Microscopy Research and Technique. Vol. 25, (5 & 6) 1993, pp. 374-383
Copyright © 1993 Wiley-Liss, Inc.
Reproduced with permission of John Wiley & Sons, Inc.
Microscopy Research and Technique
http://www.interscience.wiley.com/jpages/1059-910X/
Albumen, Art Conservation, Water, Relative Humidity, Cracking
The preservation of nineteenth-century albumen prints is of great concern to collection managers and to conservators of photographic materials. In the field of art conservation, preservation techniques incorporating aqueous treatments are often used to enhance the long and short-term stability of historical artifacts or art objects. In a study of the interaction of water with albumen photographs, experiments were carried out in the ESEM to follow the real time effects of water on the prints. The experiments were designed to observe the effects of a range of relative humidities and liquid water on samples of expendable historic albumen prints, utilizing the advantages of imaging in the presence of water vapor. All albumen photographs exhibit a fine network of cracks in the albumen protein layer. Average crack width is approximately 10 ?m. As observed in the ESEM, a 4.25-fold increase in the width of a single crack (at 50% RH), viewed normal to the surface, resulted from a single controlled excursion to high relative humidity and immersion. In an extraordinary series of images, a print viewed in cross-section exhibited a 22% swelling and shrinkage in thickness, and a 5% and 9% swelling and shrinkage along the width of a fragment of the albumen/image layer when the sample was immersed in water and dried. The visual information gained through the use of the ESEM helped to focus a materials investigation and served as a foundation for a study which shows that aqueous treatment causes increased cracking of both unsupported albumen and the albumen/image layer in prints.
Albumen photographs were the dominant photographic printing method in the latter half of the nineteenth century. Introduced by Louis-Desire Blanquart-Evrard in the year 1850 in France, albumen photographic prints became immensely popular. This was in part due to superb resolution of detail, long tonal range, and high contrast of the albumen print which was crucial for achieving optimum results with collodion wet-plate negatives. Prior to albumen prints, printing papers were limited to low contrast salted paper or early forms of albumen printing paper which had low sensitivity.
Most collections of nineteenth-century photographs in museums, anthropological archives, etc., are predominately composed of albumen photographs. Albumen prints were produced worldwide. In the United States the photographic legacies of the Civil War, the exploration of the West, and anthropological investigations of native peoples represent only a fraction of the artistic and historic achievement documented on albumen paper.
Albumen prints are made by floating a lightweight piece of uniform rag (linen and/or cotton) writing paper over a solution of hens egg white (albumen) and salt. The albumen-coated paper is then hung from a corner and dried. This initial wetting/drying process is the first of many such cycles in the fabrication of albumen photographs. Once dry, the sheet is often recoated with albumen to achieve additional gloss. After the final coating of albumen is dry, the sheet is floated on an aqueous solution of silver nitrate and dried again. The silver nitrate and the salt react to form light-sensitive silver chloride in the albumen binder layer. The paper can then be exposed to light in direct contact with the negative. Light energy converts the silver halide to metallic silver. The resulting "printed-out" silver-based image is fixed with an aqueous solution of sodium thiosulphate and gold-toned. The print is then washed extensively in clean water and dried. As a final step, albumen prints are often rewet and mounted to a heavy weight paperboard using heat and high pressure.
Figure 1 shows SEM micrographs of historic albumen photographs. Figure 1a is a normal to the surface view of the print while Figure 1b views the print in cross-section. All albumen prints, having been wet and dried several times, exhibit similar cracks in the albumen/image layer revealed by these SEM micrographs.
Because of their predominance and importance, proper storage, display, and treatment of albumen prints are matters of concern in the field of photographic conservation. In particular, aqueous treatment methods have come under scrutiny (Swan, 1981; Messier and Vitale, 1993). The common reasons for water-base treatment are that 1) aqueous surface cleaning is a quick and effective means for removing dirt and accretions which collect over time, 2) aqueous immersion is often a reliable method for removing an albumen photograph from a damaged or acidic mount which may be contributing to image degradation, and 3) the washing of albumen prints may reduce the presence of yellow degradation products in the albumen/image layer and in the paper support. The former two points are undeniable conservation goals since the long-term preservation of the photograph is enhanced. However, attempts at reducing yellowing are intended to restore the original appearance of albumen prints even though the yellowing may be caused by silver organo-metallic complexes that are inherent to the albumen medium.
Recent work (Messier and Vitale, 1994) shows that aqueous treatments increase the cracking of the albumen layer and have no effect in decreasing albumen yellowing. The most startling result is the magnitude of average crack width increase. Cracks increase 81% from an average of 10.8 µm to 19.5 µm A typical aqueous treatment also has the effect of reducing the gloss of albumen prints by 11.8%. Following these experiments a study of the fundamental mechanical and dimensional properties was undertaken (Vitale and Messier, 1994) to analyze and quantify the impact of water on albumen prints. Moisture sorption/dimensional response data indicate that unsupported albumen exhibits massive swelling and shrinkage: 17% between 15% and 85% RH.
Fig. 2. Effect or RH cycling on unsupported albumen.
Figure 2 shows large swelling and shrinkage and the effect of the one-time moisture relaxation on unsupported albumen. Mechanical stress-strain data show that the albumen is weak (tensile strength 62 psi) and can strain only 1.4% before failure. While the expansion and contraction of the albumen/image layer is restricted by the paper base, the continued active behavior of historic albumen prints (following a minimum of 2-3 previous cycles of wetting and drying) indicates that a substantial potential for cracking in artifacts still exists. Strain develops in the albumen/image layer as a result of the massive shrinkage of the albumen layer during the desorption phase of a relative humidity cycle. Failure results when the strain exceeds the 1.4% stretch capability because the tensile strength of the albumen is so low. The source of the expansion of preexisting cracks is therefore the release of the strain developed during desorption. The use of the environmental electron scanning microscope was a pivotal part of this study. It was possible to observe the effect of wetting and drying on the cracking of albumen prints rather than viewing coated and desiccated versions of the material provided by imaging in the SEM. Of primary importance, the data gained from these experiments provided empirical evidence of the crack width increase after exposure to water.
The examples of historic albumen prints required no special preparation. Samples used for the normal to the surface views were cut into small rectangles and adhered to the flat surfaces of metal mounts with standard high purity silver paint used for SEM preparation. The samples used for cross-section views were cut with a single firm stroke of a new #11 scalpel blade on a standard (3) handle.
The new blade helped insure a clean cut. The cross-section samples were then placed into a deeply grooved mount with a clamping face. The mount incorporated no adhesive and the mechanical clamping option was not used; the samples could expand, contract, and distort freely within the approximately 0.5 mm slot. The samples were cut from expendable nineteenth-century albumen prints from a private collection. The size of samples was approximately 32 mm.
The instrument used was an ElectroScan ESEM model 20 which uses a lanthanum boride electron source. Temperature adjustments, to the sample, were made with a Peltier effect thermal electric temperature control stage accessory that has the capability of varying sample temperature 20°C from ambient temperature. The environmental gas was vaporized distilled water supplied via a digitally controlled needle valve assembly contained in a sealed Erlenmeyer flask located outside the sample chamber. The most successful experiments were run at 5.9-6.1 kV. The experiments used the simple ElectroScan pole-piece environmental secondary detector which images secondary and backscattered electrons. Both temperature and vapor pressure had to be controlled separately and could not be linked. The assistance of a multi-pressure hygrometric chart (Keifer, 1945) was required to calculate specific relative humidities at pre-programmed temperatures. ElectroScan provided a table of saturation vapor pressures (Torr) from 100°C to -3°C. An abbreviated data table (Table 1) is included. Figure 3 shows 0-40 C and 0-15 Torr vapor pressure segments of a relative humidity isobar chart which is applicable to this study. The equation used for Figure 3 and the Appendix is taken from Linsley et al. (1975) and modified for vapor pressure in Torr (Pv) ±1% with temperature in celsius (T): Pv = 19.0516[(0.00738T + 0.8072)8 - 0.000019 1.8T + 48 ) + 0.001316].
