Hydraulic redistribution of water from Pinus ponderosa trees to seedlings: evidence for an ectomycorrhizal pathway

While there is strong evidence for hydraulic redistribution (HR) of soil water by trees, it is not known if common mycorrhizal networks (CMN) can facilitate HR from mature trees to seedlings under field conditions. Ponderosa pine (Pinus ponderosa) seedlings were planted into root-excluding 61-microm mesh barrier chambers buried in an old-growth pine forest. After 2 yr, several mature trees were cut and water enriched in D(2)O and acid fuchsin dye was applied to the stumps. Fine roots and mycorrhizal root tips of source trees became heavily dyed, indicating reverse sap flow in root xylem transported water from stems throughout root systems to the root hyphal mantle that interfaces with CMN. Within 3 d, D(2)O was found in mesh-chamber seedling foliage > 1 m from source trees; after 3 wk, eight of 10 mesh-chamber seedling stem samples were significantly enriched above background levels. Average mesh-chamber enrichment was 1.8 x greater than that for two seedlings for which the connections to CMN were broken by trenching before D(2)O application. Even small amounts of water provided to mycorrhizas by HR may maintain hyphal viability and facilitate nutrient uptake under drying conditions, which may provide an advantage to seedlings hydraulically linked by CMN to large trees.     

Elevated atmospheric CO2 and soil N fertility effects on growth,mycorrhizal colonization,and xylem water potential of juvenile ponderosa pine in a field soil

Interactive effects of atmospheric CO₂ enrichment and soil N fertility on above- and below-ground development and water relations of juvenile ponderosa pine (Pinus ponderosa Dougl. ex Laws.) were examined. Open-top field chambers permitted creation of atmospheres with 700 µL L^-1, 525 µL L^-1, or ambient CO₂ concentrations. Seedlings were reared from seed in field soil with a total N concentration of approximately 900 µg g^-1 or in soil amended with sufficient (NH₄)₂SO₄ to increase total N by 100 µg g^-1 or 200 µg g^-1. The 525 µL L^-1 CO₂ treatment within the intermediate N treatment was excluded from the study. Following each of three consecutive growing seasons, whole seedlings of each combination of CO₂ and N treatment were harvested to permit assessment of shoot and root growth and ectomycorrhizal colonization. In the second and third growing seasons, drought cycles were imposed by withholding irrigation during which predawn and midday xylem water potential and soil water potential were measured. The first harvest revealed that shoot weight and coarse and fine root weights were increased by growth in elevated CO₂. Shoot and root volume and weights were increased by CO₂ enrichment at the second harvest, but growth stimulation by the 525 µL L^-1 CO₂ concentration exceeded that in 700 µL L^-1 CO₂ during the first two growing seasons. At the third harvest, above- and below-ground growth increases were largely confined to the 700 µL L^-1 CO₂ treatment, an effect accentuated by high soil N but evident in all N treatments. Ectomycorrhizal formation was reduced by elevated CO₂ after one growing season, but thereafter was not significantly affected by CO₂ and was unaffected by soil N throughout the study. Results of the xylem water potential measurements were variable, as water potentials in seedlings grown in elevated CO₂ were intermittently higher on some measurement days but lower on others than that of seedlings grown in the ambient atmosphere. These results suggest that elevated CO₂ exerts stimulatory effects on shoot and root growth of juvenile ponderosa pine under field conditions which are somewhat dependent on N availability, but that temporal variation may periodically result in a greater response to a moderate rise in atmospheric CO₂ than to a doubling of the current ambient concentration.     

Cut-shoot vs root rehydration: Effects on pressure-volume analysis of shoots and fascicles of Pinus resinosa seedlings

Two methods of rehydrating red pine ( Pinus resinosa Ait.) shoots for pressure-volume (PV) analysis were compared to clarify the effects of rehydration on estimated tissue water relations of shoots and fascicles. The commonly employed cut-shoot method was compared to rehydration by means of water uptake through the roots of intact plants. Cut-shoot rehydration and increased duration of rehydration significantly decreased estimates of tissue elasticity and relative water content at zero turgor for both shoots and fascicles. Rehydration of cut shoots for 2 days significantly increased the slope of the linear region of shoot pressure-volume (PV) curves and decreased estimates of the apoplastic water fraction. Changes in these and estimates of other water relations attributes were correlated with increased initial water content during rehydration. Estimated apoplastic water fraction was higher for needle fascicles than shoots despite the large amount of woody stem tissue contained in shoots. Fascicle water status strongly influenced shoot water relations, in part due to apparent apoplastic loading with water of fascicles during rehydration.     

