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very significant resources are being invested in large surveys of the stellar content of our galaxy . we clearly are under an obligation to make every effort to extract as much science from these expensive data as we can . a survey catalogue is always dominated by selection effects : it contains stars that are nearby and luminous . moreover several of the quantities measured for stars , for example parallax @xmath2 , proper motion @xmath3 , @xmath4 enhancement @xmath5 $ ] , contain non - negligible errors , and the quantities of physical interest that we derive from them , such as distance @xmath6 , luminosity @xmath7 and velocity @xmath8 , have correlated errors with highly non - gaussian error distributions . models play a vital role in extracting science from surveys by taking into account ( i ) selection effects ( ii ) measurement errors and ( iii ) combining constraints on the properties of the galaxy from different surveys . here we illustrate these principles . there is a long tradition of extracting science from surveys with kinematic models such as the besanon model @xcite . these models are constructed by assigning to each spatial point a velocity ellipsoid , generally assumed to be gaussian . equilibrium dynamical models are superior to kinematic models in several ways .    * although the galaxy can not be in dynamical equilibrium , equilibrium models are of fundamental importance because an estimate of the galaxy s gravitational potential @xmath9 is key for any modelling enterprise and we can constrain @xmath10 only to the extent that the galaxy is in dynamical equilibrium : if it is allowed to be out of equilibrium , _ any _ distribution of stars in phase space is consistent with _ any _ gravitational potential we constrain @xmath10 by assuming that the potential is deep enough to prevent stars flying apart in the next dynamical time but not so deep as to cause them to slump into the centre in the same period . * equilibrium dynamical models have much less freedom than kinematic or non - equilibrium models because their velocity structure is firmly tied to the density structure by the assumed potential . consequently a small number of parameters suffices to specify a realistic dynamical model , and optimising the model by adjusting these parameters is reasonably straightforward . * observed velocity distributions are far from gaussian but are well reproduced by quasi - isothermal s. * a properly constructed equilibrium dynamical model can be used as the foundation for the construction of non - equilibrium models via perturbation theory . in this way the model can be extended to include non - equilibrium phenomena such as spiral structure and the warp . we have known since the numerical experiments of the 1960s that most orbits in galaxy - like flattened , axisymmetric potentials admit three integrals of motion , and by the strong jeans theorem the distribution function ( ) of an equilibrium model can be assumed to be a function @xmath11 of these integrals . since any function @xmath12 of the integrals is obviously itself an integral of motion , there is considerable choice in what we use for arguments of the . one choice stands out above all others : the action integrals @xmath13 . the special properties enjoyed by the actions include : ( i ) they alone can be complemented by canonically conjugate variables @xmath14 to form a complete set of canonical coordinates @xmath15 for phase space ; ( ii ) the space in which the actions are cartesian coordinates , action space , provides an undistorted compression of six - dimensional phase space in the sense that the volume of phase space occupied by orbits with actions in @xmath16 is @xmath17 ; ( iii ) actions are adiabatic invariants so when the galaxy s potential is slowly deepened , for example by the accretion of gas to form the disc , the orbits of stars change but their actions do not . the property of adiabatic invariance enables us to compute the effects of accretion without knowing precisely how the accretion occurred  we need to know only the initial and final potentials , not the intermediate potentials . the ability to embed the actions in a complete system of canonical coordinates is the key handling non - equilibrium aspects of the galaxy through perturbation theory angle - action coordinates were invented in the 19th century in order to compute the dynamics of the solar system using perturbation theory . particle physics , condensed - matter physics , plasma physics , and celestial mechanics are all built around perturbation theory , which is not merely the means by which we compute the implications of models but provides the concepts feynman diagrams , phonons , spin - waves , mean - motion resonances , etc . ,  with which we understand the phenomena . galactic dynamics will remain a primitive branch of physics until it too makes extensive use of perturbation theory , and our first step towards that goal must be expressing equilibrium models in terms of angle - action coordinates . the angular momentum around the galaxy s approximate symmetry axis @xmath18 is one of the three actions . the best expressions we have @xcite for the integral of motion that controls the extent of a star s excursions perpendicular to the galactic plane are for the vertical action @xmath19 . consequently the only real temptation to employ an integral that is not an action is the temptation to use the energy @xmath20 as the third integral rather than the radial action @xmath21 , which controls the extent of a star s radial oscillation . for some the arguments advanced above for choosing @xmath21 over @xmath20 do not suffice to wean them off @xmath20 , and to these people we say that if your  has the form @xmath22 it is quite tricky to find the self - consistent gravitational potential @xcite . indeed , the search for @xmath10 proceeds iteratively  one guesses @xmath10 , evaluates the density @xmath23 then implied , solves poisson s equation for the corresponding potential @xmath24 and repeats the process until convergence . at each iteration the central potential changes , with the result that the density depends upon a different range of values of @xmath20 , and the iterations converge only if some subtle scalings are employed ( e.g. , * ? ? ? * ( b ) ) . since actions always range from 0 for a star that rests at the bottom of the potential well to @xmath25 for marginally bound stars , when we adopt @xmath26 the iterations converge automatically .    in the following we take the  to have the form @xmath26 and not waste time on more traditional formulations . @xcite showed that superpositions of quasi - isothermal s give good fits to the geneva - copenhagen catalogue and successfully predict data from the sdss and rave surveys . a quasi - isothermal  has the form @xmath27 where @xmath28 is essentially the radial scale length of the disc , @xmath29 is the radius of a circular orbit of angular momentum @xmath18 , @xmath30 and @xmath31 are the radial and vertical epicycle frequencies of this orbit , and @xmath32 and @xmath33 are approximately equal to the radial and vertical velocity dispersions of the disc at @xmath34 . the name `` quasi - isothermal '' for this  derives from the observation that in the epicycle approximation @xmath35 is the in - plane epicycle energy and @xmath36 is the energy of vertical oscillations , so the  becomes an exponential function of these energies like the gibbs distribution of standard statistical mechanics . the hipparcos data showed that the velocity dispersions of thin - disc stars grow with age @xmath37 roughly as @xmath38 ( e.g. * ? ? ? * ) , so @xcite set @xmath39 where @xmath40 is a parameter that controls the velocity dispersion of the stars at birth , @xmath41 is the age of the oldest thin - disc stars and @xmath42 is essentially the present velocity dispersion at @xmath34 . this dispersion is expected to decrease outwards through the disc , and an appropriate functional form is @xmath43 where @xmath44 is a number , @xmath45 is the radius over which the velocity dispersion falls by a factor @xmath46 . @xcite showed that the hipparcos data are consistent with the hypothesis that the star formation rate ( sfr ) near the sun has varied with time as @xmath47 so a reasonable form for the  of the thin disc is @xmath48 that is , the thin disc is modelled as a superposition of quasi - isothermal discs , one for each coeval cohort of stars , with the velocity dispersion of each cohort increasing with age . b12 took the thick disc to be a single quasi - isothermal comprising exclusively old stars . the  of the complete disc is then @xmath49 where the individual s are normalised such that @xmath50 and @xmath51 is the fraction of the mass of the disk contributed by the thick disc .      