Fig. 3. Relative humidity isobar chart.
Table 1. Temperature, vapor pressure and relative humidities for the experiments conducted.
Temp. (°C) | Vapor pressure (Torr) | RH (%) |
32 | 35.7 | 100 |
32 | 0.0 | 0 |
31 | 33.7 | 100 |
31 | 0.8 | 2.5 |
30 | 31.8 | 100 |
30 | 1.7 | 5 |
29 | 30.0 | 100 |
29 | 4.2 | 15 |
28 | 28.6 | 100 |
27 | 26.7 | 100 |
26 | 25.2 | 100 |
25 | 23.8 | 100 |
25 | 3.2 | 10 |
24 | 22.4 | 100 |
23 | 21.1 | 100 |
22 | 19.8 | 100 |
21 | 18.7 | 100 |
20 | 17.5 | 100 |
20 | 2.7 | 15 |
19 | 16.5 | 100 |
18 | 15.5 | 100 |
17 | 15.5 | 100 |
16 | 13.6 | 100 |
15 | 12.8 | 100 |
15 | 2.6 | 20 |
14 | 12.0 | 100 |
13 | 11.2 | 100 |
12.5 | 2.4 | 22.5 |
12 | 10.5 | 100 |
11 | 9.8 | 100 |
10 | 9.2 | 100 |
10 | 6.8 | 75 |
10 | 5.5 | 50 |
10 | 2.3 | 25 |
Each experiment was recorded start to finish using a standard VHS video tape recorder. Individual images were created with the Seikosha VP-1500 video printer, so that the process could be captured as it occurred. With the video printer, images were created extremely fast (5 seconds) and the 3.25" x 4.25" format matches the size of conventional Polaroid process print film. Image quality and resolution is acceptable (256 tone, 300 dpi horizontal and 150 dpi vertical), but cannot match the resolution and tonal scale of standard Polaroid Type 52 prints. However, even with an experienced operator, the Polaroid images are inadequate to record dynamic changes since the process of loading film, focusing, brightness adjusting, contrast adjusting, and exposure take a minimum of 30-120 seconds. The experiments were carried out at ElectroScan Corp.
The samples were placed into the sample chamber. The samples environment was brought to a moderately low relative humidity ( 20%). The relative humidity was then incrementally adjusted by temperature manipulations of the Peltier-effect stage. Pressure and temperature adjustments were made in the sample chamber using data in Table 1. The relative humidity was increased to just over dew point at the operating temperature, until sufficient water precipitated on the sample. Once immersion was achieved, sample stage temperature was increased so that the sample could be observed during drying. In uncontrolled experiments the temperature was raised a suitable amount. In controlled experiments, a temperature ramp was established and the corresponding vapor pressure was maintained as the temperature increased. This required full-time operator manipulation of the specimen chamber environment and the temperature of the specimen holder.
The surface-observation sample was brought to 19% RH, with vapor pressure 1.7 Torr at 10°C stage temperature. The sample was immersed by increasing the vapor pressure to 9.6 Torr at constant temperature (10°C). At approximately 25% RH (2.3 Torr), constant temperature was halted because image quality was deteriorating. Gradually increasing the temperature to 32°C while decreasing relative humidity allowed an increase in environmental gas (water vapor) which had the effect of somewhat enhancing image quality. The temperature was ramped up to 32°C while controlling the humidity down to 7.5% RH at 2.4 Torr following the vapor pressure ramp (or 32°C) established in Figure 3 and the Appendix The process was halted at 19% RH, 50% RH, 75% RH and 100% RH, at 10°C. During sorption, images were made using the thermal video printer which took approximately a half minute. On reversal of the process, the ramping down was halted at 75% RH, 50% RH, and 17.5% RH, at 10°C, and 7.5% RH at 32°C, and imaged in the same manner. To avoid electron beam damage, the ElectroScan computer-controlled, motor driven specimen stage functions were used to bring the site into the beam path for brief periods after the equilibration points were attained. Equilibration time at each point in the cycle was approximately 8-20 min. The entire experiment took 1 h and 39 min., with a minimum of beam time at the site. The magnification was kept constant at 1,000 x. The electron beam was kept at a constant 5.9 kV throughout the experiment.
The cross-section experiment was carried out in a similar manner. In this case, however, more attention was paid to capturing dynamic changes in real time. The experiment was begun with the sample chamber at 60% RH, 3.9 Torr at 5°C. The sample was quickly immersed by increasing the vapor pressure to 7.8 Torr at constant temperature. The sample was then dried by lowering the pressure and increasing the temperature. Two minutes following complete hydration the sample was brought to approximately 66% RH with the sample stage set at 5.7°C and the sample chamber set at 4.7 Torr. Eventually, the sample was dried in equilibrium with 14% RH, in the chamber, at 4.2 Torr and 29°C stage temperature. The experiment took 23 min. to complete. As with the previously described experiment, the magnification was kept constant at 1,000 x. The electron beam was kept at a 6.1 kV throughout the experiment.
The low-density organic samples used in these experiments were very susceptible to beam damage. Both the albumen/image layer and the paper base were readily deformed by the electron beam at 8-10 kV and above in the presence of liquid water. At lower vapor pressure the beam damage process seemed slower but was still evident. It was found that beam-damaged samples ceased having any dynamic properties and could not be made to react to changes in relative humidity. Such samples were readily recognizable by their mottled, melted plastic appearance. This problem was overcome by a great deal of trial and error and by substantially lowering electron acceleration (5.9-6.1 kV was used in successful experiments). Though the use of low accelerating voltage caused a noticeable fall off of image resolution, the resulting micrographs were adequate for the purposes of this study. Operator adjustment to yield high contrast images was found to be essential. High contrast images were the best source of visual information.
Another limitation was imprecise control of relative humidity. The chamber is at the vapor pressure prescribed by the operator, which can be from 0-100% RH in air. Water will condense on the components in the chamber if the dew point is raised above ambient temperature. The vacuum in the chamber is maintained at the pole-piece detector which is often within millimeters of the sample, if working distance is small. Directly surrounding the sample on the Peltier-effect stage, the controlled environment extends roughly 1mm above the sample cup. The sample environment is manipulated by the pressure within the sample chamber and the temperature of the sample stage. Although it is possible to calculate relative humidity using pressure and temperature data, there is no direct method of measuring the relative humidity at the sample itself. Therefore, there is no way of knowing precisely when the environment surrounding the sample has been conditioned to the desired relative humidity.
Lastly, a practical constraint for the use of the ESEM in controlled moisture sorption/desorption experiments is that sample conditioning times are necessarily short. When constructing sorption/desorption curves, holding a sample at a specific point of relative humidity for 24-72 h before data is collected is not uncommon. Though prolonged conditioning times are technically possible with the ESEM, they are not realistic. If the first experiment in this study was carried out with 24 h conditioning times, the instrument would have been in operation continuously for eight days.
TABLE 2. Increase and decrease in crack width with adsorption and desorption of water vapor
RH adsorption(%) | RH desorption(%) | Crack width(microns) |
19 | 1.1 | |
50 | 0.8 | |
75 | 0.3 | |
100 | 100 | 0.0 |
75 | 2.0 | |
50 | 4.2 | |
17.5 | 6.0 | |
7.5 | 7.4 |
Fig. 4. Crack width plotted against RH.
