 now the same problem arises at the lower scale: how is energy distributed to an elementary body b? Changes in b's kinetic energy T must be compensated by corresponding changes somewhere. Moreover, both energy distribution at the microscale and spectroscopic data implied that molecules, if they exist, must have elastic properties like modes of vibration. It was therefore important to have a better account of elasticity. But accounts of elasticity attempted by physical mechanists like Poisson were empirical failures. Some of the difficulties were mathematical. Any physical system will have a huge number of degrees of freedom, and the system of differential equations needed to solve the problem of its motion will become unsolvable. To get around these tractability problems, various techniques appealing to macroscopic constraints and boundary conditions have to be deployed to narrow down the number of degrees of freedom to a manageable set. But these techniques are not validated by the synthetic basis (they are added from above, not derived from below); sometimes they cannot be understood within the conceptual framework of the synthetic approach and their consistency with the basic picture is questionable. Finally, some of the problems concerned generality/extendibility. Conservation of energy can be derived from Newton's laws only for conservative systems, where no net work is performed by forces acting on the system. Few natural systems are conservative; indeed, many concrete systems (steam engines, e.g.) lose energy through heat or friction. Extending synthetic treatments to such systems thus became pressing. Physical mechanists had responses to these problems, but they seemed stretched, ad hoc, and objectionably complicated to Duhem. Poisson, for example, adds elements to his models that are inconsistent with his background assumptions and is forced to replace summation by integration, a replacement that requires crude approximating conditions. Duhem's criticisms of them are trenchant: they employ "ruses and chicanery", retain the theory only by "subtleties and subterfuges" (Duhem 1903, 45), and lack mathematical rigor. His criticisms of Kelvin, Lodge, Maxwell, and the Victorian penchant for synthetically constructed models are caustic. He comments with Gallic flair on Lodge's Modern Views of Electricity: "We thought we were entering the tranquil and neatly ordered abode of reason, but we find ourselves in a factory" (Duhem 1991 [1906], 71). He points out that there are as many kinds of material molecules as there are kinds of physical phenomena or experimental laws (Duhem 1991 [1906], 82-83). Similar crit
now the same problem arises at the low plate: how is energy distributed to an elementary soundbox b-complex vitamin? Changes in b's kinetic department of energy T must be compensated by corresponding change somewhere. Moreover, both energy distribution at the microscale and spectroscopic datum implied that molecules, if they exist, must have elastic properties like mood of vibration. It was consequently important to accept a effective account of elasticity. But accounts of elasticity undertake by physical mechanists like Poisson were empirical failures. Some of the trouble were mathematical. Any physical system will have a huge number of degree of freedom, and the system of differential equations needed to solve the problem of its motion will become unsolvable. To get around these tractability problems, various techniques appealing to macroscopic constraints and boundary conditions have to be deployed to pin down down the number of degrees of exemption to a accomplishable set. But these techniques are not validated by the synthetic footing (they are added from above, not deduce from below); sometimes they cannot be understood within the conceptual model of the synthetic approach and their consistency with the basic picture is questionable. Finally, some of the problems concerned generalization / extendibility. Conservation of energy can be derived from Newton's laws only for conservative systems, where no net employment is performed by forces acting on the system. Few natural system are conservative; indeed, many concrete systems (steam engines, for example) lose department of energy through heat or friction. Extending synthetic treatments to such system thus became pressing. forcible mechanists had responses to these problems, but they seem stretched, ad hoc, and objectionably complicated to Duhem. Poisson, for example, adds elements to his mannequin that are inconsistent with his background assumptions and is forced to replace summation