GEOMETRICAL STUDY OFA CASTOFLEPTOPHLOEUMAUSTRALE(McCOY) WALTON FROM QUEENSLAND H.TREVORCLIFFORD Clifford,H.T. 19960720: AgeometricalstudyofacastofLeptophloeumaustrale(McCoy) Walton from Queensland. Memoirs ofthe QueenslandMuseum 39(2); 227-230. Brisbane. ISSN 0079-8835. GeometricalstudyofacastofLeptophloeumaustrale(McCoy)Waltonconfirmsthatduring D its compression there has been no increase in diameter. Leptophloeum, axis, cast, compression. H. TrevorClifford, QueenslandMuseum,P.O.Box3300,SouthBrisbane, Queensland4101, Australia; 1 February 1996. Axial casts of the lepidophyte Leptophloeum al., 1993). Because the cast was collected as a australe(McCoy) Walton have been recorded in surficial boulder its precise age is not deter- Australia from Queensland (Carruthers, 1872) minable. However, the taxon is well represented and Victoria(McCoy, 1874). Herein an addition- by impressions in the Ruxton Formation whose al cast is described from Queensland. The age, based on conodonts, is Late Devonian to specimen is of particular interest because over Early Carboniferous. most of its surface the outlines of leaf-cushion Two available casts (Table 1) are entirely bases are clearly defined, (Fig. 1) thereby ena- mineral in composition and a thin section of blingthelengthofitsdiameter,priortocompres- QMF3204 revealed it to be a fine sediment sion, tobe determined with reasonable accuracy. dominated by rock fragments and quartz. Other This length therefore provides a bench mark minerals present are muscovite, orthoclase, against which diameters as estimated by other plagioclase, sericite and undifferentiated iron methods may be evaluated. oxides. The unabraided condition of the grains All methodsemployed assume thecast to have and their composition indicates the cast formed been cylindrical priorto itscompression, a view- in young sediments with a proximal igneous and pointjustifiedbytheuniformity insizeand shape metamorphic provenance. The cement is ofthe leaf-cushions on its surface. Furthermore, dominated by silica and clay with subordinate thecastwasassumedtobeelliptical in transverse iron oxides (Alex Cook per. comm.). sectionwhich assumption hasbeenconfirmedby direct observation. Although casts are often RESULTS & reportedtobeellipticalinsection (Pant Srivas- ctlaiovcnaaf,tiir1o9mn9e5di)nbythwaehrdieicraehpcptetcahoremspcatoornibtseeonnntooifporntehvehioaobsussebrpevueebnd- imtaFitsresopomosfsmietbhaleseudtrioaemmmeeatnketresoosffevtthehereaclsapsietncdbieemfpeoenrned(eiTntastbcleoesmti1--) section shape with that of the ellipse calculated pression. Thattheoutlineofthecastin transverse from the maximum and minimum widths of the sectionapproximatescloselytoanellipsemaybe cast. confirmedbyreferencetoFig. 2wheretheellipse calculatedonthebasisofthemaximumand min- MATERIAL TABLE 1.FiveattributesoftwocastsofLeptophloeum australe. The cast (QMF3275) was collected by Leich- hardtduring hisexpedition from Moreton Bay to ATTRIBUTE DIMENSIONSfmm) Port Essington and is the only specimen in the Queensland Museum known to have been col- QMF3275 QMF3204 lectedbytheexplorerwhose misfortune it wasto Perimeter 283 194 lose,bymisadventureornecessaryabandonment, Maximumwidth 117 75 mostofhiscollectionswhenneartohisjourney's Minimumwidth 51 47 end (Leichhardt, 1847). The specimen is labelled Leaf-cushionwidth 13.4 12 'Clarke River' and so most probably has its Provenance in the Clarke RiverBasin (Draperet No. leaf-cushionsencirclingaxis 25 n.a. . 228 MEMOIRSOFTHEQUEENSLANDMUSEUM B jj|^^rtWi|*(^itH^i|ifl^|WWti|ijjum*jii^ FIG.l. CastofLeptophloeumaustrale (QMF3275). A, Lateral view. B, End view, imumwidthsofthecastissuperimposedupon its The number of leaf-cushions encircling the cast original outline. is half the number of the vertical rows in which Four approaches to the estimation of the they are arranged (Fig. 3). The recognition of diameterofthe cast prior to its compression will these rows is more reliable than that ofadjacent now be considered: leaf-cushion boundaries wherever the surface of 1 PerimeterofCast. Ifitisassumedthatduring the cast is irregular or the leaf-cushions are