Relationship between growth rates and xylem hydraulic characteristics in young, mature and old-growth ponderosa pine trees

The first objective of the present study was to quantify the effects of tree age and stem position on specific conductivity (k_s), vulnerability to embolism and water storage capacity (capacitance) in trunks of young, mature and old‐growth ponderosa pine. The second objective was to determine relationships between hydraulic characteristics and radial and height growth rates to increase the understanding of possible tradeoffs. Within sapwood at all heights and in all ages of trees, outer sapwood had 25–60% higher k_s than inner sapwood. The water potential at which embolism started (air entry point) was 1.3 MPa lower in inner sapwood than outer sapwood within the mature trees, but there was no difference in the other trees. There was no significant difference in capacitances between the tops of the old growth trees, the mature trees and the young trees. Taking all data together, the capacitances increased sharply with an increase in k_s and an increase in vulnerability to embolism. The hydraulic characteristics of the three age classes were correlated with the height growth rate but not with the diameter growth rate. Within these age classes, high k_s was associated with the slowest yearly increase in sapwood area and with a low percentage of latewood, whereas high vulnerability to embolism and high capacitance were more closely associated with high height growth rates.     

Effects of water stress on growth, osmotic potential and abscisic acid content of maize roots

Under water stress conditions, induced by mannitol solutions (0 to 0.66 M ) applied to the apical 12 mm of intact roots of Zea mays L. (cv. LG 11), a growth inhibition, a decrease in the osmotic potential of the cell sap and a significant accumulation of abscisic acid (ABA) were observed. When the roots were placed in a humid atmosphere after the stress, the growth rate increased again, even if elongation had been totally inhibited. Under a stress corresponding to an osmotic potential of -1.09 MPa in the solution, growth was totally inhibited, which means that the root cell turgor pressure was reduced to the yield threshold. These conditions led to the largest accumulation of ABA. The effect of water stress on the level of ABA was studied for three parts of the root. The greatest increase in ABA (about 10 fold) was obtained in the growth zone and this increase was apparently independent of the hydrolysis of the conjugated form. With a mannitol treatment of 1 h equivalent to a stress level of -1.39 MPa, a 4-fold increase in ABA efflux into the medium was obtained. These results suggest that there are interactions between water stress, root growth, osmotic potential and the ABA level. The growth under conditions of stress and the role of endogenous ABA in the control of plant metabolism, specially in the growth zone, are discussed.     

Effects of nitrogen nutrition and root medium water potential on growth, nitrogen uptake and osmotic adjustment of rice

The effects of nitrogen (N) nutrition on growth, N uptake and leaf osmotic potential of rice plants (Oryza sativa L. ev. IR 36) during simulated water stress were determined. Twenty-one-day-old seedlings in high (28.6 × 10 ^?4M) and low (7.14 × 10 ⁴M) N levels were exposed to decreased nutrient solution water potentials by addition of polyethylene glycol 6000. The roots were separated from the solution by a semi-permeable membrane. Nutrient solution water potential was ?0.6 × 10⁵ Pa and was lowered stepwise to ?1 × 10⁵, ?2 × 10⁵, ?4 × 10⁵ and ?6 × 10⁵ Pa at 2-day intervals. Plant height, leaf area and shoot dry weight of high and low nitrogen plants were reduced by lower osmotic potentials of the root medium. Osmotic stress caused greater shoot growth reduction in high N than in low N plants. Stressed and unstressed plants in 7.14 × 10⁴M N had more root dry matter than the corresponding plants in 28.6 × 10⁴M N. Dawn leaf water potential of stressed plants was 1 × 10⁵ to 5.5 × 10⁵ Pa lower than nutrient solution water potential. Nitrogen-deficient water-stressed plants, however, maintained higher dawn leaf water potential than high nitrogen water-stressed plants. It is suggested that this was due to higher root-to-shoot ratios of N deficient plants. The osmotic potentials of leaves at full turgor for control plants were about 1.3 × 10⁵ Pa higher in 7.14 × 10^?4M than in 28.6 × 10^?4M N and osmotic adjustment of 2.6 × 10⁵ and 4.3 × 10⁵ Pa was obtained in low and high N plants, respectively. The nitrogen status of plants, therefore, affected the ability of the rice plant to adjust osmotically during water stress. Plant water stress decreased transpiration and total N content in shoots of both N treatments. Reduced shoot growth as a result of water stress caused the decrease in amount of water transpired. Transpiration and N uptake were significantly correlated. Our results show that nitrogen content is reduced in water-stressed plants by the integrated effects of plant water stress per se on accumulation of dry matter and transpiring leaf area as well as the often cited changes in soil physical properties of a drying root medium.     