The results of the observations of the albumen surface clearly show the effects of relative humidity and immersion on crack width. Figure 4 shows measurements taken across a wide point on a line which is formed by the feature on the far right of the image, plotted against humidity. These points correspond to the micrographs in Figure 5 and data in Table 2. As can be seen, the crack width diminishes as the relative humidity increases. During the drying phase the crack width (and length) increases considerably. The increase in width from 50% RH during adsorption to 50% RH during desorption is nearly 3.4 mm, or a 4.25-fold increase from 0.8 µm.
Figure 6 shows the cross-section experiment. The increase in crack width is documented in real time as the albumen print is taken through a single absorption and desorption cycle. The sample is initially at 60% RH (Fig. 6a). There are two distinct cracks in the albumen/image layer. The cracks measure approximately 2-2.5 µm in width. The sample is then taken to 100% RH where the cracks are virtually closed. Figure 6c shows the sample immersed in water that has condensed on the electrically cooled stage. All but the largest pores in the paper are filled with water. In Figure 6d the sample begins the desorption cycle. Cracks begin to open and the albumen layer begins to curl upward. Note that the curl is away from the source of water--the still wet paper base. The crack increase and curl progress in Figure 6 e-h. At the lowest relative humidity (14% RH), when arcs are drawn (diameter corresponding to the point where the protein layer lifts from its previous position) and measurements made at the former uppermost point, the cracks have increased in width 4.75 µm and twofold from left to right. This series clearly shows the effect of the vigorous response of the albumen layer to water. The length of the center segment began at 76 µm; it swelled 5% (Fig. 6d) and than shrank to 91% (Fig. 6h) of its original length at 14% RH. It swelled in thickness 22% from 10.5 µm (Fig. 6d) and shrank approximately the same amount (Fig. 6h) in response to changes in moisture content. Another interesting result is that the morphology of the paper is more open after wetting than before (unbonding between the fibers has occurred).
The surface layer of albumen prints responds dramatically to water and water vapor. Both specimens (Figs. 5, 6) showed substantial increases in crack width. While results are different from the average 81% increase reported for 20 historic prints (Messier and Vitale, 1994), they are within the range of results reported, when the corresponding relative humidities are taken into consideration.
Curl in paper has been clearly described as the result of mismatch in swelling-induced differential strains of attached layers of material (Smith, 1950; Barkhau and Lobner, 1980; Green, 1983; Daniels and Fleming, 1988). The curl documented in Figure 6 is surely due to the upper layer shrinking more quickly than the layer in contact with the moist paper. Once the curl was formed, which released some of the strain of shrinkage, there was no energetic reason for it to be reversed. Thus, on drying to 15% RH the curl still exists. Curl as extensive as that documented here does not occur in all prints, but similar distortions have been observed (Messier, 1991). Shrinkage of unsupported photographic gelatin (another protein polymer) in a response to high relative humidity has been documented (Calhoun and Leister, 1959).
The use of the ESEM has many advantages over standard SEM. When these images are compared to the desiccated images seen in earlier work (Messier, 1991) the difference is arresting. The most obvious advantage, however, is that the sample can be viewed real time under controlled environmental conditions which approximate reality. The ESEM provided a powerful tool to illustrate the type and magnitude of change brought about by water. It helped to focus the materials science evaluation of materials and was used to support the conclusions of the study which showed that the weak albumen layer ruptures under the strain of its swelling and shrinkage in response to water and water vapor.
