Patent Number: 052672743
Section: claims

1. A method of determining the geological evolution of apatite grains contained within rock samples comprising obtaining a sufficiently pure quantity of representative apatite grains from a rock sample;  forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains;  chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution;  selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement;  determining the density of naturally occurring fission tracks of said first-set apatite grains;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain;  selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks;  measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain;  determining the concentration of .sup.238 U for the first-set apatite grains;  determining the fission track ages of the first-set apatite grains;  determining the chemical composition of first-set and second-set apatite grains;  calculating the pooled fission track age and pooled distribution of perceived track lengths of fluorine-rich first-set and fluorine-rich second-set apatite grains; and  calculating the pooled fission track age and pooled distribution of perceived track lengths of relatively non-fluorine-rich first-set and relatively non-fluorine-rich second-set apatite grains.  spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface;  pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form;  placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin;  allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer;  detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and  polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains.  immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched;  removing the epoxy wafer and attached petrographic slide from the solution;  washing the epoxy wafer and attached petrographic slide with distilled water; and  drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits.  observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains for fission track age measurement which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and  selecting apatite grains from among the suitable candidate apatite grains possessing a relatively high fraction of etch pits that represent etched naturally occurring fission tracks in combination with a relatively large available etched surface area.  viewing the first-set apatite grains through a magnifying device possessing a graticule grid of known dimensions and which is imposed upon viewed images;  counting the number of etch figures resulting from the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface within an area of known dimensions defined by the graticule grid; and  calculating the spontaneous fission track density according to the formula: EQU P.sub.S =N.sub.S /AREA  where N.sub.S, in units of tracks, is the number of etch figures created by the intersection of etch pits that represent etched naturally occurring fission tracks with the etched planar surface of the first-set apatite grain within the area outlined by a portion of the graticule grid; and  where AREA, in units of length squared, is the area of the surface of the first-set grain outlined by the graticule grid.  viewing the first-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point;  calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2)  where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  viewing the first-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point;  calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2)  where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains that contain etched confined fission tracks and which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and  identifying as many as 200 confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains.  viewing the second-set apatite grains under a binocular optical microscope having multiple illuminating light sources, and a projection tube by which a point source of light from a cursor apparatus attached to a digitizing tablet can be visually observed while looking through the microscope;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.5,Y.sub.5, of the point;  placing the point source of the light from the cursor apparatus at precisely the opposite extreme of each linear etched confined fission track, wholly contained within a second-set apatite grain, and electronically recording the coordinates, X.sub.6,Y.sub.6, of the point; and  calculating the perceived track length of each linear etched confined fission track, wholly contained within the second-set apatite grains, according to the formula: EQU TL=C sqrt((X.sub.6 -X.sub.5).sup.2 +(Y.sub.6 -Y.sub.5).sup.2)  where TL, in units of length, is the perceived track length of a confined fission track in a second-set apatite grain; and  where C, in units of length, is a scaling factor that converts the units of the digitizing tablet into units of length.  viewing the second-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point;  calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2)  where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  viewing the second-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point;  calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2)  where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPERi measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  placing a muscovite mica detector in intimate contact with the etched planar surface of the epoxy wafer containing the first-set apatite grains;  placing the epoxy wafer and muscovite mica detector in close proximity to the core of a nuclear reactor;  placing a portion of uranium-doped glass in intimate contact with a muscovite mica detector in close proximity to the core of a nuclear reactor;  irradiating the epoxy wafer and the uranium-doped glass and their respective muscovite mica masks with thermal neutrons thereby inducing fission of .sup.235 U in the first-set apatite grains within the epoxy wafer and the uranium-doped glass;  removing the epoxy wafer, uranium-doped glass, and muscovite mica detectors from close proximity to the core of a nuclear reactor;  chemically etching the induced fission tracks within the muscovite mica detectors;  calculating the concentration of .sup.238 U for each first-set apatite grain according to the formula: EQU [.sup.238 U]=137.88 [.sup.235 U.sub.g ] (R.sub.g /R.sub.a) (P.sub.ia /P.sub.ig)  where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in a first-set apatite grain within the apatite volume of interest;  where 137.88, in units of nuclei per nuclei, is a constant for all first-set apatite grains which represents the naturally occurring concentration ratio of the uranium isotopes .sup.238 U to .sup.235 U;  where [.sup.235 U.sub.g ],in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.235 U in the uranium-doped glass;  where R.sub.g, in units of length, is the average distance travelled by a single fission fragment nucleus in the uranium-doped glass;  where R.sub.a, in units of length, is the average distance travelled by a single fission fragment nucleus in the first-set apatite grain;  where P.sub.ia, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector within the area of the detector outlined by the graticule grid that was in intimate contact with the previously studied area of the first-set apatite grain; and  where P.sub.ig, in units of tracks per length squared, is the surface density of induced fission track etch pits that cross the etched planar surface of the detector that was in intimate contact with the uranium-doped glass.  