compression the perimeter of the cast is un- strongly compressed as in regions of maximum changed the diameter of a circle with the same curvature. Therefore, the number of leaf- perimeter is readily calculated (Table 2). cushions encircling the cast was determined as 2. Cross Sectional Area of Cast. If the cross halfthe numberofvertical rows ofleaf-cushions sectional area of the cast is unaffected by com- on the surface ofthe cast. Multiplication ofleaf- pression the areas ofthe elliptical section ofthe cushion number by leaf-cushion width provided cast and that ofits precompression circular sec- a perimeter for the uncompressed cast from tion will be the same. Accepting the maximum which its diameter was calculated (Table 2). andminimumwidthofthecastasaxis-lengthsthe area of the elliptical section may be calculated DISCUSSION OFRESULTS and from this the diameter of a circle of similar areadetermined (Table 2). 3. MaximumWidth ofCast. Assuming thatthe Each of the 4 methods employed provided a vertical compression of a horizontal cylindrical different estimate ofthe diameter ofthe original cast may occurwithout any lateral expansion the cast (Table 2). These differences are readily ac- maximum width of the cast is the same as the counted for ifit is assumed that during compres- diameterofthe uncompressed cast (Table 2). sion a cylindrical cast was deformed into one 4. Leaf-cushion numberx Leaf-cushion width. elliptical in transverse section, with the major TABLE 2. Four estimates of the diameter of a axis oftheellipse being ofthe same length asthe presumed cylindrical cast ofLeptophloeum australe diameterofthe cylinder. as determined from certain attributes of its com- Such a situation is illustrated in Fig. 4 where pressedcast(QMF3275). sections of a theoretical cast, prior to and sub- sequent to its compression, are superimposed. ESTCIAMSATTED The ellipse is similartothatofFig. 2becausethe BASISOFESTIMATE DIAMETER lengths of the major and minor axes of the two (mm) are the same. Along the perimeter of both the 1. Perimeter 90 circle and ellipse solid circles mark the positions of leaf-cushion margins. The number of leaf- 2.Crosssectionalarea 77 cushions is the same as that on the cast being 3. Maximumwidth 117 studied and theirpositions on the ellipse are ver- 4.Cushion numberxcushionwidth 107 tical projections ofthose on the circle. Therefore GEOMETRYOFCRUSHINGLEPTOPHLOEUMAUSTRALE 229 D —*-^_ C —J^~~ \"x B ///S \^^*X\> // \\ // \A // \\ if // \\ // \x ^ vV\ ^v^\VXX j^VJ^jS/y N> s "' — —"n— ~~~~ II __ ^rzrrrc:——— '"~ i 1 cm i FIG. 2. Outline of cast of Leptophloeum australe (QMF3275) with the perimeter of theoretical ellipse superimposed. A-Dareplacesoncastsurface at which leaf-cushion widths(Table3) weremeasured. the ellipse may be regarded as a compression of provide a closer estimate ofthe perimeter ofthe the circle without a change ofits diameter. inscribing circle than will the area ofthe ellipse. Both the perimeter and the area of the ellipse Thisstatementisespeciallytrueofstronglycom- will provide measurements which will lead to pressed casts. Towards the limitofcompression, underestimates of the diameter of the cir- as the length of its minor axis approaches zero, cumscribingcircle,andtheshortertheminoraxis the perimeterofan ellipse approaches a value of of the ellipse the poorer will be the estimate. twice the length ofits major axis but the area of Furthermore, of the two parameters under dis- theellipse approaches zero. Hence itis clearthat cussion the perimeter of the ellipse will always ellipses whose minor axes are short in com- -* •- leaf-cushion FIG. 3. Semidiagrammaticdrawingofthedisposition FIG. 4. Transverse sections of2 theoretical casts on of leaf-cushion outlines on the surface of cast of whose perimeters the margins of the leaf-cushion Leptophloeumaustrale(QMF3275). A=direction of outlines have been marked by solid circles -circle, stemapex; CB=leaf-cushionbase;CM=leaf-cushion before compression; ellipse, aftercompression. The margin; CW=leaf-cushion width; VC=vascular major and minor axes of the ellipse are the same cicatrix.. length as in Fig. 2. 