To our conservation colleagues who have routinely used water treatments, the experiments yielded irrefutable visual evidence that contact with water causes a dramatic response by the protein/image layer and increased crack width in albumen photographs. The video which shows the shrinkage of the albumen layer and cracking in progress is an excellent presentation tool which supports the conclusions.
RH (%) | 100 | 95 | 90 | 85 | 80 | 75 | 70 | 65 | 60 | 55 | 50 | 45 | 40 | 35 | 30 | 27.5 | 25 | 22.5 | 20 | 17.5 | 15 | 12.5 | 10 | 7.5 | 5 | 2.5 | 0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Temp(°C) | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr | Torr |
0 | 4.6 | 4.3 | 4.1 | 3.9 | 3.6 | 3.4 | 3.2 | 3.0 | 2.7 | 2.5 | 2.3 | 2.0 | 1.8 | 1.6 | 1.4 | 1.3 | 1.1 | 1.0 | 0.9 | 0.8 | 0.7 | 0.6 | 0.5 | 0.3 | 0.2 | 0.1 | 0.0 |
1 | 4.9 | 4.7 | 4.4 | 4.2 | 3.9 | 3.7 | 3.4 | 3.2 | 2.9 | 2.7 | 2.4 | 2.2 | 2.0 | 1.7 | 1.5 | 1.3 | 1.2 | 1.1 | 1.0 | 0.9 | 0.7 | 0.6 | 0.5 | 0.4 | 0.2 | 0.1 | 0.0 |
2 | 5.3 | 5.0 | 4.7 | 4.5 | 4.2 | 4.0 | 3.7 | 3.4 | 3.2 | 2.9 | 2.6 | 2.4 | 2.1 | 1.8 | 1.6 | 1.4 | 1.3 | 1.2 | 1.1 | 0.9 | 0.8 | 0.7 | 0.5 | 0.4 | 0.3 | 0.1 | 0.0 |
3 | 5.7 | 5.4 | 5.1 | 4.8 | 4.5 | 4.2 | 4.0 | 3.7 | 3.4 | 3.1 | 2.8 | 2.5 | 2.3 | 2.0 | 1.7 | 1.6 | 1.4 | 1.3 | 1.1 | 1.0 | 0.8 | 0.7 | 0.6 | 0.4 | 0.3 | 0.1 | 0.0 |
4 | 6.1 | 5.8 | 5.5 | 5.2 | 4.9 | 4.6 | 4.3 | 3.9 | 3.6 | 3.3 | 3.0 | 2.7 | 2.4 | 2.1 | 1.8 | 1.7 | 1.5 | 1.4 | 1.2 | 1.1 | 0.9 | 0.8 | 0.6 | 0.5 | 0.3 | 0.2 | 0.0 |
5 | 6.5 | 6.2 | 5.9 | 5.5 | 5.2 | 4.9 | 4.6 | 4.2 | 3.9 | 3.6 | 3.3 | 2.9 | 2.6 | 2.3 | 2.0 | 1.8 | 1.6 | 1.5 | 1.3 | 1.1 | 1.0 | 0.8 | 0.7 | 0.5 | 0.3 | 0.2 | 0.0 |
6 | 7.0 | 6.6 | 6.3 | 5.9 | 5.6 | 5.2 | 4.9 | 4.5 | 4.2 | 3.8 | 3.5 | 3.1 | 2.8 | 2.4 | 2.1 | 1.9 | 1.7 | 1.6 | 1.4 | 1.2 | 1.0 | 0.9 | 0.7 | 0.5 | 0.3 | 0.2 | 0.0 |
7 | 7.5 | 7.1 | 6.7 | 6.4 | 6.0 | 5.6 | 5.2 | 4.9 | 4.5 | 4.1 | 3.7 | 3.4 | 3.0 | 2.6 | 2.2 | 2.1 | 1.9 | 1.7 | 1.5 | 1.3 | 1.1 | 0.9 | 0.7 | 0.6 | 0.4 | 0.2 | 0.0 |
8 | 8.0 | 7.6 | 7.2 | 6.8 | 6.4 | 6.0 | 5.6 | 5.2 | 4.8 | 4.4 | 4.0 | 3.6 | 3.2 | 2.8 | 2.4 | 2.2 | 2.0 | 1.8 | 1.6 | 1.4 | 1,2 | 1,0 | 0.8 | 0.6 | 0.4 | 0.2 | 0.0 |
9 | 8.6 | 8.2 | 7.7 | 7.3 | 6.9 | 6.4 | 6.0 | 5.6 | 5.2 | 4.7 | 4.3 | 3.9 | 3.4 | 3.0 | 2.6 | 2.4 | 2.1 | 1.9 | 1.7 | 1.5 | 1.3 | 1.1 | 0.9 | 0.6 | 0.4 | 0,2 | 0.0 |
10 | 9.2 | 8.7 | 8.3 | 7.8 | 7.3 | 6.9 | 6.4 | 6.0 | 5.5 | 5.1 | 4.6 | 4.1 | 3.7 | 3.2 | 2.8 | 2.5 | 2.3 | 2.1 | 1.8 | 1.6 | 1.4 | 1.1 | 0.9 | 0.7 | 0.5 | 0.2 | 0.0 |
11 | 9.8 | 9.3 | 8.8 | 8.3 | 7.9 | 7.4 | 6.9 | 6.4 | 5.9 | 5.4 | 4.9 | 4.4 | 3.9 | 3.4 | 2.9 | 2.7 | 2.5 | 2.2 | 2.0 | 1.7 | 1.5 | 1.2 | 1,0 | 0.7 | 0.5 | 0.2 | 0.0 |
12 | 10.5 | 10.0 | 9.4 | 8.9 | 8.4 | 7.9 | 7.3 | 6.8 | 6.3 | 5.8 | 5.2 | 4.7 | 4.2 | 3.7 | 3.1 | 2.9 | 2.6 | 2.4 | 21 | 1.8 | 1.6 | 1.3 | 1.0 | 0.8 | 0.5 | 0.3 | 0.0 |
13 | 11.2 | 10.6 | 10.1 | 9.5 | 9.0 | 8.4 | 7.8 | 7.3 | 6.7 | 6.2 | 5.6 | 5.0 | 4.5 | 3.9 | 3.4 | 3.1 | 2.8 | 2.5 | 2.2 | 2.0 | 1,7 | 1.4 | 1,1 | 0.8 | 0.6 | 0.3 | 0.0 |
14 | 12.0 | 11.4 | 10.8 | 10.2 | 9.6 | 6.0 | 8.4 | 7.8 | 7.2 | 6.6 | 6.0 | 5.4 | 4.8 | 4.2 | 3.6 | 3.3 | 3.0 | 2.7 | 2.4 | 2.1 | 1.8 | 1.5 | 1.2 | 0.9 | 0.6 | 0.3 | 0.0 |
15 | 12.8 | 12.1 | 11.5 | 10.8 | 10.2 | 9.6 | 8.9 | 8.3 | 7.7 | 7.0 | 6.4 | 5.7 | 5.1 | 4.5 | 3.8 | 3.5 | 3.2 | 2.9 | 2.6 | 2.2 | 1.9 | 1.6 | 1.3 | 1.0 | 0.6 | 0.3 | 0.0 |
16 | 13.6 | 12.9 | 12.2 | 11.6 | 10.9 | 10.2 | 9.5 | 8.8 | 8.2 | 7.5 | 6.8 | 6.1 | 5.4 | 4.8 | 4.1 | 3.7 | 3.4 | 3.1 | 2,7 | 2.4 | 2.0 | 1.7 | 1.4 | 1.0 | 0.7 | 0.3 | 0.0 |
17 | 14.5 | 13.8 | 13.1 | 12.3 | 11.6 | 10.9 | 10.2 | 9.4 | 8.7 | 8.0 | 7.3 | 6.5 | 5.8 | 5.1 | 4.4 | 4.0 | 3.6 | 3.3 | 2.9 | 2.5 | 2.2 | 1.8 | 1.5 | 1.1 | 0.7 | 0.4 | 0.0 |
18 | 15.4 | 14.7 | 13.9 | 13.1 | 12.4 | 11.6 | 10.8 | 10.0 | 9.3 | 8.5 | 7.7 | 7.0 | 6.2 | 5.4 | 4.6 | 4.2 | 3.9 | 3.5 | 3.1 | 2.7 | 2.3 | 1.9 | 1.5 | 1.2 | 0.8 | 0.4 | 0.0 |
19 | 16.4 | 15.6 | 14.8 | 14.0 | 13.2 | 12.3 | 11.5 | 10.7 | 9.9 | 9.0 | 8.2 | 7.4 | 6.6 | 5.8 | 4.9 | 4.5 | 4.1 | 3.7 | 3.3 | 2.9 | 2.5 | 2.1 | 1.6 | 1.2 | 0.8 | 0.4 | 0.0 |