calculating the fission track age for each first-set apatite grain using the formula: EQU T=(1/l.sub.D) ln((l.sub.D /l.sub.F)([FT]/[.sup.238 U])+1)  where T, in units of millions of years, is the fission track age for the first-set apatite grain;  where l.sub.D, in units of nuclei per million years, is the total decay constant for .sup.238 U;  where l.sub.F, in units of nuclei per million years, is the fission decay constant for .sup.238 U;  where [FT], in units of tracks per length cubed, is the number of naturally occurring fission tracks, resulting from the spontaneous fission decay of .sup.238 U, per unit volume in a volume of interest in the first-set apatite; and  where [.sup.238 U], in units of nuclei per length cubed, is the concentration of the uranium isotope .sup.238 U in the first-set apatite grain within the apatite volume of interest.  plotting the individual apatite grain ages of the first-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis;  plotting the individual track lengths of the second-set apatite grains as a function of the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis;  grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite.  calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula: EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2  where [F], in units of weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied.  calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula: EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2  where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied.  calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula: EQU [H.sub.2 O]=-0.048074+0.28092 DPAR  where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied.  obtaining a sufficiently pure quantity of representative apatite grains from a rock sample;  forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains;  chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution;  selecting a first-set of apatite grains from among suitable candidate apatite grains;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain;  selecting a second-set of apatite grains from among suitable candidate apatite grains;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain;  measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain; and  determining the chemical composition of first-set and second-set apatite grains.  spreading the representative apatite grains on a non-stick surface within an area of approximately one square centimeter defined by a form which is 1.5 millimeters deep and in contact with the non-stick surface;  pouring a mix of epoxy resin and epoxy hardener over the sampling of representative apatite grains contained within the form;  placing a petrographic microscope slide on top of the epoxy resin and applying a slight downward force to ensure that said slide will be attached to the epoxy resin;  allowing the epoxy resin mix to harden for twenty four hours at room temperature thereby forming an epoxy wafer;  detaching the resulting epoxy wafer from the non-stick surface while allowing the epoxy wafer to remain attached to the petrographic microscope slide; and  polishing the planar surface of the resulting epoxy wafer opposite that attached to the petrographic slide to an extremely smooth finish thereby removing a portion of the epoxy wafer and a similar thickness of the apatite grains aligned with the planar surface being polished thereby exposing internal surfaces of the apatite grains.  immersing the epoxy wafer and attached petrographic slide in an acidic solution whereby all naturally occurring fission tracks and other crystallographic imperfections exposed to the acidic solution will be chemically etched;  removing the epoxy wafer and attached petrographic slide from the solution;  washing the epoxy wafer and attached petrographic slide with distilled water; and  drying the epoxy wafer and attached petrographic slide sufficiently to remove all fluid from the resulting etch pits.  observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and  selecting apatite grains from among the suitable candidate apatite grains possessing etch figures on their polished and etched planar surfaces.  viewing the first-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point;  calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2)  where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPAR.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  viewing the first-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point;  calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2)  where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the first-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each first-set apatite grain studied by summing all values of DPER.sub.i measured for each first-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  observing the etched apatite grains contained within the polished and etched surface of the epoxy wafer and identifying suitable candidate apatite grains which have their crystallographic c-axes oriented parallel to the polished and etched planar surface of the epoxy wafer; and  identifying suitable candidate apatite grains that contain confined fission tracks which are etched to their ends and which lie within approximately 10 degrees of parallel to the polished and etched planar surface of the apatite grains.  viewing the second-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.1,Y.sub.1, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter parallel to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.2,Y.sub.2, of the point;  calculating the length of the maximum diameter parallel to the crystallographic c-axis of each etch figure using the formula: EQU DPAR.sub.i =C sqrt ((X.sub.2 -X.sub.1).sup.2 +(Y.sub.2 -Y.sub.1).sup.2)  where DPAR.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter parallel to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters parallel to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPAR.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  viewing the second-set apatite grains through a magnifying device;  placing the point source of light from a cursor apparatus attached to a digitizing tablet at precisely one extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.3,Y.sub.3, of the point;  placing the point source of light from the cursor apparatus at precisely the opposite extreme of the diameter perpendicular to the crystallographic c-axis of each etch figure and electronically recording the coordinates, X.sub.4,Y.sub.4, of the point;  calculating the length of the maximum diameter perpendicular to the crystallographic c-axis of each etch figure using the formula: EQU DPER.sub.i =C sqrt ((X.sub.4 -X.sub.3).sup.2 +(Y.sub.4 -Y.sub.3).sup.2)  where DPER.sub.i, in units of length, is the numerical value of the length of the maximum etch figure diameter perpendicular to the crystallographic c-axis of the i-th etch figure on the etched planar surface of the second-set apatite grain being studied; and  where C is a scaling factor that converts the units of the digitizing tablet into units of length; and  calculating the arithmetic mean of the etch figure diameters perpendicular to the crystallographic c-axis for each second-set apatite grain studied by summing all values of DPER.sub.i measured for each second-set apatite grain and dividing the resultant sum by the number of etch figure diameters measured.  grouping each of the first-set apatite grains and second-set apatite grains into either a group which is predominantly composed of fluorine-rich apatite or a group which is predominantly composed of relatively non-fluorine-rich apatite by determining whether the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis on the planar surface of the apatite grain is less than or equal to a length of 2 micrometers, in the case of fluorine-rich apatite, or greater than 2 micrometers, in the case of relatively non-fluorine-rich apatite.  calculating the fluorine concentration or [F] for first-set and second-set apatite grains according to the following formula EQU [F]=4.6748-1.3106 DPAR+0.041759 DPAR.sup.2  where [F], in units of Weight percent, is the fluorine concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied.  calculating the chlorine concentration or [Cl] for first-set and second-set apatite grains according to the following formula EQU [Cl]=-0.31045-0.053515 DPAR+0.26067 DPAR.sup.2  where [Cl], in units of weight percent, is the chlorine concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied.  calculating the water concentration or [H2O] for first-set and second-set apatite grains according to the following formula EQU [H.sub.2 O]=-0.048074+0.28092 DPAR  where [H2O], in units of weight percent, is the water concentration in the first-set or second-set apatite grain being studied; and  where DPAR, in units of length, is the arithmetic mean maximum etch figure diameter parallel to the crystallographic c-axis in the first-set or second-set apatite grain being studied. 2. A method according to claim 1 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 3. A method according to claim 1 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 4. A method according to claim 3 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 5. A method according to claim 1 including selecting a first-set of apatite grains from among suitable candidate apatite grains for fission track age measurement comprises 6. A method according to claim 1 including determining the density of naturally occurring fission tracks of said first-set apatite grains comprises 7. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 8. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 9. A method according to claim 1 including selecting a second-set of apatite grains from among suitable candidate apatite grains for measurement of perceived track lengths of confined fission tracks comprises 10. A method according to claim 1 including measuring the perceived track lengths of confined naturally occurring fission tracks within the second-set apatite grains comprises 11. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 12. A method according to claim 1 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 13. A method according to claim 1 including the determination of the concentration of .sup.238 U for first-set apatite grains comprises 14. A method according to claim 1 including determining the fission track age of said first-set apatite grains comprises 15. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 16. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 17. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 18. A method according to claim 1 including determining the chemical composition of the first-set and second-set apatite grains comprises 19. A method of determining the chemical composition of apatite grains contained within rock samples comprising 20. A method according to claim 19 including forming at least one epoxy wafer containing said representative apatite grains for examination and polishing said epoxy wafer containing said representative apatite grains in order to expose internal planar surfaces of the apatite grains comprises 21. A method according to claim 19 including chemically etching naturally occurring fission tracks and other crystallographic imperfections that intersect the polished internal planar surfaces of the said apatite grains with an acidic solution comprises 22. A method according to claim 21 including said epoxy wafer and attached petrographic slide are immersed in a nitric acid solution of 5.5 Molar strength at 21 degrees Celsius for 20 seconds while being swirled vigorously within the solution. 23. A method according to claim 19 including selecting a first-set of apatite grains from among suitable candidate apatite grains comprises 24. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each first-set apatite grain comprises 25. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the first-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said first-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each first-set apatite grain comprises 26. A method according to claim 19 including selecting a second-set of apatite grains from among suitable candidate apatite grains comprises 27. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being parallel to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters parallel to the c-axis for each second-set apatite grain comprises 28. A method according to claim 19 including measuring the maximum diameters of etch figures formed by the intersection of said etched naturally occurring fission tracks and other crystallographic imperfections with the etched internal planar surfaces of the second-set apatite grains, said diameters being perpendicular to the crystallographic c-axes of the said second-set apatite grains, and calculating the arithmetic mean of the etch figure diameters perpendicular to the c-axis for each second-set apatite grain comprises 29. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 30. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 31. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises 32. A method according to claim 19 including determining the chemical composition of the first-set and second-set apatite grains comprises