230 MEMOIRSOFTHEQUEENSLANDMUSEUM TABLE3. Theareasandperimetersofanellipsewith TABLE 4. The widths ofleaf-cushion at 4 positions different minor and major axis ratios expressed as on the surface of a cast of Leptophloeum australe proportionsofitscircumscribingcircle. (QMF3275)as measureddirectly and as determined by projection from a circularcastonto one elliptical Ellipseasproportionifits intransversesectionwithamajoraxisthesamelength LLeennggtthhooffmmaijnoorraaxxiiss circumscribingcircle asthediameterofthecircularcast. Area Perimeter Leaf-cushionwidth(mm) 1.0 1.00 1.00 0.9 0.90 0.94 Placeonsurface Measured Predicied (Fig.2) 0.8 0.80 0.88 A 4.0±0.3 5.5 0.7 0.70 0.82 B 7.2±0.4 8.0 0.6 0.60 0.76 C 11.9±0.2 11.5 0.5 0.50 70 D 13.4±0.8 13.5 parisontotheirmajoraxesprovidepoorinforma- the cast has not increased as a result ofcompres- tion for predicting the diameter of the cir- sion comes from a comparison of the measured cumscribingcircle. and predicted widths ofleaf-cushions. Measure- However, thesituation isdifferent ifthe length mentsweremadeonfourareasofthecastsurface ofthe minoraxisoftheellipse equalsorexceeds and the predicted widths weretaken fromsimilar halfthe length ofthe majoraxis. Overthis range positionsontheellipse(Fig. 2;Table4).Standard ofvaluesboththearea(exactly)andtheperimeter errors can be attached to the means ofthe meas- (closely) ofthe ellipse are linearly related to the urements because thereare several leaf-cushions area of the circumscribing circle. Whereas for available on similar areas ofthe cast but there is highvaluesoftheratioofthelengthsoftheminor only one predicted value forcorresponding parts and major axes, both the perimeter and the area of the ellipse. Only on the surface of greatest oftheellipseareusefulpredictorsofthediameter curvature does the predicted value of leaf- ofthecircumscribingcircle, forlowvaluesofthe cushion width differ significantly from that ratios neither is useful but the perimeter is the measured.Suchcloseagreementbetweenthetwo better estimator (Table 3). This observation is setsofvaluesisfurthersupportforthehypothesis confirmedbytheestimatesofdiameter(Table2). thatcompressionofthecasthasoccurredwithout It is also clear (Fig. 4) that whereas the leaf- any lateral extension. cushion bases around the perimeter of the circle Although casts of Leptophloeum australe are are all of the same width their projections on to rare,impressionsoftheiraxesareabundant.Most the ellipse vary in width. Whereas leaf- cushion are flat and irregular in outline, but a few are B (Fig. 4) is almost the same width as that ofA, parallel-sided thereby resembling impressionsof thewidthofleaf-cushion Dismuch lessthanthat complete axes. However, it is not reasonable to ofC. Ifthe leaf-cushion is bisected by the minor assume that the impression revealed on a flat axisoftheellipse itswidth will bealmostexactly surface derives from a whole axis. It may repre- thatofits widthbeforeprojectionfromthecircle. sent any portion ofthe surface, the remainderof Therefore, provided the leaf-cushions measured which may be buried in the rockon eithersideof are situated close to where the minor axis ofthe theplane(alongwhichtherocksplit)torevealthe ellipse meets its surface their widths combined impression. Cleavage across a cast near to its with their number provide an accurate basis for surface and parallel to its length would expose estimatingthediameteroftheuncompressedcast. impressionswithparallel sidesbutwhosewidths Because only one cast is available it is not are much less than the diameter ofthe cast. That possible to determine whether the diameters of thissituationiscommonissuggestedbythemany the uncompressed cast as estimated from the impressions whose leaf-cushion bases have maximumwidthofthecompressedcast(117mm) widths typical of casts whose diameters are and by the leaf-cushion number x width method greater than the width ofthe impression. (107mm),arestatisticallydifferent.However,the data indicate that if there has been any lateral CONCLUSION spread ofthe cast during compression the exten- sion has been slight for the