Club Certificate2025
ExolistDEN 225
Danish Sailing Association
Idrættens Hus
2605 Brøndby
DENMARK
Rated boat velocities in knots
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat Angles42.8°42.8°40.4°38.9°37.5°37.0°36.7°37.2°38.1°
Beat VMG2.563.524.264.805.105.225.305.365.33
52°3.975.326.266.837.127.267.347.437.45
60°4.255.656.577.057.297.457.547.667.70
75°4.596.006.857.297.567.727.868.068.17
90°4.606.046.937.397.748.038.248.508.66
110°4.155.656.737.327.728.098.409.079.60
120°3.935.426.547.217.658.068.469.2210.27
135°3.434.825.986.847.367.788.219.1410.49
150°2.824.085.226.186.927.397.788.609.65
Run VMG2.443.534.525.376.116.717.187.938.69
Gybe Angles144.8°144.8°149.4°152.8°159.2°166.4°174.1°177.2°175.0°
APH ToD:554.0CDL: 9.323APH ToT: 1.0831CertNo:33897
BOAT
ClassX-362 SPORTDesignerJEPPESENBuilderX-YACHTSAge date01/2003Series date01/1993Offset fileX-362SP-DK.offData file33897 - X-362 Sport - DEN 225
HULL
Length Overall10.718 mMaximum Beam3.448 mDraft2.231 mDisplacement5,294 kgDLR6.0500IMS DivisionCruiser/RacerDynamic Allowance0.190%Age Allowance0.487%
PROPELLER
InstallationStrutTypeFolding 2 bladesDiameter0.406m
CREW
Maximum weight714 kg(declared)Minimum weight584 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail39.2640.11Headsail Luffed29.6229.62Headsail Flying51.7151.71Symmetric83.7783.77Asymmetric
STORM SAIL AREAS (m²)
Trysail11.34Storm Jib10.06Heavy Weather Jib27.15
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
The owner and any other person in charge is responsible that boat is complying with her certificate in accordance with RRS 78.1 and ORC Rule 304.
Club Certificate2025
ExolistDEN 225
Danish Sailing Association
Idrættens Hus
2605 Brøndby
DENMARK
Time Allowances in secs/NM
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat VMG1407.61023.6844.1750.5706.5689.3679.5671.1675.1
52°906.6676.2574.9527.1505.3495.9490.6484.4483.0
60°846.7636.7547.7510.8493.9483.1477.5470.0467.5
75°784.5599.8525.4493.8476.1466.2458.3446.8440.8
90°781.8595.6519.8487.1465.3448.6436.8423.7415.6
110°868.3637.7535.3492.1466.1445.0428.4396.7374.9
120°916.2664.7550.2499.2470.5446.5425.4390.5350.5
135°1048.6746.3601.5526.1488.8462.5438.6393.8343.2
150°1276.6883.3690.2582.1520.5487.2462.5418.5373.0
Run VMG1474.01020.0797.0670.2589.2536.2501.2453.9414.4
Selected Courses
Windward / Leeward1439.41021.8820.6710.4647.9612.7590.4562.5544.8
All purpose1075.9780.4642.8572.8534.4512.3496.5473.3455.1
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward679.30.8833
All purpose554.01.0831
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7829
Downwind "popa"0.9195
70% up, 30% down "Ilhabela"0.8194
30% up, 70% down "Ilhabela-inverso"0.8738
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Predominantly Upwind596.81.0053
Predominantly Downwind566.21.0596
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low711.60.8432
Triple Number AP Medium550.81.0894
Triple Number AP High491.81.2201
Triple Number Windward/Leeward Low962.10.6236
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Single Number Predominant Upwind620.00.9678
Single Number Predominant Reaching549.41.0920
Single Number Predominant Downwind591.11.0151
Predominant Upwind - Low850.90.7051
Predominant Upwind - Low/Med653.60.9179
Predominant Upwind - Medium577.61.0388
Predominant Upwind - Med/High540.11.1109
Predominant Upwind - High523.71.1456
Predominant Downwind Low869.40.6901
Predominant Downwind Low/Med642.50.9339
Predominant Downwind Medium545.91.0990
Predominant Downwind Med/High485.91.2347
Predominant Downwind High450.21.3329
Predominant Reaching Low756.50.7931
Predominant Reaching Low/Med583.61.0280
Predominant Reaching Medium514.81.1654
Predominant Reaching Med/High473.41.2674
Predominant Reaching High448.91.3365
SA/DSPL Upwind22.55SA/DSPL Downwind40.28
Scoring OptionTODTOT
5-Band Windward/Leeward Low1076.20.5575
5-Band Windward/Leeward Low/Med785.90.7635