20 | 17.5 | 16.6 | 15.8 | 14.9 | 14.0 | 13.1 | 12.3 | 11.4 | 10.5 | 9.6 | 8.8 | 7.9 | 7.0 | 6.1 | 5.3 | 4.8 | 4.4 | 3.9 | 3.5 | 3.1 | 2,6 | 2.2 | 1.8 | 1.3 | 0.9 | 0.4 | 0.0 |
21 | 18.6 | 17.7 | 16.8 | 15.8 | 14.9 | 14.0 | 13.0 | 12.1 | 11.2 | 10.2 | 9.3 | 8.4 | 7.4 | 6.5 | 5.6 | 5.1 | 4.7 | 4.2 | 3.7 | 3.3 | 2.8 | 2.3 | 1.9 | 1.4 | 0.9 | 0.5 | 0.0 |
22 | 19.8 | 18.8 | 17.8 | 16.8 | 15.8 | 14.8 | 13.9 | 12.9 | 11.9 | 10.9 | 9.9 | 8.9 | 7.9 | 6.9 | 5.9 | 5.4 | 4.9 | 4.5 | 4.0 | 3.5 | 3.0 | 2.5 | 2.0 | 1.5 | 1.0 | 0.5 | 0.0 |
23 | 21.0 | 20.0 | 18.9 | 17.9 | 16.8 | 15.8 | 14.7 | 13.7 | 12.6 | 11.6 | 10.5 | 9.5 | 8.4 | 7.4 | 6.3 | 5.8 | 5.3 | 4.7 | 4.2 | 3.7 | 3.2 | 2.6 | 2.1 | 1.6 | 1.1 | 0.5 | 0.0 |
24 | 22.3 | 21.2 | 20.1 | 19.0 | 17.9 | 16.8 | 15.6 | 14.5 | 13.4 | 12.3 | 11.2 | 10.1 | 8.9 | 7,8 | 6.7 | 6.1 | 5.6 | 5.0 | 4.5 | 3.9 | 3.4 | 2.8 | 2.2 | 1.7 | 1.1 | 0.6 | 0.0 |
25 | 23.7 | 22.5 | 21.3 | 20.2 | 19.0 | 17.8 | 16.6 | 15.4 | 14.2 | 13.0 | 11.9 | 10.7 | 9.5 | 8.3 | 7.1 | 6.5 | 5.9 | 5.3 | 4.7 | 4.2 | 3.6 | 3.0 | 2.4 | 1.8 | 1.2 | 0.6 | 0.0 |
26 | 25.2 | 23.9 | 22.7 | 21.4 | 20.1 | 18.9 | 17.6 | 16.4 | 15.1 | 13.8 | 12.6 | 11.3 | 10.1 | 8.8 | 7.6 | 6.9 | 6.3 | 5.7 | 5.0 | 4.4 | 3.8 | 3.1 | 2.5 | 1.9 | 1.3 | 0.6 | 0.0 |
27 | 26.7 | 25.4 | 24.0 | 22.7 | 21.4 | 20.0 | 18.7 | 17,4 | 16.0 | 14.7 | 13.3 | 12.0 | 10.7 | 9.3 | 8.0 | 7.3 | 6.7 | 6.0 | 5.3 | 4.7 | 4.0 | 3.3 | 2.7 | 2.0 | 1.3 | 0.7 | 0.0 |
28 | 28.3 | 26.9 | 25.5 | 24.1 | 22.6 | 21.2 | 19.8 | 18.4 | 17.0 | 15.6 | 14.2 | 12.7 | 11.3 | 9.9 | 8.5 | 7.8 | 7.1 | 6.4 | 5.7 | 5.0 | 4.2 | 3.5 | 2.8 | 2.1 | 1.4 | 0.7 | 0.0 |
29 | 30.0 | 28.5 | 27.0 | 25.5 | 24.0 | 22.5 | 21.0 | 19.5 | 18.0 | 16.5 | 15.0 | 13.5 | 12.0 | 10.5 | 9.0 | 8.2 | 7.5 | 6.7 | 6.0 | 5.2 | 4.5 | 3.7 | 3.0 | 2.2 | 1.5 | 0.7 | 0.0 |
30 | 31.8 | 30.2 | 28.6 | 27.0 | 25.4 | 23.8 | 22.2 | 20.7 | 19.1 | 17.5 | 15.9 | 14.3 | 12.7 | 11.1 | 9.5 | 8.7 | 7.9 | 7.2 | 6.4 | 5.6 | 4.8 | 4.0 | 3.2 | 2.4 | 1.6 | 0.8 | 0.0 |
31 | 33.7 | 32.0 | 30.3 | 28.6 | 26.9 | 25.2 | 23.6 | 21.9 | 20.2 | 18.5 | 16.8 | 15.1 | 13.5 | 11.8 | 10.1 | 9.3 | 8.4 | 7.6 | 6.7 | 5.9 | 5.0 | 4.2 | 3.4 | 2.5 | 1.7 | 0.8 | 0.0 |
32 | 35.6 | 33.8 | 32.1 | 30.3 | 28.5 | 26.7 | 24.9 | 23.2 | 21.4 | 19.6 | 17.8 | 16.0 | 14.2 | 12.5 | 10.7 | 9.8 | 8.9 | 8.0 | 7.1 | 6.2 | 5.3 | 4.5 | 3.6 | 2.7 | 1.8 | 0.9 | 0.0 |
33 | 37.7 | 35.8 | 33.9 | 32.0 | 30.2 | 28.3 | 26.4 | 24.5 | 22.6 | 20.7 | 18.8 | 17.0 | 15.1 | 13.2 | 11.3 | 10.4 | 9.4 | 8.5 | 7.5 | 6.6 | 5.7 | 4.7 | 3.8 | 2.8 | 1.9 | 0.9 | 0.0 |
34 | 39.9 | 37.9 | 35.9 | 33.9 | 31.9 | 29.9 | 27.9 | 25.9 | 23.9 | 21.9 | 19.9 | 17.9 | 15.9 | 14.0 | 12.0 | 11.0 | 10.0 | 9.0 | 8.0 | 7.0 | 6.0 | 5.0 | 4.0 | 3.0 | 2.0 | 1.0 | 0.0 |
35 | 42.1 | 40.0 | 37.9 | 35.8 | 33.7 | 31.6 | 29.5 | 27.4 | 25.3 | 23.2 | 21.1 | 19.0 | 16.9 | 14.7 | 12.6 | 11.6 | 10.5 | 9.5 | 8.4 | 7.4 | 6.3 | 5.3 | 4.2 | 3.2 | 2.1 | 1.1 | 0.0 |
36 | 44.5 | 42.3 | 40.1 | 37.9 | 35.6 | 33.4 | 31.2 | 28.9 | 26.7 | 24.5 | 22.3 | 20.0 | 17.8 | 15.6 | 13.4 | 12.2 | 11.1 | 10.0 | 8.9 | 7.8 | 6.7 | 5.6 | 4.5 | 3.3 | 2.2 | 1.1 | 0.0 |
37 | 47.0 | 44.7 | 42.3 | 40.0 | 37.6 | 35.3 | 32.9 | 30.6 | 28.2 | 25.9 | 23.5 | 21.2 | 18.8 | 16.5 | 14.1 | 12.9 | 11.8 | 10.6 | 9.4 | 8.2 | 7.1 | 5.9 | 4.7 | 3.5 | 2.4 | 1.2 | 0.0 |
38 | 49.7 | 47.2 | 44.7 | 42.2 | 39.7 | 37.3 | 34.8 | 32.3 | 29.8 | 27.3 | 24.8 | 22.4 | 19.9 | 17.4 | 14.9 | 13.7 | 12.4 | 11.2 | 9.9 | 8.7 | 7.5 | 6.2 | 5.0 | 3.7 | 2.5 | 1.2 | 0.0 |
39 | 52.4 | 49.8 | 47.2 | 44.6 | 42.0 | 39.3 | 36.7 | 34.1 | 31.5 | 28.8 | 26.2 | 23.6 | 21.0 | 18.4 | 15.7 | 14.4 | 13.1 | 11.8 | 10.5 | 9.2 | 7.9 | 6.6 | 5.2 | 3.9 | 2.6 | 1.3 | 0.0 |
40 | 55.3 | 52.6 | 49.8 | 47.0 | 44.3 | 41.5 | 38.7 | 36.0 | 33.2 | 30.4 | 27.7 | 24.9 | 22.1 | 19.4 | 16.6 | 15.2 | 13.8 | 12.5 | 11.1 | 9.7 | 8.3 | 6.9 | 5.5 | 4.2 | 2.8 | 1.4 | 0.0 |
41 | 58.4 | 55.5 | 52.5 | 49.6 | 46.7 | 43.8 | 40.9 | 37.9 | 35.0 | 32.1 | 29.2 | 26.3 | 23.4 | 20.4 | 17,5 | 16.1 | 14.6 | 13.1 | 11.7 | 10.2 | 8.8 | 7.3 | 5.8 | 4.4 | 2.9 | 1.5 | 0.0 |
42 | 61.6 | 58.5 | 55.4 | 52.3 | 49.3 | 46.2 | 43.1 | 40.0 | 36.9 | 33.9 | 30.8 | 27.7 | 24.6 | 21.5 | 18.5 | 16.9 | 15.4 | 13.9 | 12.3 | 10.8 | 9.2 | 7.7 | 6.2 | 4.6 | 3.1 | 1.5 | 0.0 |