in principle every observationally distinguishable class of star can have its own . kinematics and chemistry are highly correlated , so stars with different metallicities must have different s. we can model this situation by extending the  above to an extended distribution function ( ) , which is a function of chemical composition in addition to actions . we start by supposing that the chemical composition of the interstellar medium ( ism ) is at any given time a function of galactocentric radius @xmath52 only , and that the chemical composition of a star is the same as that of the ism at the coordinates @xmath53 of its birth . the upper panel of fig . [ jjbfig : zhist ] shows the time dependence of metallicity at several radii in the model of @xcite . we model this dependence with @xmath54 \left[\tanh\left(\tau_m-\tau\over\tau_f\right)-1\right],\ ] ] where from sb09 we adopt the current metallicity - radius relation @xmath55 which yields a linear decline of [ fe / h ] near the sun flattening to @xmath56 at large @xmath52 . here @xmath57 is the maximum age of any star in the galaxy , @xmath58 is that star s value of @xmath59 , and @xmath60 is a parameter that controls the rate of enrichment at early times . following sb09 we adopt @xmath61 and @xmath62 . the lower panel of fig . [ jjbfig : zhist ] shows a reasonable fit to the sb09 model is afforded by @xmath63 .     in the ism according to the model of schnrich & binney ( 2009 ) . each curve corresponds to a radius that increases from top to bottom in steps of @xmath64 , the curve for @xmath65 being shown in red . the lower panel shows the analytic approximation to this evolution afforded by eqs . ( [ jjbeq : mrt ] ) and ( [ jjbeq : mr ] ) . the increment in @xmath52 between curves is again @xmath64 with the curve for @xmath66 shown in red . the region to the right of the dotted vertical line is taken to constitute the thick disc , which has the  of a single quasi - isothermal . ]     in the ism according to the model of schnrich & binney ( 2009 ) . each curve corresponds to a radius that increases from top to bottom in steps of @xmath64 , the curve for @xmath65 being shown in red . the lower panel shows the analytic approximation to this evolution afforded by eqs . ( [ jjbeq : mrt ] ) and ( [ jjbeq : mr ] ) . the increment in @xmath52 between curves is again @xmath64 with the curve for @xmath66 shown in red . the region to the right of the dotted vertical line is taken to constitute the thick disc , which has the  of a single quasi - isothermal . ]    with the assumption that a star s metallicity is given by equation ( [ jjbeq : mrt ] ) with @xmath52 interpreted as @xmath29 the  becomes @xmath67 on account of churning @xcite , the present angular momentum @xmath18 of a star differs from its birth angular momentum @xmath68 by a random offset , which we assume is drawn from a gaussian distribution with dispersion @xmath69 that grows with time , so @xmath70 with churning taken into account , the  becomes @xmath71 where @xmath72 and @xmath73 . when we use the @xmath74-function to execute the integral over @xmath68 we obtain @xmath75 where @xmath68 is given by @xmath76 . to test a model by comparing it with a catalogue , we have to `` observe '' the model in in the same way that the survey observes the galaxy . most of the major surveys now underway make strenuous efforts to be photometrically complete in some well - defined way . nevertheless this completeness is achieved , if at all , only in the final data release because a host of complex constraints and considerations affect the order in which targets are selected  bright stars are likely to be selected ahead of faint ones , and in crowded fields it may be impossible to sweep up adjacent targets in the first visit to the field . fortunately , these considerations are almost always velocity - blind in the sense that the probability that a given star is included in a particular data release is rigorously independent of its velocity . in these circumstances it is easy to test a model with a catalogue for which we have estimates of distance and chemical composition as follows . we bin the stars spatially and chemically in any convenient way . for each star in a bin we choose a hypothetical true distance @xmath77 using either a simple gaussian distribution in @xmath77 or , more rigorously , using the a posteriori probability distribution of @xmath77 for each star that is returned by a bayesian distance - determination algorithm @xcite . the probability distributions from a bayesian algorithm are clearly to be preferred because they take into account the higher density of stars near us than further away and also distance ambiguities associated with uncertainty as to whether a star is a dwarf or some type of giant . in the same spirit we select a hypothetical true metallicity @xmath78 by sampling the product of the model s metallicity distribution along that line of sight and the probability distribution of measurement errors in @xmath59 . once hypothetical true values of all relevant observables have been selected in this way , we sample the model s velocity distribution at the hypothesised location @xmath79 we convert @xmath8 into the line of sight velocity @xmath80 and proper motion @xmath81 using the hypothesised distance @xmath77 . next we add to @xmath80 and @xmath81 appropriate measurement errors before converting them back to a space