Water storage and osmotic pressure influences on the water relations of a dicotyledonous desert succulent

Abstract Water storage and nocturnal increases in osmotic pressure affect the water relations of the desert succulent Ferocactus acanthodes, which was studied using an electrical circuit analog based on the anatomy and morphology of a representative individual. Transpiration rates and osmotic pressures over a 24-h period were used as input variables. The model predicted water potential, turgor pressure and water flow for various tissues. Plant capacitances, storage resistances and nocturnal increases in osmotic pressure were varied to determine their role in the water relations of this dicotyledonous succulent. Water coming from storage tissues contributed about one-third of the water transpired at night: the majority of this water came from the nonphotosynthetic, water storage parenchyma of the stem. Time lags of 4 h were predicted between maximum transpiration and maximum water uptake from the soil. Varying the capacitance of the plant caused proportional changes in osmotically driven water movement but changes in storage resistance had only minor effects. Turgor pressure in the chlorenchyma depended on osmotic pressure, but was fairly insensitive to doubling or halving of the capacitance or storage resistance of the plant. Water uptake from the soil was only slightly affected by osmotic pressure changes in the chlorenchyma. For this stem succulent, the movement of water from the chlorenchyma to the xylem and the internal redistribution of water among stem tissues were dominated by nocturnal changes in chlorenchyma osmotic pressure, not by transpiration.     

Hydraulic redistribution of soil water in two old-growth coniferous forests: quantifying patterns and controls

Although hydraulic redistribution of soil water (HR) by roots is a widespread phenomenon, the processes governing spatial and temporal patterns of HR are not well understood. We incorporated soil/plant biophysical properties into a simple model based on Darcy's law to predict seasonal trajectories of HR. We investigated the spatial and temporal variability of HR across multiple years in two old-growth coniferous forest ecosystems with contrasting species and moisture regimes by measurement of soil water content (theta) and water potential (Psi) throughout the upper soil profile, root distribution and conductivity, and relevant climate variables. Large HR variability within sites (0-0.5 mm d(-1)) was attributed to spatial patterns of roots, soil moisture and depletion. HR accounted for 3-9% of estimated total site water depletion seasonally, peaking at 0.16 mm d(-1) (ponderosa pine; Pinus ponderosa) or 0.30 mm d(-1) (Douglas-fir; Pseudotsuga menziesii), then declining as modeled pathway conductance dropped with increasing root cavitation. While HR can vary tremendously within a site, among years and among ecosystems, this variability can be explained by natural variability in Psi gradients and seasonal courses of root conductivity.     

Relationship between transpiration and water potential in grafted scions of Picea

Total water and osmotic potential, turgor pressure and transpiration rate were measured on scions of Picea pungens (Englemann) during union development. In controlled environments, declines in water potential were correlated with lower transpiration rates to about −2.0 MPa. Water potentials below −2.0 MPa resulted in graft failure and were associated with sharply increased transpiration rates. Bulk turgor pressures remained high in the needles during this period of declining water potential and increasing transpiration. Transpiration rates of successful and unsuccessful greenhouse grafts were not significantly different during union development. Transpiration rates of these grafts were highest around dawn, then declined throughout the day only to increase again after sunset. High bulk needle turgor values (1.3 MPa), maintained by osmotic adjustment, may prevent stomatal closure of Picea scions at water potentials below −2.0 MPa.     