43 | 64.9 | 61.7 | 58.4 | 55.2 | 51.9 | 48.7 | 45.4 | 42.2 | 38.9 | 35.7 | 32.4 | 29.2 | 26.0 | 22.7 | 19.5 | 17.8 | 16.2 | 14.6 | 13.0 | 11.4 | 9.7 | 8.1 | 6.5 | 4.9 | 3.2 | 1.6 | 0.0 |
44 | 68.4 | 65.0 | 61.5 | 58.1 | 54.7 | 51.3 | 47.9 | 44.5 | 41.0 | 37.6 | 34.2 | 30.8 | 27.4 | 23.9 | 20.5 | 18.8 | 17.1 | 15.4 | 13.7 | 12.0 | 10.3 | 8.5 | 6.8 | 5.1 | 3.4 | 1.7 | 0.0 |
45 | 72.0 | 68.4 | 64.8 | 61.2 | 57.6 | 54.0 | 50.4 | 46.8 | 43.2 | 39.6 | 36.0 | 32.4 | 28.8 | 25.2 | 21.6 | 19.8 | 18.0 | 16.2 | 14.4 | 12.6 | 10.8 | 9.0 | 7.2 | 5.4 | 3.6 | 1.8 | 0.0 |
46 | 75.9 | 72.1 | 68.3 | 64.5 | 60.7 | 56.9 | 53.1 | 49.3 | 45.5 | 41.7 | 37.9 | 34.1 | 30.3 | 26.6 | 22.8 | 20.9 | 19.0 | 17.1 | 15.2 | 13.3 | 11.4 | 9.5 | 7.6 | 5.7 | 3.8 | 1.9 | 0.0 |
47 | 79.9 | 75.9 | 71.9 | 67.9 | 63.9 | 59.9 | 55.9 | 51.9 | 47.9 | 43.9 | 39.9 | 35.9 | 31.9 | 27.9 | 24.0 | 22.0 | 20.0 | 18.0 | 16.0 | 14.0 | 12.0 | 10.0 | 8.0 | 6.0 | 4.0 | 2.0 | 0.0 |
48 | 84.0 | 79.8 | 75.6 | 71.4 | 67.2 | 63.0 | 58.8 | 54.6 | 50.4 | 46.2 | 42.0 | 37.8 | 33.6 | 29.4 | 25.2 | 23.1 | 21.0 | 18.9 | 16.8 | 14.7 | 12.6 | 10.5 | 8.4 | 6.3 | 4.2 | 2.1 | 0.0 |
49 | 88.4 | 84.0 | 79.6 | 75.1 | 70.7 | 66.3 | 61.9 | 57.5 | 53.0 | 48.6 | 44.2 | 39.8 | 35.4 | 30.9 | 26.5 | 24.3 | 22.1 | 19.9 | 17.7 | 15.5 | 13.3 | 11.1 | 8.8 | 6.6 | 4.4 | 2.2 | 0.0 |
50 | 93.0 | 88.3 | 83.7 | 79.0 | 74.4 | 69.7 | 65.1 | 60.4 | 55.8 | 51.1 | 46.5 | 41.8 | 37.2 | 32.5 | 27.9 | 25.6 | 23.2 | 20.9 | 18.6 | 16.3 | 13.9 | 11.6 | 9.3 | 7.0 | 4.6 | 2.3 | 0.0 |
51 | 97.7 | 92.9 | 88.0 | 83.1 | 78.2 | 73.3 | 68.4 | 63.5 | 58.6 | 53.8 | 48.9 | 44.0 | 39.1 | 34.2 | 29.3 | 26.9 | 24.4 | 22.0 | 19.5 | 17.1 | 14.7 | 12.2 | 9.8 | 7.3 | 4.9 | 2.4 | 0.0 |
52 | 102.7 | 97.6 | 92.5 | 87.3 | 82.2 | 77.1 | 71.9 | 66.8 | 61.6 | 56.5 | 51.4 | 46.2 | 41.1 | 36.0 | 30.8 | 28.3 | 25.7 | 23.1 | 20.5 | 18.0 | 15.4 | 12.8 | 10.3 | 7.7 | 5.1 | 2.6 | 0.0 |
53 | 107.9 | 102.5 | 97.1 | 91.8 | 86.4 | 81.0 | 75.6 | 70.2 | 64.8 | 59.4 | 54.0 | 48.6 | 43.2 | 37.8 | 32.4 | 29.7 | 27.0 | 24.3 | 21.6 | 18.9 | 16.2 | 13.5 | 10.8 | 8.1 | 5.4 | 2.7 | 0.0 |
54 | 113.4 | 107.7 | 102.0 | 96.4 | 90.7 | 85.0 | 79.4 | 73.7 | 68.0 | 62.4 | 56.7 | 51.0 | 45.4 | 39.7 | 34.0 | 31.2 | 28.3 | 25.5 | 22.7 | 19.8 | 17.0 | 14.2 | 11.3 | 8.5 | 5.7 | 2.8 | 0.0 |
55 | 119.1 | 113.1 | 107.1 | 101.2 | 95.2 | 89.3 | 83.3 | 77.4 | 71.4 | 65.5 | 59.5 | 53.6 | 47.6 | 41.7 | 35.7 | 32.7 | 29.8 | 26.8 | 23.8 | 20.8 | 17.9 | 14.9 | 11.9 | 8.9 | 6.0 | 3.0 | 0.0 |
56 | 125.0 | 118.7 | 112.5 | 106.2 | 100.0 | 93.7 | 87.5 | 81.2 | 75.0 | 68.7 | 62.5 | 56.2 | 50.0 | 43.7 | 37.5 | 34.4 | 31.2 | 28.1 | 25.0 | 21.9 | 18.7 | 15.6 | 12.5 | 9.4 | 6.2 | 3.1 | 0.0 |
57 | 131.2 | 124.6 | 118.0 | 111.5 | 104.9 | 98.4 | 91.8 | 85.3 | 78.7 | 72.1 | 65.6 | 59.0 | 52.5 | 45.9 | 39.3 | 36.1 | 32.8 | 29.5 | 26.2 | 23.0 | 19.7 | 16.4 | 13.1 | 9.8 | 6.6 | 3.3 | 0.0 |
58 | 137.6 | 130.7 | 123.8 | 117.0 | 110.1 | 103.2 | 96.3 | 89.4 | 82.6 | 75.7 | 68.8 | 61.9 | 55.0 | 48.2 | 41.3 | 37.8 | 34.4 | 31.0 | 27.5 | 24.1 | 20.6 | 17.2 | 13.8 | 10.3 | 6.9 | 3.4 | 0.0 |
59 | 144.3 | 137.1 | 129.9 | 122.7 | 115.5 | 108.2 | 101.0 | 93.8 | 86.6 | 79.4 | 72.2 | 64.9 | 57.7 | 50.5 | 43.3 | 39.7 | 36.1 | 32.5 | 28.9 | 25.3 | 21.6 | 18.0 | 14.4 | 10.8 | 7.2 | 3.6 | 0.0 |
60 | 151.3 | 143.8 | 136.2 | 128.6 | 121.1 | 113.5 | 105.9 | 98.4 | 90.8 | 83.2 | 75.7 | 68.1 | 60.5 | 53.0 | 45.4 | 41.6 | 37.8 | 34.0 | 30.3 | 26.5 | 22.7 | 18.9 | 15.1 | 11.3 | 7.6 | 3.8 | 0.0 |
61 | 158.6 | 150.7 | 142.8 | 134.8 | 126.9 | 119.0 | 111.0 | 103.1 | 95.2 | 87.2 | 79.3 | 71.4 | 63.4 | 55.5 | 47.6 | 43.6 | 39.7 | 35.7 | 31.7 | 27.8 | 23.8 | 19.8 | 15.9 | 11.9 | 7.9 | 4.0 | 0.0 |
62 | 166.2 | 157.9 | 149.6 | 141.3 | 133.0 | 124.7 | 116.4 | 108.0 | 99.7 | 91.4 | 83.1 | 74.8 | 66.5 | 58.2 | 49.9 | 45.7 | 41.6 | 37.4 | 33.2 | 29.1 | 24.9 | 20.8 | 16.6 | 12.5 | 8.3 | 4.2 | 0.0 |
63 | 174.1 | 165.4 | 156.7 | 148.0 | 139.3 | 130.6 | 121.9 | 113.2 | 104.5 | 95.8 | 87.1 | 78.4 | 69.7 | 61.0 | 52.2 | 47.9 | 43.5 | 39.2 | 34.8 | 30.5 | 26.1 | 21.8 | 17.4 | 13.1 | 8.7 | 4.4 | 0.0 |