velocity @xmath8 using the measured distance @xmath6 . these velocities constitute the model s predictions for the distribution of velocities of catalogued stars in the given spatial bin . these predictions take fully into account all measurement errors , no matter how gross , in distances , velocities and metal abundances . if the measurement errors have been correctly assessed , any statistically significant discrepancy between this theoretical velocity distribution and the observed one must reflect a shortcoming of the model . b12 fitted a  @xmath26 to the geneva - copenhagen catalogue ( gcs ) of f and g stars @xcite as follows . first the thin - disc  was fitted to the histograms of @xmath82 , @xmath83 and @xmath84 velocity components . then the data set was augmented by the @xcite estimates of the stellar density @xmath85 at distance @xmath86 from the plane , and the entire  was fitted . since the fits to all the data , especially the distribution of @xmath84 components and the gr83 density points , were excellent , it was evident that the gravitational potential adopted is not far from the truth . however , more rigorous tests of the ( , @xmath10 ) combination of this model are provided by using it to predict the velocity distributions of rave stars , which , unlike the gcs stars , extend far beyond a sphere around the sun of radius @xmath87 . , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ] , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ]    , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ] , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ]    , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ] , right column @xmath88 . the red points are the prediction of the model for thin - disc stars , the black points show velocities measured by rave . the numbers in brackets at the bottom give the mean values of @xmath52 and @xmath89 for stars in that bin.,title="fig:",width=172 ]     components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]   components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]     components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]   components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]     components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]   components of rave giants . left column : stars with @xmath90 , right column @xmath88 . the red points are the prediction of the model , the black points show velocities measured by rave . the numbers in brackets at top left give the mean values of @xmath52 and @xmath89 for stars in that bin followed by the mean observational error . the dotted curves show models of the underlying error - corrected distribution and the black curves show the result of convolving these distributions with the stated errors.,title="fig:",width=172 ]    figs . [ jjbfig : gw ] and [ jjbfig : gvphi ] show results for giants . we divide the stars into those inside / outside the solar radius , and into three bins in @xmath89 . the black points show histograms for @xmath91 rave giants ; each point s vertical bar shows the statistical error in that bin . the red points show the corresponding theoretical predictions .    shows histograms for the vertical velocity component @xmath92 ( the direction of this component changes from point to point in the @xmath93 plane to track a principal axis of the velocity ellipsoid ) . the mean @xmath94 coordinates of the contributing stars appear in brackets in the lower centre of each panel above the error - corrected velocity dispersion in the bin ( sd ) and the mean velocity ( mv ) . in all panels the red and black histograms agree nearly perfectly , even though the stars that contribute to the lower four panels lie far outside the region occupied by the gcs stars , to which the  was fitted .    shows histograms for @xmath95 . although not perfect , the agreement between the red and black histograms is again impressive given that the red points are predictions rather than fits to these data . the fit becomes near - perfect if one assumes that the distances to the most remote stars have been overestimated by @xmath96 . in the last section we merely tested against rave data a previously selected basic . now we report fitting an  to a combination of segue and gcs data . in this work we include a halo described by a classical isothermal @xmath97 . the parameters of the halo , including the local density of its stars , are fixed . its metallicity distribution is a gaussian centred on @xmath98 with dispersion @xmath99 . it contributes @xmath100 of local stars . the thick disc was taken to be a single quasi - isothermal distribution with the metallicity - angular momentum relation that one gets by integrating with respect to @xmath37 within the