ratioofthe formerto Although ithasbeenwidely acceptedthatcom- the latter is 1.09 which value is close to unity. pressionofplanttissuesandcastsusuallyoccurs, Further support for the view that the width of without a concomitant increase in their width at GEOMETRY OFCRUSHINGLEPTOPHLOEUMAUSTRALE 231 right angles to the force applied, the process has ly comparable with the observational data been subject to little theoretical or experimental reported above for none of the experimenters study. included casts in their studies. Nonetheless, the Using a series of projections similar to that applicationofpressuretoembedded material did employed above, Walton (1936) compared the not result in its lateral extension except for one shapesofsomesolidspre-andpost-compression. reportbyNiklas(1978).Thesimilarityofthepre- His approach was qualitative and non-ex- and post-compressional diameters ofthe Leich- perimental. However, accordingto Harris (1974: hardt cast (QMF3275) suggest that even when 144)Walton'sobservationswereunderpinnedby subjected to pressures much greater than those a series of experiments in which he had com- employed in the laboratory plant axes do not pressed 'various solidplantorgans -plant stems, expand lateral to the force applied. apples and the like in wet sand in a power press ACKNOWLEDGEMENTS so constructed as to allow surplus waterto drain away*. Apples so compressed were converted into hemispheres filled with sand but with their ThanksareextendedtoMaryWade,AlexCook diameters unchanged. and Vincent Hart for helpful discussions during The pioneering study of Walton (1936) has thepreparationofthispaperandtoNatalieCamil- been extended by Harris (1974), Niklas (1978) leri and Maryanne Venables for assistance in and Rex & Chaloner (1983). Harris (1974) em- preparing the diagrams. The photographs were beddedhollowballsofwaxorplastic,inavariety taken by Gary Cranitch. of matrices which were then compressed. After compressiontheballswereapproximatelyhemis- LITERATURECITED phericalandcircularinoutline. Noneofthecom- pressions showed any obvious evidence of CARRUTHERS. W. 1872. Noteson fossil plantsfrom horizontal extension. Simulated compression Queensland. Quarterly Journal ofthe Geological studiesofNiklas(1978)werequiteextensivebut, SocietyofLondon 28: 2-9 unfortunately, the procedures adopted were not DRAPER,J.J.,SCOTT, M.&WITHNALLI.W. 1993. adequatelydescribed.However,hedemonstrated Clarke River Basin and associated rocks. that whereas hollow and solid, but dehydrated Queensland Geology 4: 203-219. stems compress without lateral extension HARRIS, T.M. 1974. Williamsoniella lignieri: its pol- hydrated solid stems 'show a maximum increase Pleanlaaenodntthoelcoogymp1r7e:s1s2i5o-n1o4f9sphericalpollengrains. oafdop1t0e%d bdyiamReetxer*&. CEhxapleorniemren(t1a9l83p)roacreedufurlelsy LEICpHeHdiAtRioDnTi,n LA.ust1r8a4l7i.a'fJroourmnaMlorocftaonnoBvaerylatnodPeoxr-t explained and so their results can be critically Essington during theyears 1844-1845'. (T. & W. assessed. Foam rubber was used to represent Boone: London). 544p. plant material and saw dust the embedding McCOY, F. 1874. Lepidodendron (Bergenia) oustrale matrix. Pressure was appliedeither with a single (McCoy). Pp. 37-39. In 'Prodromus of the pistonoraparallel systemofindependentpistons palaeontologyofVictoria.Decade 1\(Geological Survey ofVictoria:Melboume). each of which was spring loaded, but with the NIKLAS, K.J. 1978. Morphometric relationships and whole set controlled by a single screw mechan- rates of evolution among Palaeozoic vascular ism.Aftercompression,transversesectionsofthe plants. Evolutionary Biology 1 1: 509-543. original cylinders (stems), differed in shape ac- PANT,D.D. &SRIVASTAVA,P.C. 1995.LowerCar- cordingtothepistonsystememployed. Nonethe- boniferousplantsfromWallarannaSeriesofPun- less in both systems and for several cylinder jab-Kashmir Himalaya. Palaeontographica B, diameters the maximum width of the stem fol- 235: 23-49. lowing compression was equal toorslightly less REX, G.M. & CHALONER, W.G. 1983. The ex- than theoriginal diameter. That is, the resultsare