64 | 182.4 | 173.3 | 164.2 | 155.0 | 145.9 | 136.8 | 127.7 | 118.6 | 109.4 | 100.3 | 91.2 | 82.1 | 73.0 | 63.8 | 54.7 | 50.2 | 45.6 | 41.0 | 36.5 | 31.9 | 27.4 | 22.8 | 18.2 | 13.7 | 9.1 | 4.6 | 0.0 |
65 | 191.0 | 181.4 | 171.9 | 162.3 | 152.8 | 143.2 | 133.7 | 124.1 | 114.6 | 105.0 | 95.5 | 85.9 | 76.4 | 66.8 | 57.3 | 52.5 | 47.7 | 43.0 | 38.2 | 33.4 | 28.6 | 23.9 | 19.1 | 14.3 | 9.5 | 4.8 | 0.0 |
66 | 199.9 | 189.9 | 179.9 | 169.9 | 159.9 | 149.9 | 140.0 | 130.0 | 120.0 | 110.0 | 100.0 | 90.0 | 80.0 | 70.0 | 60.0 | 55.0 | 50.0 | 45.0 | 40.0 | 35.0 | 30.0 | 25.0 | 20.0 | 15.0 | 10.0 | 5.0 | 0.0 |
67 | 209.2 | 198.8 | 188.3 | 177.9 | 167.4 | 156.9 | 146.5 | 136.0 | 125.5 | 115.1 | 104.6 | 94.2 | 83.7 | 73.2 | 62.8 | 57.5 | 52.3 | 47.1 | 41.8 | 36.6 | 31.4 | 26.2 | 20.9 | 15.7 | 10.5 | 5.2 | 0.0 |
68 | 218.9 | 208.0 | 197.0 | 186.1 | 175.1 | 164.2 | 153.2 | 142.3 | 131.4 | 120.4 | 109.5 | 98.5 | 87.6 | 76.6 | 65.7 | 60.2 | 54.7 | 49.3 | 43.8 | 38.3 | 32.8 | 27.4 | 21.9 | 16.4 | 10.9 | 5.5 | 0.0 |
69 | 229.0 | 217.5 | 206.1 | 194.6 | 183.2 | 171.7 | 160.3 | 148.8 | 137.4 | 125.9 | 114.5 | 103.0 | 91.6 | 80.1 | 68.7 | 63.0 | 57.2 | 51.5 | 45.8 | 40.1 | 34.3 | 28.6 | 22.9 | 17.2 | 11.4 | 5.7 | 0.0 |
70 | 239.5 | 227.5 | 215.5 | 203.6 | 191.6 | 179.6 | 167.6 | 155.7 | 143.7 | 131.7 | 119.7 | 107.8 | 95.8 | 83.8 | 71.8 | 65.9 | 59.9 | 53.9 | 47.9 | 41.9 | 35.9 | 29.9 | 23.9 | 18.0 | 12.0 | 6.0 | 0.0 |
71 | 250.4 | 237.9 | 225.3 | 212.8 | 200.3 | 187.8 | 175.3 | 162.7 | 150.2 | 137.7 | 125.2 | 112.7 | 100.1 | 87.6 | 75.1 | 68.9 | 62.6 | 56.3 | 50.1 | 43.8 | 37.6 | 31.3 | 25.0 | 18.8 | 12.5 | 6.3 | 0.0 |
72 | 261.7 | 248.6 | 235.5 | 222.4 | 209.4 | 196.3 | 183.2 | 170.1 | 157.0 | 143.9 | 130.8 | 117.8 | 104.7 | 91.6 | 78.5 | 72.0 | 65.4 | 58.9 | 52.3 | 45.8 | 39.3 | 32.7 | 26.2 | 19.6 | 13.1 | 6.5 | 0.0 |
73 | 273.5 | 259.8 | 246.1 | 232.4 | 218.8 | 205.1 | 191.4 | 177.8 | 164.1 | 150.4 | 136.7 | 123.1 | 109.4 | 95.7 | 82.0 | 75.2 | 68.4 | 61.5 | 54.7 | 47.9 | 41.0 | 34.2 | 27.3 | 20.5 | 13.7 | 6.8 | 0.0 |
74 | 285.7 | 271.4 | 257.1 | 242.8 | 228.6 | 214.3 | 200.0 | 185.7 | 171.4 | 157.1 | 142.8 | 128.6 | 114.3 | 100.0 | 85.7 | 78.6 | 71.4 | 64.3 | 57.1 | 50.0 | 42.9 | 35.7 | 28.6 | 21.4 | 14.3 | 7.1 | 0.0 |
75 | 298.4 | 283.5 | 268.6 | 253.6 | 238.7 | 223.8 | 208.9 | 194.0 | 179.0 | 164.1 | 149.2 | 134.3 | 119.4 | 104.4 | 89.5 | 82.1 | 74.6 | 67.1 | 59.7 | 52.2 | 44.8 | 37.3 | 29.8 | 22.4 | 14.9 | 7.5 | 0.0 |
76 | 311.6 | 296.0 | 280.4 | 264.9 | 249.3 | 233.7 | 218.1 | 202.5 | 187.0 | 171.4 | 155.8 | 140.2 | 124.6 | 109.1 | 93.5 | 85.7 | 77.9 | 70.1 | 62.3 | 54.5 | 46.7 | 39.0 | 31.2 | 23.4 | 15.6 | 7.8 | 0.0 |
77 | 325.3 | 309.0 | 292.8 | 276.5 | 260.2 | 244.0 | 227.7 | 211.5 | 195.2 | 178.9 | 162.7 | 146.4 | 130.1 | 113.9 | 97.6 | 89.5 | 81.3 | 73.2 | 65.1 | 56.9 | 48.8 | 40.7 | 32.5 | 24.4 | 16.3 | 8.1 | 0.0 |
78 | 339.5 | 322.6 | 305.6 | 288.6 | 271.6 | 254.7 | 237.7 | 220.7 | 203.7 | 186.7 | 169.8 | 152.8 | 135.8 | 118.8 | 101.9 | 93.4 | 84.9 | 76.4 | 67.9 | 59.4 | 50.9 | 42.4 | 34.0 | 25.5 | 17.0 | 8.5 | 0.0 |
79 | 354.3 | 336.6 | 318.9 | 301.2 | 283.5 | 265.7 | 248.0 | 230.3 | 212.6 | 194.9 | 177.2 | 159.4 | 141.7 | 124.0 | 106.3 | 97.4 | 88.6 | 79.7 | 70.9 | 62.0 | 53.1 | 44.3 | 35.4 | 26.6 | 17.7 | 8.9 | 0.0 |
80 | 369.6 | 351.2 | 332.7 | 314.2 | 295.7 | 277.2 | 258.8 | 240.3 | 221.8 | 203.3 | 184.8 | 166.3 | 147.9 | 129.4 | 110.9 | 101.7 | 92.4 | 83.2 | 73.9 | 64.7 | 55.4 | 46.2 | 37.0 | 27.7 | 18.5 | 9.2 | 0.0 |
81 | 385.6 | 366.3 | 347.0 | 327.7 | 308.4 | 289.2 | 269.9 | 250.6 | 231.3 | 212.1 | 192.8 | 173.5 | 154.2 | 134.9 | 115.7 | 106.0 | 96.4 | 86.8 | 77.1 | 67.5 | 57.8 | 48.2 | 38.6 | 28.9 | 19.3 | 9.6 | 0.0 |
82 | 402.1 | 382.0 | 361.9 | 341.8 | 321.7 | 301.5 | 281.4 | 261.3 | 241.2 | 221.1 | 201.0 | 180.9 | 160.8 | 140.7 | 120.6 | 110.6 | 100.5 | 90.5 | 80.4 | 70.4 | 60.3 | 50.3 | 40.2 | 30.2 | 20.1 | 10.1 | 0.0 |
83 | 419.2 | 398.2 | 377.3 | 356.3 | 335.3 | 314.4 | 293.4 | 272.5 | 251.5 | 230.6 | 209.6 | 188.6 | 167.7 | 146.7 | 125.8 | 115.3 | 104.8 | 94.3 | 83.8 | 73.4 | 62.9 | 52.4 | 41.9 | 31.4 | 21.0 | 10.5 | 0.0 |
84 | 436.9 | 415.1 | 393.2 | 371.4 | 349.6 | 327.7 | 305.9 | 284.0 | 262.2 | 240.3 | 218.5 | 196.6 | 174.8 | 152.9 | 131.1 | 120.2 | 109.2 | 98.3 | 87.4 | 76.5 | 65.5 | 54.6 | 43.7 | 32.8 | 21.8 | 10.9 | 0.0 |