Effect of temperature,hydrogen ion concentration and osmotic potential on zoospore production by threePythium species isolated from pond water

Pythium fluminum produced zoospores most abundantly at 15°C, whereas the optima forPythium group F andP. marsipium were 20 and 25°C, respectively. Increasing the incubation temperature above the optimum resulted in the decrease of the duration of zoospore production. InPythium group F the ability to produce zoospores was not lost even after incubation at 40°C for 24 h. On the other hand,P. marsipium andP. fluminum lost the ability under these conditions. Zoospore production was inhibited at pH 4.5 and 10.5 in all the species tested.Pythium fluminum andP. marsipium were found to have two pH optima for zoospore production (7.5 and 9.5 for the former and 5.5 and 8.5 for the latter). The optimum pH for zoospore production byPythium group F was 6.5–7.5. Moderate osmotic potentials (–0.27–0.47 MPa) appeared to favor zoospore production by the pythia tested. The effect of temperature, pH and osmotic potential on zoospore production was discussed in relation to pollution of pond water.     

Gradients and dynamics of inner bark and needle osmotic potentials in Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies L. Karst)

Preconditions of phloem transport in conifers are relatively unknown. We studied the variation of needle and inner bark axial osmotic gradients and xylem water potential in Scots pine and Norway spruce by measuring needle and inner bark osmolality in saplings and mature trees over several periods within a growing season. The needle and inner bark osmolality was strongly related to xylem water potential in all studied trees. Sugar concentrations were measured in Scots pine, and they had similar dynamics to inner bark osmolality. The sucrose quantity remained fairly constant over time and position, whereas the other sugars exhibited a larger change with time and position. A small osmotic gradient existed from branch to stem base under pre‐dawn conditions, and the osmotic gradient between upper stem and stem base was close to zero. The turgor in branches was significantly driven by xylem water potential, and the turgor loss point in branches was relatively close to daily minimum needle water potentials typically reported for Scots pine. Our results imply that xylem water potential considerably impacts the turgor pressure gradient driving phloem transport and that gravitation has a relatively large role in phloem transport in the stems of mature Scots pine trees.     

Effect of temperature,hydrogen ion concentration and osmotic potential on oospore germination of fivePythium spp. isolated from pond water

Oospore germination occurred over a temperature ranging of 15–35°C forPythium coloratum, 10–35°C forP. diclinum, 15–30°C forP. dissotocum, 7–30°C forP. monospermum, and 10–30°C forP. pleroticum. Optimum temperature was 25°C for all species tested. In case of pH, oospore germination occurred over a range of 4.76–8.55 with an optimum of 6.40–7.40. The least germination occurred at pH 4.76 forP. coloratum, P. diclinum, P. monospermum andP. pleroticum, whileP. dissotocum germinated from pH 5.02. Oospores of the all tested pythia were able to germinate at –0.13 to –1.65 MPa and could not germinate at –3.40 MPa, with the highest germination rate at –0.27 to –0.47 MPa. The effect of temperature, pH and osmotic potential on oospore germination was discussed in relation to pollution of pond water.     

Water flow and water storage in Agave deserti: osmotic implications of crassulacean acid metabolism

Abstract Water flow and water storage were investigated for Agave deserti, a desert succulent showing crassulacean acid metabolism (CAM). The anatomy and water relations of the peripheral chlorenchyma, where CAM occurs, and the central water-storage parenchyma were investigated for its massive leaves so that these tissues could be incorporated as discrete elements into an electrical-circuit analogue of the whole plant. The daily cycling of osmotic pressure was represented by voltage sources in series with the storage capacitors. With soil water potential and leaf transpiration rate as input variables, axial water flow through the vascular bundles and radial flows into and out of storage during the day/night cycle were determined. The predominantly nocturnal transpiration was coincident with increases in cell osmotic pressure and in titratable acid of the leaf chlorenchyma. In the outer layers of the chlorenchyma, water potential was most negative at the beginning of the night when transpiration was maximum, while the water-storage parenchyma reached its minimal water potential 9 h later. The roots plus stem contributed 7% and the leaves contributed 50% to the total water flow during maximal transpiration; peak water flow from the soil to the roots occurred at dawn and was only 58% of the maximal transpiration rate. Over each 24-h period, 39% of the water lost from the plant was derived from storage, with flow into storage occurring mainly during the daytime. Simulations showed that the acid accumulation rhythm of CAM had little impact on water uptake from the soil under the conditions employed. In the outer chlorenchyma, water potential and water flows were more sensitive to the day/night changes in transpiration than in osmotic pressure. Nevertheless, cell osmotic pressure had a large influence on turgor pressure in this tissue and determined the extent to which storage was recharged during the latter part of the night.     