5-Band Windward/Leeward Medium662.00.9064
5-Band Windward/Leeward Med/High594.31.0097
5-Band Windward/Leeward High564.21.0634
Windward/Leeward 60-40 Low1075.90.5577
Windward/Leeward 60-40 Low/Med792.10.7575
Windward/Leeward 60-40 Medium673.60.8907
Windward/Leeward 60-40 Med/High611.80.9807
Windward/Leeward 60-40 High586.01.0238
5-Band AP Low786.60.7628
5-Band AP Low/Med622.40.9640
5-Band AP Medium543.01.1050
5-Band AP Med/High498.41.2038
5-Band AP High474.21.2653
5-Band SF Bay Tour - Low926.10.6479
5-Band SF Bay Tour - Low/Med751.20.7987
5-Band SF Bay Tour - Medium640.00.9374
5-Band SF Bay Tour - Med/High580.81.0330
5-Band SF Bay Tour - High552.71.0855
Chicago-Mac Upwind0.9387
Chicago-Mac All Purpose0.9627
Chicago-Mac Downwind0.9776
Bayview-Mac Cove Island0.7034
Bayview-Mac Shore0.7101
Harvest Moon Regatta481.91.2451
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance603.1
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating603.10.9948
FinRating, kevyt tuuli1055.50.9474
FinRating, kova tuuli476.51.0493
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.9948
Triple Number Coastal/Long Distance Low0.8432
Triple Number Coastal/Long Distance Medium1.0895
Triple Number Coastal/Long Distance High1.2201
Triple Number Windward/Leeward Low0.6513
Triple Number Windward/Leeward Medium0.8898
Triple Number Windward/Leeward High1.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
For information
General Purpose Handicap (GPH)621.7
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low711.6
Triple Number Coastal/Long Distance Medium550.7
Triple Number Coastal/Long Distance High491.8
Triple Number Windward/Leeward Low921.2
Triple Number Windward/Leeward Medium674.3
Triple Number Windward/Leeward High585.5
Predominantly Upwind596.8
Predominantly Downwind566.2
Predominantly Reaching539.8
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8432
Triple Number Coastal/Long Distance Medium1.0895
Triple Number Coastal/Long Distance High1.2201
Triple Number Windward/Leeward Low0.6513
Triple Number Windward/Leeward Medium0.8898
Triple Number Windward/Leeward High1.0248
Coastal/Long Distance0.9948
Predominantly Upwind1.0053
Predominantly Downwind1.0596
For information
General Purpose Handicap (GPH)621.7
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)1.0831
Distanseseilas Trippeltall svak vind0.8432
Distanseseilas Trippeltall mellomvind1.0895
Distanseseilas Trippeltall sterk vind1.2201
Pølsebane Trippeltall svak vind0.6513
Pølsebane Trippeltall mellomvind0.8898
Pølsebane Trippeltall sterk vind1.0248
Motvind Singeltall1.0053
Medvind Singeltall1.0596
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Coastal/Long Distance603.10.9948
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind596.81.0053
Predominantly Downwind566.21.0596
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore550.11.0908
Cape Doctor Coastal460.61.3026
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8432
Triple Number Coastal/Long Distance Medium1.0895
Triple Number Coastal/Long Distance High1.2201
Triple Number Windward/Leeward Low0.6513
Triple Number Windward/Leeward Medium0.8898
Triple Number Windward/Leeward High1.0248
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.8432
Triple Number Coastal/Long Distance Medium1.0895
Triple Number Coastal/Long Distance High1.2201
Triple Number Windward/Leeward Low0.6513
Triple Number Windward/Leeward Medium0.8898
Triple Number Windward/Leeward High1.0248
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Predominantly Upwind596.81.0053
Predominantly Downwind566.21.0596
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance603.10.9948
Triple Number Coastal/Long Distance Low711.60.8432
Triple Number Coastal/Long Distance Medium550.71.0895
Triple Number Coastal/Long Distance High491.81.2201
Triple Number Windward/Leeward Low921.20.6513