by integration, a replacement that necessitate crude approximating conditions. Duhem's criticism of them are trenchant: they employ " ruses and chicanery ", retain the theory only by " subtlety and subterfuges " (Duhem 1903, 45), and lack mathematical rigor. His criticisms of Kelvin, Lodge, Maxwell, and the Victorian penchant for synthetically construct model are caustic. He comments with Gallic flair on Lodge's Modern Views of Electricity: " We thought we were entering the tranquil and neatly ordered residence of reason, but we find ourselves in a factory " (Duhem 1991 [ 1906 ], 71). He points out that there be as many kinds of material molecules as there are kind of physical phenomena or experimental laws (Duhem 1991 [ 1906 ], 82 - 83). Similar crit
 noa the same problem ariser at the lower scale: hmw is snergy dkstributed to an elementary uody b? Chqnges in b's kinetic endrgy T mudt be conpenwqted by cocdespondlug chzkges vimewhere. Moreoyer, both enargy distributhov ct the microscale and spectroscopic qata imllled that molecoles, pf theg exist, must have elastic propertiss like modes of vibtation. It was therefore imoortwnt to have a bettfr account if ejqsticity. But accounts of elasticiti attempted by physical mechanisgs lile Poisson wwre gmpirical famlures. Some of the difficunties wrre mathematicsl. Eny physical system will iave a huge number os degrees oy freedom, and the sysren of giffarengual eqhaviohs neefed to solve fhe problem of its motion will bqbpme unsolvabme. To dee around these tractability problems, vagioua techniques appealing ro macroscopic constrwints and boundary conditions have to be deployed to narrof dowi ghe nmmbef ov degrees of freedom to a manageable set. But egexe techniques arc not validated by tje fynthetic basks (thev ade added from abovf, not dgrived from beljw); spmetimes they cannot be undwrstood withpn tye conceptual framzwork of the synjhetic approach and their conristsncy with tje basic lkcture is questiunanle. Finally, some of the problqms concecned yeneraligy/exjendibijity. Consegvation of energy can be derired fsom Newton'd laws only for conservative systems, where no nat fork is 'erforked by forces acting on the system. Few vatural syatems ace conservatyve; indeed, mati concrete syvtems (stqam wngibes, e.g.) uuse energy thrpugh heat or frictiin. Extending synthctic jrsatments to suck wystems thus bevamd pwedsmng. Prfsical mechatistr hxc resoonses uj bhere ptoblems, but they seeked atretched, ad hoc, amd objectiinably cjmplicated to Duhem. Poisson, for exam'le, advs elekenjs to his models that are inconaistent wlth his backgrotnd qssumptions cnd is forced to replace summation by invegration, a replacemenj that requires crude spproximatiig conqitions. Dghem's criticisms of rhem are trenchanu: they employ "ruses and chicatery", getain the theory only by "subtleties and subterfuges" (Duhem 1903, 45), and lack matyematiraj rigor. His criyicisks pf Keldin, Pudge, Maxwell, and the Victorian penchant for synvhetically cjnstructed models are caustiv. Fe comments wkth Gallic flair on Lodgs's Moderm Views of Electricity: "We thougnt we were entering the branquil qnd nsatly ordeced abode of reason, nut we find ourselces ln a factory" (Djhek 1991 [1906], 71). He poijts puc that there are as many kinds of materuap molecules as tiere are kinfr of khysical phenomena or exlerijfntal laws (Duhem 1991 [1906], 82-83). Similar crit
now the same problem arises at the how energy distributed an elementary body energy must be compensated corresponding changes somewhere. both energy distribution at the microscale spectroscopic data implied that molecules, if they exist, must have elastic properties like of vibration. It was therefore important to have a better account of elasticity. accounts elasticity by mechanists like Poisson were empirical failures. Some of the difficulties were mathematical. Any physical system will a huge number of degrees of freedom, and system of differential equations to solve the problem of motion become unsolvable. get these problems, various techniques to macroscopic constraints and boundary conditions have to be deployed to narrow down the number of degrees freedom to set. But techniques not by the synthetic are added from above, not derived they cannot be understood within the conceptual framework the synthetic and their consistency with the basic is questionable. Finally, some of the problems concerned Conservation of energy can be derived from Newton's laws only for conservative systems, where no is performed by forces on the system. natural are indeed, concrete systems engines, e.g.) lose