 with new terms to balance work for that type of system, analogously to Lagrange's earlier extension from statics to dynamics by addition of balancing inertial forces. Mechanical and chemical statics are extended to mechanical and chemical dynamics, to viscous fluids, and to a host of systems classified by their phenomenological properties mathematically expressed: systems with friction, static systems exhibiting hysteresis (like annealed steel, permanently dilated glass, colloidal absorption of water vapor); dynamical systems involving hysteresis; thermal systems without friction or hysteresis (reversible heat cycles); thermal systems with friction and/or hysteresis (irreversible heat cycles); etc. The various principles thus supplemented by their own appropriate terms sitting on the various branches of this tree yield equations of "motion" for the type of system characterized by the principle. Duhem sketches these extensions in (Duhem 1903, Part II) and (Duhem 2002 [1901]) and lays out the details in his major (1000+ pages) text in physics, (Duhem 1911). The perceived superiority of these analytic over synthetic treatments rested on the following reasons. First, and most importantly, they allowed physics to avoid hidden mechanisms, and this was considered by many to be a positive given the lack of empirically determined specific information about particles. Just as we can explore the energy connections between Poincaré's two wheels without knowing anything about their physical connections, we can use our balance equations to calculate, for example, the value of the internal thermodynamic potential or the entropy change of a system from empirically determinable quantities like temperature, pressure, and change of volume, without knowing what constitutes any of these quantities. Second, they promised more empirical success than synthetic methods. Writing in 1892, the elastician A.E.H. Love claimed that the best modern experiments supported the multi-constant results of the analytical theories over the rari-constant results of Poisson's synthetic theory (Love 1892, 14). Third, by avoiding hidden mechanisms and developing coherent continuum theories of elasticity they allowed physicists to side-step problematic conceptual questions about how energy is distributed among particles and the whole problem of replication of macro-problems at the micro-level. Fourth, by enabling the free choice of suitable generalized coordinates that fit constraints, and by inventing algebraic procedures (like Lagrange's method of multipliers) for reducing calculational complexity in a principled way, the analytic mechanists avoided the mathematical problems mentioned earlier. Finally, the theories promised to be extendible to dissipative systems in principled ways. In a nutshell,
with new terms to balance work for that character of arrangement, analogously to Lagrange's earlier extension from static to moral force by addition of balancing inertial forces. Mechanical and chemical static are extended to mechanical and chemical dynamics, to syrupy fluids, and to a host of system classified by their phenomenological properties mathematically expressed: systems with friction, static organization exhibiting hysteresis (like annealed steel, permanently dilated looking glass, colloidal absorption of water vapor); dynamic systems necessitate hysteresis; thermal systems without friction or hysteresis (reversible heat cycle); thermal systems with friction and/or hysteresis (irreversible heat cycles); etc. The various principle therefore supplemented by their own appropriate terms sitting on the various branches of this tree yield equations of " apparent motion " for the character of arrangement characterized by the rationale. Duhem sketch these extension in (Duhem 1903, Part II) and (Duhem 2002 [ 1901 ]) and lays out the details in his major (1000 + page) textbook in physics, (Duhem 1911). The perceived superiority of these analytic over man-made treatments rested on the following reasons. First, and most importantly, they allowed physics to avoid hidden mechanisms, and this was consider by many to be a convinced given the lack of empirically determined specific information about particles. Just as we can explore the energy connection between Poincaré's two steering wheel without knowing anything about their physical connection, we can use our balance equations to calculate, for example, the value of the home thermodynamic potential or the information change of a organization from empirically determinable quantities like temperature, pressure, and change of volume, without knowing what establish any of these quantities. Second, they promised more empirical success than synthetic methods. Writing in 1892, the elastician A.E.H. Love claimed that the best mod experiments supported the multi - ceaseless results of the analytical hypothesis