Sciencehasnotsimplytorecognisethatmotiondeclines，buttoshowatwhatrate，andunderwhatconditionsitdeclines。Then，aswecannotmeasure’absolutemotion，’orassignanyfixedpointinspace，wecanobtainnoruleastoabsolutemotion。Ifweassume，however，thatwehavetoaccountnotformotionbutforchangeofmotion，wecangetaconsistent’law’whichatoncegivesasufficientaccountofmanyobservedphenomena。Weproceedtodefineforceasthecauseofchangeinmotion。Thenitbecomesanidenticalpropositionthatallchangeofmotionimpliesforce，orthatbodiesnotacteduponcontinuetomoveuniformly。Thusthedefinitionofforcetakestheshapeofanaprioriaxiomastoforce。Weimaginethatinsteadofsimplyco-ordinatingourexperienceweare’applyingafundamentalidea’toit，theidea，namely，ofa’cause’or’force。’102*Theaxiomisnot’independentofexperience。’Rightlyunderstood，thewholeprocessisoneofinterpretingexperience。Mill，however，ishardlycorrectinsayingthatthelawwasprovedbyexperiment。
Wecannotobservea’force’apartfromthemovingbody。ForceisoneofBentham’s’fictitiousentities，’awordwhichenablesustostatetherelationsofmovingbodiesaccurately。Itharmonisesourconceptions。Theoldbeliefthatallmotionsstopisnotdisprovedbydiscoveringcasesinwhichforceisabsent，butbypostulatingthepresenceofforcewhereverwefindchangeofmotion。Therealproofisnotindirectexperimentbutintheharmonisingofanindefinitenumberofcomplexstatementswhenoncetheprincipleissystematicallyapplied。Itcanrevealnofacttous，fornothingbutexperiencecanshowthattherearesuchthingsastheplanetsfortunatelyare，bodiesmovingfreely，soastoillustratethelawcontinuously。Millputsthefirstlawofmotiononalevelwiththelawthattheperiodoftheearth’srotationisuniform。Both’inductions，’hesays，areaccuratelytrue。103*Infact，however，theearth’smotionisnotabsolutelyuniform，atruthwhichwediscoverbyapplyingthelawsofmotion，thoughnodirectexperimentcouldexhibitthefact。Thelawofmotionhastheauthorityderivedfromitsrenderingpossibleaconsistentinterpretationofexperiences，whereastheearth’srotationissimplyaparticularfactwhichmightchangeiftheconditionswerealtered。The’law’implies，therefore，areconstructionofexperiencenotgivenbysimpleobservation。
ThisappliestoacontroversybetweenMillandWhewellastoKepler’sgreatdiscoveries。Theybothacceptthefamiliarfacts。
Kepler’sproblemwastoshowhowasimpleconfigurationofthesolarsystemwouldpresentthecomplexappearanceswhichwedirectlyobserve。Theoldobservationsgaveapproximatelycorrectstatementsofthemovementsoftheplanets，assumingtheearthtobefixed，or，aswemaysay，neglectingtheconsiderationofitsmotion。Histheoryshowshowtheapparentmovementsmustresultifwesupposethesuntobefixed，orratherasthesunisnotreallyfixedifwemeasurefromitasfixed。Whewelltreatsthisasacaseof’induction。’Itillustrateswhathecallsthe’colligationoffacts’——ahappyphrase，acceptedbyMill，forthearrangementoffactsinaneworder，andtheapplicationtothefactsoftheappropriateconceptions；inthiscase，ofthetheoremsofconicsectionsandsolidgeometry。Theargumenttakestheformofadiscussionastowhetherthisshouldbecalledinductionoranoperationsubsidiarytoinduction。104*Kepler，asMillurges，wassimplydescribingfacts。Hediscoveredafactinwhichallthepositionsoftheplanetagreed——namely，thattheywereinanellipse。Ifhehadbeensomewhereinspace，ortheplanethadleftavisibletrack，hemighthaveactuallyseenittobeanellipse。Hehadonlyto’piecetogether’hisobservations，asamanwhosailsroundanislanddiscoversitsinsularity。Theonlyinduction，then，wasthatasMarshadbeeninanellipsehewouldstayinanellipse。Apartfromtheverbalquestionwhethertheprocessberightlycalledinductionorsubsidiarytoinduction，therealissueisinMill’scomplaintthatWhewellsupposeda’conceptiontobesomethingaddedtothefacts。’Theconception，Milladmits，isinthemind，butitmustbeaconceptionof’somethinginthefacts。’TheellipsewasinthefactsbeforeKeplersawit。Hedidnotputit，butfounditthere。WhetherKepler’sprocesswasinductiveordeductiveorsubsidiary，itwasanessentialpartofscientificinvestigation。
Themanofsciencemust，asMilltrulysays，interpretthefacts，andnothingbutthefacts；hemustalso，asWhewelltrulyreplies，’colligate’orarrangethefactsinaneworder。Theconstructiveprocesswhichjustifiesmeinsayingthisisanisland，orthisisanellipse，ispreciselywhatmakesscientificknowledgepossible，andinvolvessomethingmorethanamereputtingtogetherofrawfact。Everyfact，asWhewellsees，mayberegardedasacaseofcountlesslaws，eachofwhichmaybetrueunderappropriateconditions。Toeliminatetheirrelevant，toorganisethewholesystemoftruths，soastomaketheorderofnatureasMillforciblysays105*deduciblefromthesmallestpossiblenumberofgeneralpropositions，istheaimofscience；