lower panel of from @xmath101 to @xmath102 . likelihood maximisation was first used to fit the  of the thick disc to g dwarfs in the dr9 segue catalogue with @xmath88 and @xmath86 in @xmath103 . @xmath104 possible values of @xmath105 , @xmath8 and @xmath59 were chosen for each star @xmath4 from that star s error distribution . for each such coordinate set the ratio @xmath106 is the normalised probability density of the assigned velocity given the position and metallicity assignments . crucially , by dividing by the velocity integral we have made @xmath107 insensitive to the spatial and metallicity coordinates , and therefore to the survey s selection function . the average @xmath108 over all randomly sampled velocities @xmath109 is a statistically more stable measure of the probability of the star s measured velocity ( around which the @xmath109 cluster ) that inherits the same insensitivity to the selection function . in order to ensure that the density profile @xmath85 of the thick disc is appropriate , the parameters of the thick - disc  were chosen by maximising the function @xmath110\over\sigma_{\rm gr}(z)}\right|^2,\ ] ] where @xmath111 is the density profile from gr83 , @xmath112 are the errors in @xmath113 , and @xmath114 is the density profile predicted by the .    after pinning down the parameters of the thick - disc  in this way , the gcs velocities , with @xmath59 values from @xcite were used to maximise a log likelihood similar to equation ( [ jjbeq : logl ] ) but ( a ) using all the gr83 points in the sum over @xmath86 , and ( b ) with @xmath115 in eq . ( [ jjbeq : defsn ] ) made sensitive to @xmath59 in addition to @xmath8 by adding integration over @xmath59 to the denominator @xmath116 where @xmath117 is the complete  rather than just of just that of the thick disc .    . ]            shows that the final model provides reasonable if not spectacular fits to the velocities of segue dwarfs that were not used in the fitting procedure . the lower - left panel of shows that the model provides an excellent fit to the distribution of @xmath84 components of gcs stars , while the upper two panels show that the fits to the @xmath82 and @xmath83 components are imperfect at low velocities , presumably on account of the prominence of streams near the origin of the @xmath118 plane @xcite . our fitting procedure yields the joint probability distributions of the parameters of each disc . we do not have space to describe these distributions fully here , but we note a few points :    * the thick disc is hotter vertically than horizontally : @xmath119 . the velocity dispersion parameters of the thin disc are as expected ( @xmath120 ) . * the thick - disc  has a small scale length parameter ( @xmath121 ) . however , this parameter describes the distribution of birth radii of stars , and on account of strong radial migration described by the parameter @xmath69 in equation ( [ jjbeq : defssigmal ] ) , the present distribution of thick - disc stars would be described by a significantly larger scale length @xmath122 . * the scale length parameter of the thin disc is larger than that of the thick disc ( @xmath122 ) . the spatial distribution of thin - disc stars is broadened by radial migration , even if not to the same extent as in the thick disc , so the current scale length is at the upper end of former estimates . the thin disc has a remarkably large value , @xmath123 , of the scale length on which the dispersions decrease radially . * the thick disc contributes @xmath124 of local stars , a value that is smaller than those ( @xmath125 and @xmath126 ) estimated by @xcite and @xcite but a factor of 3 larger the the original estimate of gr83 . given that the model density profile @xmath85 falls below the gr83 points in the range @xmath127 ( lower right - hand panel of ) , the normalisation of the thick disc may be too low . however , shows that the metallicity distribution of the gcs stars provide a contrary indication : when the thick - disc normalisation is large enough to fit the gr83 points , the gcs metallicity distribution shows fewer metal - poor stars than the segue data require . @xcite derived a profile @xmath85 from the sdss data that is slightly less steep than the gr83 data , so using this profile would raise the normalisation of the thick disc s contribution to the  and thus exacerbate the conflict with the gcs metallicity distribution . how serious is is our inability to fit the metal - weak tail of the gcs metallicity distribution simultaneously with the gr83 density profile and the segue metallicity distribution ? possible explanations include : ( i ) one or both of the gcs and segue metallicity scales is wrong ; ( ii ) during the formation of the thick disc , the star - formation rate varied rapidly , with the consequence that the actual metallicity distribution in the thick disc is not adequately approximated by the one we have gleaned from the right - hand end of the lower panel of under the assumption that of a constant sfr . ( iii ) the thick disc s  is not approximately quasi - isothermal . specifically , if the  were not a monotonically decreasing function of @xmath19 , it would be possible to have the required number of metal - poor stars at @xmath128 without exceeding the number seen at @xmath129 because the density profile @xmath85 of the thick disc could be non - decreasing at @xmath130 . two strong objections can be raised to this fix : ( a ) the proposed density profile conflicts with the conclusion of @xcite that mono - abundance populations have double - exponential density profiles , as predicted by quasi - isothermal s ; ( b ) if , as seems likely , the thick disc formed by stars being scattered from near - circular orbits during an early disorderly phase in the life of the galaxy , the  must decrease in the direction that stars diffused , namely that of increasing @xmath19 . for these reasons we consider it unlikely that the conflict arises from the assumed form of the  and is more likely to arise from either differences in metallicity scales or rapid early fluctuation in the sfr . equilibrium dynamical models are crucial for the scientific exploitation of surveys . we have given two examples of their use . first we have shown that a  fitted to the velocity distribution of local stars plus the gr83 density profile predicts the velocity distributions of rave stars with remarkable success given that most rave stars lie far from the sun . second we have introduced an analytic  to model the correlations between kinematics and chemistry . the  is inspired by a particular picture of disc formation but its validity is ultimately independent of its original physical motivation . we fitted this  to a combination of the segue data for g dwarfs seen @xmath131 from the plane and the local gcs stars . the resulting  makes reasonably successful predictions for kinematic data not used in the fitting process , but provides an unsatisfactory fit to the distribution in [ fe / h ] of the gcs stars in the sense of requiring more low - metallicity stars than observed . we discussed possible resolutions of this discrepancy , and none is very attractive . aumer , m. & binney , j. , 2009 , mnras , 397 , 1286 binney , j. , 2010 , mnras , 401 , 2318 binney , j. , 2012a , mnras , 426 , 1328 binney , j. , 2012b , mnras , 426 , 1342 ( b12 ) binney et al . , 2013 , mnras , to be submitted binney , j. , & tremaine , s. , 2008 , _ galactic dynamics _ , princeton university press , princeton bovy j. , rix h .- w . , liu c. , hogg d.w . , beers t.c . , lee y.s . , 2012 , apj , 753 , 148 burnett , b. & binney j. , 2010 , mnras , 407 , 339 casagrande , l. , schnrich , r. , asplund , m. , cassisi , s. , ramirez , i. , melndez , j. , bensby , t. , & feltzing , s. , 2011 , a&a , 530 , 138 dehnen w. , 1998 , aj , 115 , 2384 fuhrmann k. , 2011 , mnras , 414 , 2893 gilmore g. , reid n. , 1983 , mnras , 202 , 1025 holmberg j. , nordstrm b. , andersen j. , 2007 , a&a 475 , 519 juric et al . , 2008 , apj , 673 , 864 nordstrom , b. , mayor m. , andersen j. , holmberg j. , pont f. , jorgensen b.r . , olsen e.h . , udry s. , mowlavi n. , 2004 , a&a , 418 , 989 prendergast , k.h . , & tomer , e. , 1970 , aj , 75 , 674 robin a. , reyl c. , derrire s. , picaud s. , 2003 , a&a , 409 , 523 rowley , g. , 1988 , apj , 331 , 124 sanders , j.l . , 2012 , mnras , 426 , 128 schnrich , r. & binney , j. , 2009 , mnras , 396 , 203 ( sb09 ) selwood , j.a . & binney , j. , 2002 , mnras , 336 , 785
equilibrium dynamical models are essential tools for extracting science from surveys of our galaxy . 
 we show how models can be tested with data from a survey before the survey s selection function has been determined . 
 we illustrate the application of this method by presenting some results for the rave survey . 
 we extend our published analytic distribution functions to include chemistry and fit the chosen functional form to a combination of the geneva  copenhagen survey ( gcs ) and a sample of g - dwarfs observed at @xmath0 by the segue survey . by including solid dynamics we are able to predict the contribution that the thick disc / halo stars surveyed by segue should make to the gcs survey . 
 we show that the measured [ fe / h ] distribution from the gcs includes many fewer stars at @xmath1 than are predicted . 
 the problem is more likely to lie in discordant abundance scales than with incorrect dynamics .    # 
 1to 0pt#1    = cmmib10 = cmmib7 = =    # 1    ii aa # 1#2 # 1#1 = # 1fig .  [ # 1 ]