Results
Plot Library
Figure 12. Plot 1, estimated weight percent gelatin by year.
We have used plots as the primary means of reporting our research results. Most of the plots are accompanied by statistical information designed to help clarify the strength of the relationship between the two variables displayed. To see a plot in the table below, click on the plot number. Then click “Previous” or “Next” to move between plots sequentially. To return to the Plot Library table, use your browser Back button or close the plot window. Unless stated otherwise, all the plots shown are based on data from the interior of the specimen only; i.e., locations 2–5 indicated with blue arrows in figure 11. Any plot shown in gray type in the table below is planned but under development.
Plots appear in order of interest to the coauthors; our thoughts on what they reveal appear in the DISCUSSION section.
Inclusion of Error/Precision/Uncertainty in Plots
A simplified overview of our plotting work includes the following guidelines: (1) the black dots represent the observed data reported by the instrument, (2) the light gray circles indicate the range of error in the analysis method, (3) the red line shows the estimated mean as a function of year, and (4) the blue outer curves indicate the reliability of these mean estimates. In other words, with 95% confidence the actual means are between the two blue curves. Thus, in summary, to get a more reliable sense of the trend for the weight percent gelatin concentration over the centuries in figure 12, plot 1 (above), one should consider not only the red line, but the swath described by the space between the two blue outer curves. Even more telling are the tabletop graphics at the top of the plot that illustrate, by their relative heights, the change in mean values from century to century. If the tops appear at different heights, the changes can be considered statistically significant. The tabletop units coincide with the vertical axis units but their scale has been compressed for display purposes. It is important to point out that a statistically significant difference does not necessarily imply a significant practical difference. In other words, within certain mathematical parameters, we can have confidence an observed difference is not a chance occurrence; however, whether that difference has realworld implications is open to discussion.
A more detailed description of our plotting work follows below.
Sources of error, and uncertainty, and the degree of precision possible with different instruments are included in some but not all plots. For instance in plot 1 (above) the gelatin data (solid black symbols) are shown for the 1,578 specimens plotted over time. The vertical scale displays the predicted weight percent gelatin concentration. The tabletop display across the top of the graph depicts the mean levels across the centuries. The thickness of the tabletop gives the 95% confidence interval for the mean. Nonoverlapping tabletops imply that the difference between the means is statistically significant.
The red (center) curve represents a locally smoothed estimate of the mean, as a function of year. The blue (outer) curves give the pointwise 95% confidence intervals for the means over the years. We used LOESS (locally weighted scatterplot smoothing) in R to compute the smoothed estimate of the mean. The confidence bands were derived using Monte Carlo simulation. The confidence bands account for the measurement error as described in the next paragraph
The black points in the scatter plot represent the observed values. These observed values were measured with some error, so if we had carried out the same measurement procedures on the same samples, we would have come up with slightly different values. As discussed earlier, precision in our work was calculated differently for the XRF and the UVVisNIR instrumentations. Using the respective precision parameters, corresponding to each observed datum (solid black symbol), we generated ten auxiliary data points (light gray circles) that represent data we would expect to see if the same measurement process was repeated ten times. The light gray circles represent potential values under replicate measurements. The spread of these potential values reflects the lack of precision in the measurements; i.e., the more spread out these potential values are, the less precision.
The statistic R is a generalization of the Pearson correlation coefficient. Whereas the correlation measures the strength of the linear relationship between X and Y, the statistic R measures the strength of the functional (linear or nonlinear) relationship between X and Y. If the observed (X, Y) values fall close to a smooth, nonconstant function of X, then R will take on a value close to 1. If X and Y are linearly related, then R will be numerically identical to the absolute value of the correlation coefficient. Numerically, R is the correlation between the smoothed estimates of the Y means and the observed Y values. As mentioned above, we used the function LOESS in R to compute the smoothed estimates of the Y means, and the P value was computed using a nonparametric bootstrap approach.
Plot Library Table
*Plot numbers with asterisks have error incorporated; all other plots are based on “observed” data. Units for elements (Ca, K, S, and Fe or Log Ca, Log K, Log S, and Log Fe) are displayed in parts per million (ppm).
PLOT CLASS, NUMBER 
VARIABLE 1 versus 
VARIABLE 2 
COMMENTS 
CHRONOLOGICAL 

FULL DATA SET 

1* 
Gelatin 
Year 

2* 
Log Ca 
Year 
The natural log transformation was used to compresses the spread of high and low values by reducing the amount of skew leaving patterns in the data more clearly visible. 
Log K 
Year 
ditto 

Log S 
Year 
ditto 

Log Fe 
Year 
ditto 

Log S 
Log K 
by century 

Thickness one sheet 
Year 

Thickness ten sheets 
Year 

Delta L* 
Year 
The delta L* vertical scale progresses from 0 (white) toward 30 (colors increasingly closer to black) 

Chlorine (Cl) peak intensity 
Year 
Cl was not in the calibration so reported values in this plot indicate Cl peak height intensity rather than ppm 

Calcium Carbonate 
Year 
Based on all observed Ca = calcium carbonate 

Log CaCO_{3} 
Year 
Based on all observed Ca = calcium carbonate 

Ratio gelatin:CaCO_{3} 
Year 
Based on all observed Ca = calcium carbonate 

Ratio gelatin:CaCO_{3, }zoom 1 
Year 
Based on all observed Ca = calcium carbonate 