Extraction and analysis of sap from individual wheat leaf cells: the effect of sampling speed on the osmotic pressure of extracted sap

Abstract. A modification to the pressure probe is described which allows very rapid extraction of sap samples from single higher plant cells. The performance of this rapid-sampling probe was assessed and compared with the unmodified probe for cells of both wheat and Tradescantia. Under some conditions, the unmodified probe operated too slowly to avoid dilution of cell sap during the extraction process. This led to values for apparent sample osmotic pressures that were below the turgor pressures for the same cells. The problem was particularly acute in young wheatleaf epidermal cells which are small, elongate and have high turgor pressure. These exhibited rapid water influx when their turgor was depressed during the sampling of their contents (half-time for pressure recovery in wheat cells was less than 1 s while in Tradescantia cells it was 3–5 s). Dilution during sampling was apparently negligible when the rapid sampling probe was used. The study was complemented by a simple model of the way cells dilute during sampling. Quantitative predictions of the model were consistent with our observed findings. The model is used to assess the major factors which determine a cell's susceptibility to dilution during sampling.     

Maize stomatal conductance in the field: its relationship with soil and plant water potentials, mechanical constraints and ABA concentration in the xylem sap

Abstract. Stomatal conductance, leaf water potential, soil water potential and concentration of abscisic acid (ABA) in the xylem sap were measured on maize plants growing in the field, in two treatments with contrasting soil structures. Soil compaction affected the stomatal conductance, but this effect was no longer observed if the soil water potential was increased by irrigation. Differences in leaf water potential did not account for the differences in conductance between treatments. Conversely, the relationship between stomatal conductance and concentration of ABA in the xylem sap was consistent during the experiment. The proposed interpretation is that stomatal conductance was controlled by the root water potential via an ABA message. Control of the stomatal conductance by the leaf water potential or by an effect of mechanical stress on the roots is unlikely.     

Influence of nutrient versus water supply on hydraulic architecture and water balance in Pinus taeda

We investigated the hydraulic consequences of a major decrease in root‐to‐leaf area ratio (A_R:A_L) caused by nutrient amendments to 15‐year‐old Pinus taeda L. stands on sandy soil. In theory, such a reduction in A_R:A_L should compromise the trees’ ability to extract water from drying sand. Under equally high soil moisture, canopy stomatal conductance (G_S) of fertilized trees (F) was 50% that of irrigated/fertilized trees (IF), irrigated trees (I), and untreated control trees (C). As predicted from theory, F trees also decreased their stomatal sensitivity to vapour pressure deficit by 50%. The lower G_S in F was associated with 50% reduction in leaf‐specific hydraulic conductance (K_L) compared with other treatments. The lower K_L in F was in turn a result of a higher leaf area per sapwood area and a lower specific conductivity (conducting efficiency) of the plant and its root xylem. The root xylem of F trees was also 50% more resistant to cavitation than the other treatments. A transport model predicted that the lower A_R:A_L in IF trees resulted in a considerably restricted ability to extract water during drought. However, this deficiency was not exposed because irrigation minimized drought. In contrast, the lower A_R:A_L in F trees caused only a limited restriction in water extraction during drought owing to the more cavitation resistant root xylem in this treatment. In both fertilized treatments, approximate safety margins from predicted hydraulic failure were minimal suggesting increased vulnerability to drought‐induced dieback compared with non‐fertilized trees. However, IF trees are likely to be so affected even under a mild drought if irrigation is withheld.     

Stomatal control by fed or endogenous xylem ABA in sunflower: interpretation of correlations between leaf water potential and stomatal conductance in anisohydric species