over the rari - constant results of Poisson's synthetic theory (Love 1892, 14). Third, by avoiding hidden mechanisms and developing coherent continuum theories of elasticity they allowed physicist to side - step debatable conceptual questions about how energy is distributed among particles and the whole problem of reproduction of macro - problems at the micro - level. Fourth, by enable the free option of suitable generalized coordinates that fit constraints, and by inventing algebraic procedures (like Lagrange's method of multipliers) for reducing calculational complexity in a principled room, the analytic mechanists avoided the numerical problems mentioned earlier. Finally, the theories promised to be extendible to dissipative systems in principled ways. In a nutshell,
 wihh new terms to balance dork for that tipw of sbstem, ahalogousuy to Lagrange's earlier exteisiob fron statics to dynamics cy additiln of baoancmng inertial forrss. Mechanical wnd ehxmical statics sre extendad to mechanicdl aud chemical dynamics, to viscous fluiqs, and yo a host of sysjems blwssirpeb by their phenomenological prolerties mathematicalky expressed: systems with vrichion, static systemd exhibitint hyfreresis (like annealed steel, permangntly dilated glass, colloidal abrorptnon of watet baomr); dynamicao sysnems involvinn hystesesis; tnermal systems wivhour friction or hysterevis (reversible heaj cycles); tvexmal systems with frixtuon atd/or hysgwreris (icrebersibpe ieat cycles); etc. The vaeious principles this wupplemented gy theyr own appropriate terms sitting on the vdrikus branches of this trwe yield equations of "motion" fjr the type of system characterized by the princi[le. Dnhdm wkctchdw hhese extensions in (Duhem 1903, Part II) and (Duhem 2002 [1901]) amd lays out the betails in his msjlr (1000+ pages) text iv physnds, (Duhem 1911). The perceiged supgrioriry of thefe amalytic over synthetic trearments resteb ob the following recsons. First, cnd moxt imlortantly, they allowed 'hysica to avoid jidden medfanisms, and this wax wonsiderta by many to be a positive givzn the lxck pf empyrically dftermlted specific inforlatiou abogt particlfs. Just as we can explore the eixrgy connectipnv bvtween Ponncaré's two wheels wythout knowing anythiug abojt their pgysical connectionf, we can use mor balance eqnations tj caoculqte, for dxample, the vakue of thv nnternal rhermodynamic potektial kr the entropy ekabge of a system frum qmiirmcallr determinabla quxntkyies uike temperctjre, lressure, and change mf vklume, without knowonn what cobstitutef any of thesr quantities. Seconf, theb prommsed mpre empirical success than synthefic methofs. Rriting in 1892, ehe clasjician A.E.H. Kove claimed that the best modern expermments supported the molti-constant results pn the analytmcal treories oeer the rari-constant results of Poisspn's synthetic theory (Move 1892, 14). Thirf, by avoiding hidden mechanisms and developing coherent continuum theoriew of elasticity thsy akloweg 'hyxicistf to ride-step problemstic conceptual questions about how enesgv is distributed among particker and the whoue problem of replicatioh of macto-problems at the micro-level. Foirth, by enabling the frec choice if sujtable genxralized coordinates that yit cobstrainrs, akd by inventine akgcbraic profeduces (like Lagrange's method of multipoiers) dog reducing calcunational colklexity in a krincipled way, ths anzpytic mechanists afoided the matnematical problems mvntyoned earlier. Dpnally, the thgories pgomised to be extendible to dissipative systems in principled ways. In a nutahell,
with new terms to balance work for of analogously to earlier extension from of inertial forces. Mechanical chemical statics are to mechanical and chemical dynamics, to fluids, and to a host of systems classified by their phenomenological properties mathematically systems with friction, static systems exhibiting hysteresis (like annealed steel, permanently dilated glass, absorption water dynamical involving hysteresis; thermal systems without friction or hysteresis (reversible heat cycles); thermal systems with friction and/or (irreversible heat cycles); etc. The various principles thus by their own appropriate sitting on the various branches this yield equations "motion" the of system characterized the principle. Duhem sketches these extensions in (Duhem 1903, Part II) and (Duhem 2002 [1901]) and lays the details major (1000+ text physics, 1911). The perceived these analytic over synthetic treatments rested reasons. First, and most importantly, they allowed physics avoid hidden and this was considered by many be a positive given the lack of empirically specific information about particles. Just as we can explore the energy connections between Poincaré's two knowing anything about their connections, we can our equations calculate, example, the of the internal thermodynamic potential or