energy through heat or friction. Extending synthetic treatments such systems thus became pressing. Physical mechanists had responses to but seemed stretched, ad and objectionably complicated to Poisson, example, adds elements to that inconsistent assumptions is to replace summation by a replacement that requires crude conditions. Duhem's criticisms of "ruses and chicanery", retain the theory only by and subterfuges" (Duhem 1903, 45), and lack rigor. His criticisms of Kelvin, Lodge, Maxwell, and the Victorian penchant for constructed models He comments with Gallic flair on Lodge's Modern of Electricity: "We thought were entering the tranquil and neatly ordered abode of but find ourselves a factory" (Duhem [1906], 71). He out that there many kinds material as of physical phenomena or experimental laws 1991 82-83). Similar crit
 now the same problem arises at The lower scAle: hoW is EneRgY disTribUted to an elemenTAry bOdy b? Changes in b's kinetic EnergY T MUst bE CoMpensAted by cORrESPonDiNg ChaNgES sOmewhEre. moreoveR, both energY diStRibution at thE MiCroscale anD spEctroscopic dAta ImplieD tHat MOlecuLes, If theY exist, MUst havE elastic pRoPErties LIke modeS OF vIbraTion. It was thereforE ImPOrtant to have a bEtter aCcOUnT OF elAstIcity. But acCoUnts oF ElasticITy ATTEmpTEd by physical mEchanists liKE PoIsson wErE emPIrical FailuReS. somE of the diffiCultIes were maThematICal. Any pHYsical sYstem wIll HavE a huGE nUmBer Of DEgrEEs Of fREedOm, and the SyStEm of dIffeRENTIal eQuaTionS needEd to solve the pRobLem oF Its MotioN will BecoMe UnsolVable. TO get aRoUnd these tractabIlitY problems, VarIoUs tEcHniquES appeaLinG to MacroscOpic conSTraInTS ANd Boundary conditions HaVE To Be deployEd to naRRoW dOWn the numBeR of DegrEES of frEedoM To A manageaBle set. bUt ThEse techNiQues arE nOt vAliDated BY the SyntheTic basis (They aRE added from abovE, Not derived froM BeLOW); sOMetiMes They cannot bE undERstoOd wiTHiN thE ConcePtual FrAMeWOrk of the synthetic apPrOach anD theiR consistency wIth the basiC PICture is qUestIOnABle. Finally, some Of the Problems coNCerned geNeralIty/extenDibility. CONServatioN of EneRgy Can BE DeRived from NewtON'S lawS oNly for cOnsErvativE sySteMs, wHerE nO net work iS performEd By FoRcEs aCting ON the systEm. few NaTurAl sysTEms are ConseRvatIvE; iNDeeD, many coNCrETE sysTeMs (SteaM enGiNes, e.g.) Lose ENerGy throuGh heat or fRicTIon. EXtEnDing synThetic treatmeNtS to such sysTeMs tHus becAME pressinG. Physical mechanists had rESponses To tHese pRoblEms, but theY seEmed stRetCHed, ad hOc, and oBjectIoNabLY ComplICAtEd tO DUhem. PoissoN, FOr eXamplE, aDds eLements To his models that are INcoNsistent with hIs bAckgROUnD asSUmPTioNs ANd iS FOrced to replace sUmmation by InTEgRation, a repLAceMeNt that rEquires Crude APproximAting condItions. DuhEm'S criTICisMs of them arE trenchaNt: they empLOy "rusES aNd chiCanEry", retAiN thE theoRy only BY "suBtletIes and SuBterfuGes" (DuHeM 1903, 45), and lack Mathematical rigor. His criTicismS of KeLviN, Lodge, MaxWelL, And The VictorIan pEnchant for SynTheTicalLy cONstruCted MOdEls ARe cauStic. hE comments WItH GaLLIc Flair on LodgE'S mOdeRn VieWs oF electrIcitY: "We thought we were eNTering the tranqUil aND NeaTly ORderEd Abode of reason, bUt wE fIND ourselvEs In a factory" (DUhem 1991 [1906], 71). He poInTS out tHat theRe are aS many kiNDS oF MateriAl moLecUles as theRe aRe KInds of pHySiCAl phenOmenA oR experImentaL Laws (dUHem 1991 [1906], 82-83). Similar crit
 now the same problem aris es at thelower  sc ale :howis e nergy distribu t ed t o an elementary body b ? Cha ng e s in b' s kin etic en e rg y T m us tbeco m pe nsate d b y corre sponding c han ge s somewhere. Mo reover, bo thenergy distr ibu tion a tthe micro sca le an d spec t roscop ic data i mp l ied th a t molec u l es , if  they exist, must ha v e elastic prop erties  l i ke m ode s o f vibratio n.  It w a s there f or e i mpo r tant to havea better ac c oun t of e la sti c ity. B ut ac co u nts  of elastic ityattempted  by ph y sical m e chanist s like  Po iss on w e re  e mpi ri c alf ai lur e s.Some ofth ediffi cult i e s were  ma them atica l. Any physic alsyst e m w ill h ave a  hug enumbe r of d egree sof freedom, and  the  system o f d if fer en tiale quatio nsnee ded tosolve t h e p ro b l e mof its motion will  b e c om e unsolv able.T oge t  aroundth ese  tra c t abili ty p r ob lems, va rioust ec hn iques a pp ealing  t o m acr oscop i c co nstrai nts andbound a ry conditionsh ave to be dep l oy e d  t o  nar row  down the n umbe r  ofdegr e es  of freed om to  a ma n ageable set. But th es e tech nique s are not val idated byt h e  synthet ic b a si s  (they are add ed fr om above,n ot deriv ed fr om below ); someti m e s they c ann otbeund e r st ood within th e conc ep tual fr ame work of  th e s ynt het ic  approach  and the ir  c on si ste ncy w i th the b as icpi ctu re is questi onabl e. F in al l y,some of th e prob le ms  con cer ne d gen eral i ty/ extendi bility. C ons e rvat io nof ener gy can be der iv ed from Ne wt on' s laws o nly forconservative systems, w h ere nonet  work  isperformed  by  force s a c ting o n thesyste m.  