05 × 10 3 m 2 size 12{1" acre" $$"ac"$$  =4 "." "05" times "10" rSup { size 8{3} } " m" rSup { size 8{2} } } {} 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 1 square foot ( ft 2 ) = 9 . 29 × 10 − 2 m 2 size 12{1"square""foot" $$"ft" rSup { size 8{2} }$$  =9 "." "29" times "10" rSup { size 8{ - 2} } " m" rSup { size 8{2} } } {} 1 barn ( b ) = 10 − 28 m 2 1 barn ( b ) = 10 − 28 m 2 size 12{1" barn" $$b$$  ="10" rSup { size 8{ - "28"} } " m" rSup { size 8{2} } } {} Volume 1 liter ( L ) = 10 − 3 m 3 1 liter ( L ) = 10 − 3 m 3 size 12{1" liter" $$L$$  ="10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {} 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 1 U.S. gallon ( gal ) = 3 . 785 × 10 − 3 m 3 size 12{1" U" "." S "." " gallon" $$"gal"$$  =3 "." "785" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{3} } } {} Mass 1 solar mass = 1 . 99 × 10 30 kg 1 solar mass = 1 . 99 × 10 30 kg size 12{1" solar"" mass" =1 "." "99" times "10" rSup { size 8{"30"} } " kg"} {} 1 metric ton = 10 3 kg 1 metric ton = 10 3 kg size 12{1" metric"" ton" ="10" rSup { size 8{3} } " kg"} {} 1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg 1 atomic mass unit ( u ) = 1 . 6605 × 10 − 27 kg size 12{1" atomic"" mass"" unit" $$u$$  =1 "." "6605" times "10" rSup { size 8{ - "27"} } " kg"} {} Time 1 year ( y ) = 3 . 16 × 10 7 s 1 year ( y ) = 3 . 16 × 10 7 s size 12{1" year" $$y$$  =3 "." "16" times "10" rSup { size 8{7} } " s"} {} 1 day ( d ) = 86 , 400 s 1 day ( d ) = 86 , 400 s size 12{1" day" $$d$$  ="86","400"" s"} {} Speed 1 mile per hour ( mph ) = 1 . 609 km / h 1 mile per hour ( mph ) = 1 . 609 km / h size 12{1" mile""per""hour" $$"mph"$$ =1 "." "609" {"km"} slash {h} } {} 1 nautical mile per hour ( naut ) = 1 . 852 km / h 1 nautical mile per hour ( naut ) = 1 . 852 km / h size 12{1" nautical""mile""per""hour" $$"naut"$$ =1 "." "852" {"km"} slash {h} } {} Angle 1 degree ( ° ) = 1 . 745 × 10 − 2 rad 1 degree ( ° ) = 1 . 745 × 10 − 2 rad size 12{1" degree" $$°$$  =1 "." "745" times "10" rSup { size 8{ - 2} } " rad"} {} 1 minute of arc ( ' ) = 1 / 60 degree 1 minute of arc ( ' ) = 1 / 60 degree size 12{1" minute""of""arc" { { $$}} sup { ' }$$ = {1} slash {"60"} " degree"} {} 1 second of arc ( '' ) = 1 / 60 minute of arc 1 second of arc ( '' ) = 1 / 60 minute of arc size 12{1" second""of""arc" { { $$}} sup { '' }$$ = {1} slash {"60"} " minute of arc"} {} 1 grad = 1 . 571 × 10 − 2 rad 1 grad = 1 . 571 × 10 − 2 rad size 12{1" grad" =1 "." "571" times "10" rSup { size 8{ - 2} } " rad"} {} Energy 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J 1 kiloton TNT ( kT ) = 4 . 2 × 10 12 J size 12{1" kiloton"" TNT" $$"kT"$$  =4 "." 2 times "10" rSup { size 8{"12"} } " J"} {} 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J 1 kilowatt hour ( kW ⋅ h ) = 3 . 60 × 10 6 J size 12{1" kilowatt"" hour" $$"kW" cdot h$$  =3 "." "60" times "10" rSup { size 8{6} } " J"} {} 1 food calorie ( kcal ) = 4186 J 1 food calorie ( kcal ) = 4186 J size 12{1" food""calorie" $$"kcal"$$ ="4186"" J"} {} 1 calorie ( cal ) = 4 . 186 J 1 calorie ( cal ) = 4 . 186 J size 12{1" calorie" $$"cal"$$ =4 "." "186"" J"} {} 1 electron volt ( eV ) = 1 . 60 × 10 − 19 J 1 electron volt ( eV ) = 1 . 60 × 10 − 19 J size 12{1" electron"" volt" $$"eV"$$  =1 "." "60" times "10" rSup { size 8{ - "19"} } " J"} {} Pressure 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa 1 atmosphere ( atm ) = 1 . 013 × 10 5 Pa size 12{1" atmosphere" $$"atm"$$  =1 "." "013" times "10" rSup { size 8{5} } " Pa"} {} 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa 1 millimeter of mercury ( mm Hg ) = 133 . 3 Pa size 12{1" millimeter""of""mercury" $$"mm""Hg"$$ ="133" "." 3" Pa"} {} 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa 1 torricelli ( torr ) = 1 mm Hg = 133 . 3 Pa size 12{1" torricelli" $$"torr"$$ =1" mm""Hg "="133" "." 3" Pa"} {} Nuclear decay rate 1 curie ( Ci ) = 3 . 70 × 10 10 Bq 1 curie ( Ci ) = 3 . 70 × 10 10 Bq size 12{1" curie" $$"Ci"$$  =3 "." "70" times "10" rSup { size 8{"10"} } " Bq"} {}
 Circumference of a circle with radius rr size 12{r} {} or diameter dd size 12{d} {} C = 2 πr = πd C = 2 πr = πd size 12{C=2πr=πd} {} Area of a circle with radius rr size 12{r} {} or diameter dd size 12{d} {} A = πr 2 = πd 2 / 4 A = πr 2 = πd 2 / 4 size 12{A=πr rSup { size 8{2} } = {πd rSup { size 8{2} } } slash {4} } {} Area of a sphere with radius rr size 12{r} {} A = 4 πr 2 A = 4 πr 2 size 12{A=4πr rSup { size 8{2} } } {} Volume of a sphere with radius rr size 12{r} {} V = 4 / 3 πr 3 V = 4 / 3 πr 3 size 12{V= left ( {4} slash {3} right ) left (πr rSup { size 8{3} } right )} {}

## Footnotes

1. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
2. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.

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