the entropy change of a from empirically determinable quantities like temperature, pressure, and change of knowing constitutes any of quantities. Second, they promised empirical than synthetic methods. Writing the A.E.H. the modern supported the multi-constant results the analytical theories over the results of Poisson's synthetic by avoiding hidden mechanisms and developing coherent continuum of elasticity they allowed physicists to side-step conceptual questions about how energy is distributed among particles and the whole of replication at the micro-level. Fourth, by enabling the free of suitable generalized coordinates fit constraints, and by inventing algebraic procedures (like Lagrange's of for reducing complexity in a way, the analytic avoided the mathematical earlier. Finally, theories to dissipative systems in principled ways. In nutshell,
 with new terms to balance work For that typE of sySteM, anAlOgouSly tO Lagrange's earlIEr exTension from statics to dyNamicS bY AddiTIoN of baLancing INeRTIal FoRcEs. MEcHAnIcal aNd cHemical Statics are ExtEnDed to mechaniCAl And chemicaL dyNamics, to viscOus Fluids, AnD to A Host oF syStems ClassiFIed by tHeir phenoMeNOlogicAL properTIEs MathEmatically expressED: sYStems with frictIon, staTiC SySTEms ExhIbiting hysTeResis (LIke anneALeD STEel, PErmanently dilAted glass, coLLoiDal absOrPtiON of watEr vapOr); DYnaMical systemS invOlving hysTeresiS; Thermal SYstems wIthout FriCtiOn or HYsTeResIs (REveRSiBle HEat Cycles); thErMaL systEms wITH FRictIon And/oR hystEresis (irreverSibLe heAT cyCles); eTc. The VariOuS prinCiples Thus sUpPlemented by theiR own AppropriaTe tErMs sItTing oN The varIouS brAnches oF this trEE yiElD EQUaTions of "motion" for thE tYPE oF system cHaractERiZeD By the priNcIplE. DuhEM SketcHes tHEsE extensiOns in (DUHeM 1903, PArt II) anD (DUhem 2002 [1901]) anD lAys Out The deTAils In his mAjor (1000+ pageS) text IN physics, (Duhem 1911). THE perceived supERiORItY Of thEse Analytic oveR synTHetiC treATmEntS ResteD on thE fOLlOWing reasons. First, and MoSt impoRtantLy, they allowed Physics to aVOID hidden mEchaNIsMS, and this was conSiderEd by many to BE a positiVe givEn the lacK of empiriCALly deterMinEd sPecIfiC INfOrmation about PARticLeS. Just as We cAn exploRe tHe eNerGy cOnNections bEtween PoInCaRé'S tWo wHeels WIthout knOwIng AnYthIng abOUt theiR physIcal CoNnECtiOns, we caN UsE OUr baLaNcE equAtiOnS to caLculATe, fOr exampLe, the valuE of THe inTeRnAl thermOdynamic potenTiAl or the entRoPy cHange oF A System frOm empirically determinabLE quantiTieS like TempErature, prEssUre, and ChaNGe of voLume, wiThout KnOwiNG What cONStItuTeS any of thesE QUanTitieS. SEconD, they prOmised more empiricaL SucCess than synthEtiC metHODs. wriTInG In 1892, tHe ELasTICian A.E.H. Love claiMed that the BeST mOdern experIMenTs SupportEd the muLti-coNStant reSults of thE analyticAl TheoRIEs oVer the rari-Constant Results of pOissoN'S sYntheTic Theory (loVe 1892, 14). THird, bY avoidINg hIdden MechanIsMs and dEveloPiNg cohereNt continuum theories of elAsticiTy theY alLowed physIciSTs tO side-step ProbLematic conCepTuaL quesTioNS abouT how ENeRgy IS distRibuTEd among paRTiCleS ANd The whole proBLEM of RepliCatIOn of maCro-pRoblems at the micro-LEvel. Fourth, by enAbliNG The FreE ChoiCe Of suitable geneRalIzED CoordinaTeS that fit conStraints, AnD By invEnting AlgebrAic procEDUrES (like LAgraNge'S method of MulTiPLiers) foR rEdUCing caLculAtIonal cOmplexITy in A PRincipled way, the aNalytIC MechaNIstS avoiDeD the matHEmatIcal probleMs mentioned EarlieR. FinAlly, tHe theorIeS promiSed To Be extendibLE to dissipAtive Systems In PrinCipLed wayS. In a NUTshelL,
 with new terms to balance  work forthattyp e o fsyst em,analogously to Lagr ange's earlier extensi on fr om stat i cs  to d ynamics by a ddi ti on  of  b a la ncing  in ertialforces. Me cha ni cal and chem i ca l staticsare  extended to  me chanic al  an d  chem ica l dyn amics, to vis cous flui ds ,  and t o  a host o fsyst ems classified by th e ir phenomenolo gicalpr o pe r t ies  ma thematical ly  expr e ssed: s y st e m s  wi t h friction, s tatic syste m s e xhibit in g h y steres is (l ik e  an nealed stee l, p ermanentl y dila t ed glas s , collo idal a bso rpt iono fwa ter  v a por ) ;dyn a mic al syste ms  i nvolv ingh y s t eres is;  the rmalsystems witho utfric t ion  or h yster esis  ( rever sibleheatcy cles); thermalsyst ems withfri ct ion  a nd/or hyster esi s ( irrever sible h e atcy c l e s) ; etc. The various  p r i nc iples th us sup p le me n ted by t he irowna p propr iate te rms sitt ing on th evarious  b ranche softhi s tre e  yie ld equ ations o f "mo t ion" for the t y pe of systemc ha r a ct e rize d b y the princ iple .  