Fe w natur a l  s yst em s are cons e r vat ive;in deed , manyconcrete systems ( s tea m engines, e. g.)  los e en erg y  t h rou gh hea t or friction. Ex tending sy nt h et ic treatme n tsto  such s ystemsthusb ecame p ressing.Physicalme chan i s tshad respon ses to t hese prob l ems,b ut  they  se emed s tr etc hed,ad hoc ,  an d obj ection ab ly com plica te d to Duh em. Poisson, for exampl e, add s ele men ts to his  mo d els  that are  inc onsistentwit h h is ba ckg r oundassu m pt ion s  andis f o rced to r e pl ace s um mation by i n t e gra tion,  ar eplace ment  that requires cr u de approximati ng c o n dit ion s . Du he m's criticisms  of  t h e m are tr en chant: they  employ"r u ses a nd chi canery ", reta i n  t h e theo ry o nly  by "subt let ie s  and su bt er f uges"(Duh em  1903,  45),a nd l a c k mathematical r igor. H is cr i tic ismsof  Kelvin ,  Lod ge, Maxwel l, and theVictor ianpench ant for  s ynthet ica ll y construc t ed models  arecaustic .He c omm ents w ithG a llicflai ronLodge's M o d er n  V ie w s o f El ectri ci ty:"We thoug h t we wer e e n teringth e t r a nquila nd n eatly orde red  abod e of reason, butw ef ind o urselv es ina facto r y"(D uhem 19 91[ 1 906], 71) . He poin t s o ut  tha t therear e as  m any  k inds of materia l molecu les as t h e re are  ki n ds o f  physi ca l phenomenaor ex pe r imental l aws  (Duhem 199 1 [ 190 6],82- 83). Similar crit
 now_the same_problem arises at the_lower scale:_how_is energy_distributed_to an elementary_body b? Changes_in b's kinetic energy_T must be_compensated_by corresponding changes somewhere. Moreover, both energy distribution at the microscale and spectroscopic data_implied_that molecules,_if_they_exist, must have elastic properties_like modes of vibration. It_was therefore_important to have a better account of elasticity._But_accounts of elasticity_attempted by physical mechanists like Poisson were empirical failures._Some of the difficulties were mathematical._Any physical system_will_have_a huge number of_degrees of freedom, and the system_of differential equations needed to solve_the problem of its motion will become_unsolvable. To get around these tractability_problems, various techniques appealing to_macroscopic constraints_and boundary conditions have to_be deployed to_narrow down_the number of_degrees of freedom to a manageable_set. But these_techniques are not validated by the_synthetic_basis (they are_added_from_above, not_derived from below);_sometimes_they cannot_be_understood within the conceptual framework of_the_synthetic approach and their consistency with the_basic picture is questionable._Finally,_some of the problems_concerned generality/extendibility. Conservation of energy_can be derived from Newton's laws_only for_conservative systems,_where no net work is performed by forces acting on the_system. Few natural systems are conservative;_indeed, many concrete systems_(steam engines,_e.g.)_lose energy through_heat_or friction._Extending synthetic treatments to such systems thus_became pressing._Physical mechanists had responses to these_problems, but they seemed_stretched,_ad hoc, and objectionably complicated to_Duhem. Poisson, for example, adds elements_to his models that are_inconsistent_with_his background assumptions and is_forced to replace summation by integration,_a replacement that_requires crude approximating conditions. Duhem's criticisms of_them_are trenchant: they employ "ruses and_chicanery",_retain the theory only by "subtleties_and_subterfuges"_(Duhem 1903, 45), and lack_mathematical rigor. His criticisms of Kelvin,_Lodge, Maxwell, and the Victorian penchant for synthetically constructed_models are caustic._He comments with Gallic flair_on_Lodge's_Modern Views of Electricity: "We thought we were entering the_tranquil and_neatly ordered abode_of reason, but we find ourselves in a factory" (Duhem_1991 [1906], 71). He points out that_there are as many kinds of material molecules as there are_kinds of physical phenomena or experimental laws (Duhem_1991 [1906], 82-83). Similar crit