The stomatal conductance of several anisohydric plant species, including field-grown sunflower, frequently correlates with leaf water potential (φ₁), suggesting that chemical messages travelling from roots to shoots may not play an important role in stomatal control. We have performed a series of experiments in which evaporative demand, soil water status and ABA origin (endogenous or artificial) were varied in order to analyse stomatal control. Sunflower plants were subjected to a range of soil water potentials under contrasting air vapour pressure deficits (VPD, from 0.5 to 2.5 kPa) in the field, in the glasshouse or in a humid chamber. Sunflower plants were also fed through the xylem with varying concentrations of artificial ABA, in the glasshouse and in the field. Finally, detached leaves were fed directly with varying concentrations of ABA under three contrasting VPDs. A unique relationship between stomatal conductance (g_s) and the concentration of ABA in the xylem sap (xylem [ABA]) was observed in all cases. In contrast, the relationship between φ₁ and g_s varied substantially among experiments. Its slope was positive for droughted plants and negative for ABA-fed whole plants or detached leaves, and also varied appreciably with air VPD. All observed relationships could be modelled on the basis of the assumption that φ₁ had no controlling effect on g_s. We conclude that stomatal control depended only on the concentration of ABA in the xylem sap, and that φ₁ was controlled by water flux through the plant (itself controlled by stomatal conductance). The possibility is also raised that differences in stomatal ‘strategy’ between isohydric plants (such as maize, where daytime φ₁ does not vary appreciably with soil water status) and anisohydric plants (such as sunflower) may be accounted for by the degree of influence of φ₁ on stomatal control, for a given level of xylem [ABA]. We propose that statistical relationships between φ₁ and g_s are only observed when φ₁ has no controlling action on stomatal behaviour.     

The relationship between stomatal conductance, transpiration rate and tracheid structure in Pinus radiata clones grown at different water vapour saturation deficits

Abstract. Stomatal conductance and needle water potential of P. radiata clones were measured after 2, 5 and 8 months on plants grown in controlled environment rooms with markedly different water vapour saturation deficits (D). Conductance was significantly lower at high D, but water potential differences between treatments were not significant. When trees were moved between treatments most of the changes in conductances occurred within 2 h, with residual changes after 24 h. Water potentials were not different 24 h after the trees were moved. The effects were completely reversible.
Transpiration rates of individual trees were highest in the high D treatment and lowest in the low D treatment. They were not linearly related to D because of decreasing conductance with increasing D.
Height growth, diameter growth and foliage areas were not significantly different between treatments. Tracheid lumen diameters tended to be larger in trees grown at higher D although treatment differences were not significant.
There were significant clonal differences in shoot conductance and tracheid dimensions.     

The effects of salinity and osmotic stress on barley germination rate: sodium as an osmotic regulator

Background and Aims

Seed germination is negatively affected by salinity, which is thought to be due to both osmotic and ion-toxicity effects. We hypothesize that salt is absorbed by seeds, allowing them to generate additional osmotic potential, and to germinate in conditions under which they would otherwise not be able to germinate.

Methods

Seeds of barley, Hordeum vulgare, were germinated in the presence of either pure water or one of five iso-osmotic solutions of polyethylene-glycol (PEG) or NaCl at 5, 12, 20 or 27 °C. Germination time courses were recorded and germination indices were calculated. Dry mass, water content and sodium concentration of germinating and non-germinating seeds in the NaCl treatments at 12 °C were measured. Fifty supplemental seeds were used to evaluate the changes in seed properties with time.

Key Results

Seeds incubated in saline conditions were able to germinate at lower osmotic potentials than those incubated in iso-osmotic PEG solutions and generally germinated faster. A positive correlation existed between external salinity and seed salt content in the saline-incubated seeds. Water content and sodium concentration increased with time for seeds incubated in NaCl. At higher temperatures, germination percentage and dry mass decreased whereas germination index and sodium concentration increased.

Conclusions

The results suggest that barley seeds can take up sodium, allowing them to generate additional osmotic potential, absorb more water and germinate more rapidly in environments of lower water potential. This may have ecological implications, allowing halophytic species and varieties to out-compete glycophytes in saline soils.     

Leaf hygrometer v. pressure chamber: a comparison of pressure–volume curve data obtained on single leaves by alternating measurements

Abstract. Data for the construction of pressure-volume curves were obtained by measuring water potentials of detached leaves repeatedly and alternately, with a pressure chamber and a leaf hygrometer. Good agreement between the parameters of the two resulting curves was observed. Regression lines on values after the loss of turgor were always more negative for the thermocouple data, with a maximum difference for the osmotic potential at full saturation of 0.25 MPa in Triticum and a minimum of 0.01 MPa in Populus. Neither the slopes of the regression lines nor the intercepts with the axes were statistically different. We see no reason for using one of these two unrelated methods as a standard against which the other is calibrated. Implications for the theory of pressure-volume curves are discussed.