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1535.81021.6771.8642.7569.6531.2501.5454.2433.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low711.60.8432
Triple Number AP Medium550.81.0894
Triple Number AP High491.81.2201
Triple Number Windward/Leeward Low962.10.6236
Triple Number Windward/Leeward Medium674.30.8898
Triple Number Windward/Leeward High585.51.0248
Single Number Predominant Upwind620.00.9678
Single Number Predominant Reaching549.41.0920
Single Number Predominant Downwind591.11.0151
Predominant Upwind - Low850.90.7051
Predominant Upwind - Low/Med653.60.9179
Predominant Upwind - Medium577.61.0388
Predominant Upwind - Med/High540.11.1109
Predominant Upwind - High523.71.1456
Predominant Downwind Low869.40.6901
Predominant Downwind Low/Med642.50.9339
Predominant Downwind Medium545.91.0990
Predominant Downwind Med/High485.91.2347
Predominant Downwind High450.21.3329
Predominant Reaching Low756.50.7931
Predominant Reaching Low/Med583.61.0280
Predominant Reaching Medium514.81.1654
Predominant Reaching Med/High473.41.2674
Predominant Reaching High448.91.3365
SA/DSPL Upwind22.55SA/DSPL Downwind40.28
Scoring OptionTODTOT
5-Band Windward/Leeward Low1076.20.5575
5-Band Windward/Leeward Low/Med785.90.7635
5-Band Windward/Leeward Medium662.00.9064
5-Band Windward/Leeward Med/High594.31.0097
5-Band Windward/Leeward High564.21.0634
Windward/Leeward 60-40 Low1075.90.5577
Windward/Leeward 60-40 Low/Med792.10.7575
Windward/Leeward 60-40 Medium673.60.8907
Windward/Leeward 60-40 Med/High611.80.9807
Windward/Leeward 60-40 High586.01.0238
5-Band AP Low786.60.7628
5-Band AP Low/Med622.40.9640
5-Band AP Medium543.01.1050
5-Band AP Med/High498.41.2038
5-Band AP High474.21.2653
5-Band SF Bay Tour - Low926.10.6479
5-Band SF Bay Tour - Low/Med751.20.7987
5-Band SF Bay Tour - Medium640.00.9374
5-Band SF Bay Tour - Med/High580.81.0330
5-Band SF Bay Tour - High552.71.0855
Chicago-Mac Upwind0.9387
Chicago-Mac All Purpose0.9627
Chicago-Mac Downwind0.9776
Bayview-Mac Cove Island0.7034
Bayview-Mac Shore0.7101
Harvest Moon Regatta481.91.2451
Club Certificate2025
ExolistDEN 225
Danish Sailing Association
Idrættens Hus
2605 Brøndby
DENMARK
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassX-362 SPORTMeasurement10/05/2019HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA10.718Max. Beam3.448Draft2.231Displacement5,294Wetted area25.30IMS L9.712LSM09.564Acc. length10.718Sink (kg/mm) 18.94
VCGD-0.036VCGM0.029RM Rated (kg·m) 129.7Limit of positive stability(°) N/AStability IndexN/ADefault crew weight646Declared crew weight714
PROPELLER
Propeller TypeFolding 2 blades
InstallationStrutTwin screwNoHydro generatorNo
PRD0.406PBW0.110PIPA0.0033
EDL1.915ST10.042ST20.180
ST30.180ST40.112ST50.238
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0CheckstaysSpreaders2Rotating mastNo
P13.840IG14.180ISP14.180MDT10.113MDL10.185MDT2MDL2TLTaperMW0.185GO0.185
E4.680J3.800BAS1.665FSD0.030SFJ0.000SPL3.880WPLTPS3.980BD0.180MWT150.00MCG5.255
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM entered directlyRM entered130.6Flotation Date11/05/2000
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
ExolistDEN 225
Danish Sailing Association
Idrættens Hus
2605 Brøndby
DENMARK
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment10.171.101.903.073.9239.26
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment80.021.112.164.065.466.4014.08NoYes051.7120.100.671.232.163.034.0214.04YesNo 29.62Let fok30.100.671.232.163.034.0214.04YesNo 29.62
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment414.0414.0414.047.236.8883.77514.0414.0414.047.230.8869.73
CRUISER/RACER REQUIREMENTS*
Accommodation length10.7 mTable area0.55 m²Headroom1.75 mMinimum number of berths5Personal gear stowage0.20 m³Fresh water capacity117 lMinimum number of seats in cockpit5Food stowage0.30 m³Fuel capacity64 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.