85 | 455.3 | 432.6 | 409.8 | 387.0 | 364.3 | 341.5 | 318.7 | 296.0 | 273.2 | 250.4 | 227.7 | 204.9 | 182.1 | 159.4 | 136.6 | 125.2 | 113.8 | 102.5 | 91.1 | 79.7 | 68.3 | 56.9 | 45.5 | 34.2 | 22.8 | 11.4 | 0.0 |
86 | 474.4 | 450.7 | 427.0 | 403.3 | 379.5 | 355.8 | 332.1 | 308.4 | 284.7 | 260.9 | 237.2 | 213.5 | 189.8 | 166.1 | 142.3 | 130.5 | 118.6 | 106.7 | 94.9 | 83.0 | 71.2 | 59.3 | 47.4 | 35.6 | 23.7 | 11.9 | 0.0 |
87 | 494.2 | 469.5 | 444.8 | 420.1 | 395.4 | 370.7 | 346.0 | 321.2 | 296.5 | 271.8 | 247.1 | 222.4 | 197.7 | 173.0 | 148.3 | 135.9 | 123.6 | 111.2 | 98.8 | 86.5 | 74.1 | 61.8 | 49.4 | 37.1 | 24.7 | 12.4 | 0.0 |
88 | 514.7 | 489.0 | 463.2 | 437.5 | 411.8 | 386.0 | 360.3 | 334.6 | 308.8 | 283.1 | 257.4 | 231.6 | 205.9 | 180.2 | 154.4 | 141.5 | 128.7 | 115.8 | 102.9 | 90.1 | 77.2 | 64.3 | 51.5 | 38.6 | 25.7 | 12.9 | 0.0 |
89 | 536.0 | 509.2 | 482.4 | 455.6 | 428.8 | 402.0 | 375.2 | 348.4 | 321.6 | 294.8 | 268.0 | 241.2 | 214.4 | 187.6 | 160.8 | 147.4 | 134.0 | 120.6 | 107.2 | 93.8 | 80.4 | 67.0 | 53.6 | 40.2 | 26.8 | 13.4 | 0.0 |
90 | 558.0 | 530.1 | 502.2 | 474.3 | 446.4 | 418.5 | 390.6 | 362.7 | 334.8 | 306.9 | 279.0 | 251.1 | 223.2 | 195.3 | 167.4 | 153.4 | 139.5 | 125.5 | 111.6 | 97.6 | 83.7 | 69.7 | 55.8 | 41.8 | 27.9 | 13.9 | 0.0 |
91 | 580.7 | 551.7 | 522.7 | 493.6 | 464.6 | 435.6 | 406.5 | 377.5 | 348.4 | 319.4 | 290.4 | 261.3 | 232.3 | 203.3 | 174.2 | 159.7 | 145.2 | 130.7 | 116.1 | 101.6 | 87.1 | 72.6 | 58.1 | 43.6 | 29.0 | 14.5 | 0.0 |
92 | 604.3 | 574.1 | 543.9 | 513.7 | 483.5 | 453.3 | 423.0 | 392.8 | 362.6 | 332.4 | 302.2 | 272.0 | 241.7 | 211.5 | 181.3 | 166.2 | 151.1 | 136.0 | 120.9 | 105.8 | 90.7 | 75.5 | 60.4 | 45.3 | 30.2 | 15.1 | 0.0 |
93 | 628.8 | 597.3 | 565.9 | 534.5 | 503.0 | 471.6 | 440.1 | 408.7 | 377.3 | 345.8 | 314.4 | 282.9 | 251.5 | 220.1 | 188.6 | 172.9 | 157.2 | 141.5 | 125.8 | 110.0 | 94.3 | 78.6 | 62.9 | 47.2 | 31.4 | 15.7 | 0.0 |
94 | 654.1 | 621.4 | 588.7 | 556.0 | 523.3 | 490.6 | 457.8 | 425.1 | 392.4 | 359.7 | 327.0 | 294.3 | 261.6 | 228.9 | 196.2 | 179.9 | 163.5 | 147.2 | 130.8 | 114.5 | 98.1 | 81.8 | 65.4 | 49.1 | 32.7 | 16.4 | 0.0 |
95 | 680.2 | 646.2 | 612.2 | 578.2 | 544.2 | 510.2 | 476.2 | 442.2 | 408.1 | 374.1 | 304.1 | 306.1 | 272.1 | 238.1 | 204.1 | 187.1 | 170.1 | 153.1 | 136.0 | 119.0 | 102.0 | 85.0 | 68.0 | 51.0 | 34.0 | 17.0 | 0.0 |
96 | 707.3 | 672.0 | 636.6 | 601.2 | 565.9 | 530.5 | 495.1 | 459.8 | 424.4 | 389.0 | 353.7 | 318.3 | 282.9 | 247.6 | 212.2 | 194.5 | 176.8 | 159.2 | 141.5 | 123.8 | 106.1 | 88.4 | 70.7 | 53.1 | 35.4 | 17.7 | 0.0 |
97 | 735.4 | 698.6 | 661.8 | 625.1 | 588.3 | 551.5 | 514.8 | 478.0 | 441.2 | 404.5 | 367.7 | 330.9 | 294.1 | 257.4 | 220.6 | 202.2 | 183.8 | 165.5 | 147.1 | 128.7 | 110.3 | 91.9 | 73.5 | 55.2 | 36.8 | 18.4 | 0.0 |
98 | 764.4 | 726.1 | 687.9 | 649.7 | 611.5 | 573.3 | 535.1 | 496.8 | 458.6 | 420.4 | 382.2 | 344.0 | 305.7 | 267.5 | 229.3 | 210.2 | 191.1 | 172.0 | 152.9 | 133.8 | 114.7 | 95.5 | 76.4 | 57.3 | 38.2 | 19.1 | 0.0 |
99 | 794.4 | 754.6 | 714.9 | 675.2 | 635.5 | 595.8 | 556.1 | 516.3 | 476.6 | 436.9 | 397.2 | 357.5 | 317.7 | 278.0 | 238.3 | 218.4 | 198.6 | 178.7 | 158.9 | 139.0 | 119.2 | 99.3 | 79.4 | 59.6 | 39.7 | 19.9 | 0.0 |
100 | 825.4 | 784.1 | 742.8 | 701.6 | 660.3 | 619.0 | 577.8 | 536.5 | 495.2 | 454.0 | 412.7 | 371.4 | 330.2 | 288.9 | 247.6 | 227.0 | 206.3 | 185.7 | 165.1 | 144.4 | 123.8 | 103.2 | 82.5 | 61.9 | 41.3 | 20.6 | 0.0 |
The authors thank Trisha Rice-McGrath, Consulting Applications Specialist, and Edward Griffith, Sales Representative of the ElectroScan Corporation, for their support of this project. Carol Grissom, Chief of Objects Conservation, and Marion Mecklenburg, Assistance Director for Conservation Research, both at the Conservation Analytical Laboratory of the Smithsonian Institution, provided incisive editing and constructive criticism. Many thanks to H.E. "Doc" Dougherty, Office of Printing and Photographic Services, Smithsonian Institution, for the reproduction of images in Figure 6.
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