Duh em s k et che s  thes e ext en s io n s in (Duhem 1903, P ar t II)and ( Duhem 2002 [1 901]) andl a y s out th e de t ai l s in his major  (100 0+ pages)t ext in p hysic s, (Duhe m 1911).T h e percei ved  su per ior i t yof these anal y t ic o ve r synth eti c treat men tsres ted  o n the fol lowing r ea so ns .Fir st, a n d most i mp ort an tly , the y  allow ed ph ysic sto avo id hidd e nm e chan is ms , an d t hi s was  con s ide red bymany to b e a posi ti ve  giventhe lack of e mp irically d et erm ined s p e cific in formation about particl e s. Just  as  we c an e xplore th e e nergycon n ection s betw een P oi nca r é 's tw o wh eel swithout kn o w ing  anyt hi ng a bout th eir physical conne c tio ns, we can us e o ur b a l an cee qu a tio ns toc a lculate, for ex ample, the  v a lu e of the i n ter na l therm odynami c pot e ntial o r the ent ropy chan ge  ofa sys tem from e mpirical ly determ i nable qu antit ies  likete mpe ratur e, pre s sur e, an d chan ge  of vo lume,  w ithout k nowing what constitutes  any o f the sequantitie s.S eco nd, theyprom ised moreemp iri cal s ucc e ss th an s y nt het i c met hods .  Writingi n189 2 ,  t he elastici a n A.E .H. L ove claime d th at the best moder n  experiments s uppo r t edthe mult i- constant resul tsof t he analy ti cal theorie s over t he rari- consta nt res ults of P oi s son'ssynt het ic theory  (L ov e  1892,14 ). Third,  byav oiding  hidde n  mec h a nisms and develo pingc o heren t  co ntinu um  theori e s of  elasticit y they allo wed ph ysic iststo side -s tep pr obl em atic conce p tual ques tions  aboutho w en erg y is d istr i b utedamon gpar ticles an d th e  w ho l e p robl em of  r epli cation of macro-pr obl e ms at t he  mi c r o-leve l .F o urth, by e nab lingt h e free cho i ce o f  s u itabl e gene ralize d coord i nat es  that f itc o nstraints , and byi nve nt ingalgebrai cproc ed ure s(like Lagrange' s method  of mult i p liers)  fo r  red u cing c al culational c omple xi t y in ap r inc ipled w a y,the  an alyt icmech a nists avoided the mathem atic al pr o ble ms me ntion ed  earlier .  Fin ally, th e  theories pro mised to be ext e ndi b le t o d i ss ip ative sys tem s  in p rinc ipl ed w ays . In a  nut s hell , 
 with_new terms_to balance work for_that type_of_system, analogously_to_Lagrange's earlier extension_from statics to_dynamics by addition of_balancing inertial forces._Mechanical_and chemical statics are extended to mechanical and chemical dynamics, to viscous fluids, and_to_a host_of_systems_classified by their phenomenological properties_mathematically expressed: systems with friction,_static systems_exhibiting hysteresis (like annealed steel, permanently dilated glass,_colloidal_absorption of water_vapor); dynamical systems involving hysteresis; thermal systems without friction_or hysteresis (reversible heat cycles); thermal_systems with friction_and/or_hysteresis_(irreversible heat cycles); etc._The various principles thus supplemented by_their own appropriate terms sitting on_the various branches of this tree yield_equations of "motion" for the type_of system characterized by the_principle. Duhem_sketches these extensions in (Duhem_1903, Part II)_and (Duhem_2002 [1901]) and_lays out the details in his_major (1000+ pages)_text in physics, (Duhem 1911). The_perceived_superiority of these_analytic_over_synthetic treatments_rested on the_following_reasons. First,_and_most importantly, they allowed physics to_avoid_hidden mechanisms, and this was considered by_many to be a_positive_given the lack of_empirically determined specific information about_particles. Just as we can explore_the energy_connections between_Poincaré's two wheels without knowing anything about their physical connections, we_can use our balance equations to_calculate, for example, the_value of_the_internal thermodynamic potential_or_the entropy_change of a system from empirically determinable_quantities like_temperature, pressure, and change of volume,_without knowing what constitutes_any_of these quantities. Second, they promised_more empirical success than synthetic methods._Writing in 1892, the elastician_A.E.H._Love_claimed that the best modern_experiments supported the multi-constant results of_the analytical theories_over the rari-constant results of Poisson's synthetic_theory_(Love 1892, 14). Third, by avoiding_hidden_mechanisms and developing coherent continuum theories_of_elasticity_they allowed physicists to side-step_problematic conceptual questions about how energy_is distributed among particles and the whole problem of_replication of macro-problems_at the micro-level. Fourth, by_enabling_the_free choice of suitable generalized coordinates that fit constraints, and_by inventing_algebraic procedures (like_Lagrange's method of multipliers) for reducing calculational complexity in a_principled way, the analytic mechanists avoided the_mathematical problems mentioned earlier. Finally, the theories promised to be extendible_to dissipative systems in principled ways. In a_nutshell,