perimentalformationofplantcompressionfossils. inIatcicsonrodtwpiotshsitbhleeptroedciocmtpiaonrseowfiWthalcteortnai(n1t9y36t)h.e WALTePOxatlNear,enoaJnl.tfo1ol9ro3g6m.yoO2f6nf:ost2sh3iel1-fpa2lc5atn2ot.rss:wwihtihchdeisncfrliupetnicoenstohef results obtained from the several experimental the foliage of some species of Palaeozoic equi- studies because of the diversity of materials setalean genus Annularia Sternberg. Philosophi- employed and the differences in procedures cal Transactions ofthe Royal Society ofLondon adopted.Furthermore,theseresultsarenotdirect- 226B: 219-237. : 232 MEMOIRS OFTHEQUEENSLAND MUSEUM POSSIBLE AFFINITIES BETWEEN VARANUS ESTES, R., DE QUEIROZ, K. & GAUTHIER, J. 1988. GIGANTEUSANDMEGALANIAPRISCA,Memoirsofthe Phylogenetic relationships within Squamata. Pp. 119- Queensland Museum 39(2):232. 1996:- Molnar (1990) 281 In Estes, R. & Pregill, G. K. (eds). 'Phylogenetic describedtwo frontals, and aparietal, ofagiant Pleistocene relationshipsofthelizardfamilies'.(StanfordUniver- varanidatKingCreek,eastern DarlingDowns.Thematerial sityPress: Stanford). wasassignedtoMegalaniaprisca,theonly varanidofcom- MOLNAR, R.E. 1990. New cranial elements of a giant parable size. This identification is probably correct since varanidfromQueensland. MemoirsoftheQueensland undoubtedremainsofMegalaniaoccurinthesamedeposits. Museum29:437-444. Molnar(1990) noted that the frontals and parietal ofthe PIANKA,E.R. 1995. Evolutionofbodysize: varanidlizards KingCreekvaranidexhibitedmany unusual features, which asamodelsystem. AmericanNaturalist 146: 398-414. couldnotbefoundinanyvaranidskullsexamined,andwere PREGILL,G.,GAUTHER,J.&GREENE, H.W. 1986.The thus presumably derived within varanids. Among these fea- evolutionofhelodermatidsquamates,withdescription turesweretheprominentsagittalcrestalongthemediansuture ofanewtaxonandanoverviewofVaranoidea.Trans- betweenthefrontals,andtheparalleltransverseridgesextend- actionsoftheSanDiegoSocietyofNaturalHistory21 ing at right angles to this crest. Both these features are also 167-202. found in Varanusgiganteus(Fig. 1) and are absent in other RIEPPEL,O. 1980.Thephylogenyofanguinomorphlizards. speciesofVaranus(Molnar, 1990)andinthenearestoutgroup Denkschrifte Schweizerbartsche Naturf. Gesellshaft taxa, Latuhanotttsand Heloderma(Rieppel, 1980; Pregill et 94: 1-86. al., 1986; Estes et al., 1988). They are thus derived within M.S.Y. Lee, SchoolofBiologicalSciences, UniversityofSyd- V«ra/?M^suggestingaffinitiesbetweentheKingCreekvaranid ney,NSW2006,Australia; 10December1995. andV.giganteus.Molnar(1990)notedthat,intheKingCreek varanid as in V. giganteus (Fig.l), the sagittal crest and parallel transverse ridges were confined to the frontals, and didnotextendontotheparietals.Thisphylogeny isbasedon veryincompletematerialandonlytwocharacters. Megalaniaprisca, Varanusgiganteus, V. salvadoriand V. komodoensisarethe4largestknown varanids(Pianka, 1995). DespitethelattertwonotbeingAustraliannatives,all4belong to a discrete radiation of Australian monitors, the 'gouldii speciesgroup' (Baverstocketal.,1993). If Megalaniaprisca has affinities with V. giganteus and thus belongs within the gouldiispeciesgroupMegalaniawillhavetobesynonymised with Varanus. Relationships within thegouldii species group arenotyetwellestablished(Baverstocketal. 1993).:thereisa distinctpossibilitythat,whenrelationshipswithinthisradiation are resolved, V. giganteus, V. salvadori, V, komodoensis, and Megalaniapriscawillformaclade.Ifso,thiswouldmeanthat the four largest varanid species represent a single discrete radiationofgiantpredatory lizards. IthanktheAustralianResearchCouncilforfunding,Jenny ClackandRaySymondsforloanofthefiguredspecimen,and MalcomRickettsforphotography. LiteratureCited BAVERSTOCK, P.R., KING, D., KING, M., BIRRELL,J. &KRIEG,M. 1993.Theevolutionofthespeciesofthe Varanidae: Microcomplement fixation analysis of serum albumins. Australian Journal of Zoology 41: 621-638. A B FIG. I.SkullofVaranusgiganteus(UniversityMuseumofZoology,CambridgeR9586)in(A)dorsal,and(B)rightlaterodorsal view,showingthesagittalcrestanddermal sculptureonthefrontalsbetweentheorbits. Scalebar=3cm.