Ratio gelatin:CaCO_{3, }zoom 2 
Year 
Based on all observed Ca = calcium carbonate 

Calcium (ppm) 
Year 

Alum 
Year 
Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800 

Potash alum K 
Year 
Based on all observed K = potassium aluminum sulfate prior to 1800 only 

Log potash alum 
Year 
ditto 

Potash alum S 
Year 
Based on all observed S = potassium aluminum sulfate prior to 1800 

% alum on gelatin 
Year 
Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800 

% alum on gelatin, zoom 
Year 
Based on all observed S = potassium aluminum sulfate prior to 1800, aluminum sulfate post 1800 

% alum on CaCO_{3} 
Year 
ditto 

% alum on CaCO_{3} , zoom 
Year 
ditto 

LEAF TYPES 

Log Ca 
Year by leaf type 
All leaf types 

Log Ca 
Year by leaf type 
Art prints, blank leaves, MS books, MS leaves 

Log Ca 
Year by leaf type 
Printed leaves, printed books 

Ca (ppm) 
Year by leaf type 
All leaf types 

Ca (ppm) 
Count by leaf type 
Bar graph 

Log K 
Year by leaf type 
All leaf types 

K (ppm) 
Count by leaf type 
Bar graph 

Log S 
Year by leaf type 
All leaf types 

S (ppm) 
Count by leaf type 
Bar graph 

Log Fe 
Year by leaf type 
All leaf types 

Fe (ppm) 
Count by leaf type 
Bar graph 

Gelatin 
Year by leaf type 
All leaf types 

Gelatin 
Year by leaf type 
Art prints, blank leaves, MS books, MS leaves 

Gelatin 
Year by leaf type 
Printed leaves, printed books 

Gelatin 
Year by leaf type 
Printed books 

Gelatin 
Year by leaf type 
Printed leaves 

Gelatin 
Count by leaf type 
Bar graph 

NONCHRONOLOGICAL 

FULL DATA SET 

Gel 
Delta L* 
The delta L* vertical scale progresses from 0 (white) toward 30 (colors increasingly closer to black) 

Log Ca 
Delta L* 
ditto 

Log K 
Delta L* 
ditto 

Log S 
Delta L* 
ditto 

Fe 
Delta L* 
ditto 

Delta L* 
% alum on gelatin 
ditto 

Delta L* 
% alum on CaCO_{3} 
ditto 

Gel 
Delta a* 
The delta a* scale indicates more red as the positive numbers increase, more green as negative numbers decrease. 

Log Ca 
Delta a* 
ditto 

Log K 
Delta a* 
ditto 

Log S 
Delta a* 
ditto 

Fe 
Delta a* 
ditto 

Delta a* 
% alum on gelatin 
ditto 

Delta a* 
% alum on CaCO_{3} 
ditto 

Gelatin interior 
Gelatin edge 

Ca interior 
Ca edge 

Fe interior 
Fe edge 

S interior 
S edge 

Log Ca 
Gelatin 

"ORNAMENT" PLOTS 

FULL DATA SET 

Gelatin 
M&W (materials and workmanship) 
Ornament plot showing the average estimated concentrations for M&W grade 1 (worst) to grade 5 (best). 

Log Ca 
M&W 
ditto 

Log K 
M&W 
ditto 

Log S 
M&W 
ditto 

Log Fe 
M&W 
ditto 

Thickness 1 sheet 
M&W 
ditto 

Delta L* 
M&W 
ditto 

300 DARKEST vs 300 LIGHTEST SUBSET 
300 darkest and lightest specimens from the full 1,578specimen data set. 

300 darkest & 300 lightest 
Delta L* 

300 D & 300 L 
Year 
Plot shows distribution of specimens by year. 

300 D & 300 L 
Gelatin 

300 D & 300 L 
Log Ca 

300 D & 300 L 
Log K 

300 D & 300 L 
Log S 

300 D & 300 L 
Log Fe 

300 D & 300 L 
Thickness 1 sheet 
ditto 

FROST = GRADE A SUBSET 
295 specimens graded "A" for "aqueous intervention unlikely" by conservator G. Frost. 

50% darkest & 50% lightest 
Delta L* 

50% D & 50% L 
Year 
Plot shows distribution of specimens by year. 

50% D & 50% L 
Gelatin 

50% D & 50% L 
Log Ca 

50% D & 50% L 
Log K 

50% D & 50% L 
Log S 

50% D & 50% L 
Log Fe 

50% D & 50% L 
Thickness 1 sheet 

"SAME BOOK DIFFERENT PAPERS SUBSET" 

Delta L* 
Gelatin 
Trends evident in paired specimens in the same book: one darker, one lighter. 

Delta L* 
Log Ca 
ditto 

Delta L* 
Log K 
ditto 

Delta L* 
Log S 
ditto 

Delta L* 
Fe 
ditto 

82 
Delta L* 
% alum on gelatin 
ditto 
83 
Delta L* 
% alum on CaCO_{3} 
ditto 
84 
Delta a* 
Gelatin 
ditto 
85 
Delta a* 
Log Ca 
ditto 
86 
Delta a* 
Log K 
ditto 
87 
Delta a* 
Log S 
ditto 
88 
Delta a* 
Log Fe [or Fe] 
ditto 
89 
Delta a* 
% alum on gelatin 
ditto 
90 
Delta a* 
% alum on CaCO_{3} 
ditto 