# Can it be possible to know the percentage loss without the absolute numbers?

Is there any way to knew or at least estimate the absolute proportion change from a percentage change? I am studying the corrosion of glass, and have several sets of chemical compound percentages, such as these, taken from the core and the surface of a Roman shard:

$$\begin{array}{lrcr} \hline \text{Element} & \text{Core} && \text{Surface}\\ \hline \mathrm{Na} & 19.39\% & \to & 1.04\%\\ \mathrm{Mg} & 0.43\% & \to & 0.51\%\\ \mathrm{Al} & 1.8\% & \to & 2.25\%\\ \mathrm{Si} & 68.15\% & \to & 83.89\%\\ \mathrm{S} & 0.49\% & \to & 0.64\%\\ \mathrm{Cl} & 1.34\% & \to & 1.61\%\\ \mathrm{K} & 0.42\% & \to & 0.42\%\\ \mathrm{Ca} & 6.66\% & \to & 8.18\%\\ \mathrm{Fe} & 0.4\% & \to & 0.44\%\\ \mathrm{Sb} & 1.07\% & \to & 1.45\%\\ \hline \mathrm{Total} & 100\% & \to & 100\%\\ \hline \end{array}$$

As glass naturally degrades, it loses alkali, such as $\mathrm{Na}$, $\mathrm{Ca}$, etc. (seen in the difference between the two sets). However, some elements like $\mathrm{Al}$ retain a comparatively stable absolute amount, while their percentage changes significantly. Obviously, no material was added to the glass, but some percentages increased. So is there a calculation that could tell that, for instance "Sodium decreased twofold" or "Silica stayed the same" using just percents? The absolute amounts of each element only decrease with time, however I do not know how to quantify this loss.

As an example of what I mean, say there are $100$ coloured balls:

$$\begin{array}{lrr} \hline \text{Color} & \text{Amount} & \text{Percentage}\\ \hline \text{Yellow} & 25 & 25\%\\ \text{Red} & 41 & 41\%\\ \text{Green} & 24 & 24\%\\ \text{Blue} & 10 & 10\%\\ \hline \end{array}$$

We take some of them away, now there are $78$ left:

$$\begin{array}{lrr} \hline \text{Color} & \text{Amount} & \text{Percentage}\\ \hline \text{Yellow} & 10 & 13\%\\ \text{Red} & 36 & 46\%\\ \text{Green} & 22 & 28\%\\ \text{Blue} & 10 & 13\%\\ \hline \end{array}$$

Again, some of them, like the blue, were not taken, but the percentage changed, while the others, like red, were taken, but their percentage actually increased. However, in the case of glass, the absolute numbers are unknown. Therefore, is there any way to say, for instance, that $3/5$ of the yellow balls were taken or that the blue were not taken etc., while only having the percent values of this set?

1. We've got $5$ blue balls and $3$ red balls. We take away $2$ blue ones and leave red ones the same, then blue has $50\%$ and red has $50\%$.
2. We've got $5$ blue balls and $3$ red balls. We take away $4$ blue balls and $2$ red balls, then blue has $50\%$ and red has $50\%$.