This feels like an important paper, to me, even if it's not about eagles and didn't include any testing for organic chemicals like DDE or flame retardants, for example. If you're game, you can read the Discussion section of the paper for more insight into the authors' conclusions.
Variation in egg size, shell thickness, and metal and calcium content in eggshells and egg contents in relation to laying order and embryonic development in a small passerine bird
http://sci-hub.cc/10.1642/AUK-16-16.1ABSTRACT
Although there are quite a number of studies examining the effect of egg laying order on the levels of elements and various chemical substances, none have taken into account the presence or absence of embryonic development in the eggs. In this study, we measured the morphometry (length, breadth, volume, and mass), shell thickness, and concentrations of calcium and 10 other metals (including 8 essential elements: chromium, copper, nickel, manganese, iron, cobalt, zinc, and magnesium; and 2 nonessential elements: lead and cadmium) in the shells and contents of embryonated and nonembryonated eggs across the laying order of Eurasian Reed-Warblers (Acrocephalus scirpaceus).
We found a significant increase in egg volume in both nonembryonated and embryonated eggs, and an increase in egg length and mass in embryonated eggs, with laying order. Analysis confirmed significant differences related to laying order between nonembryonated and embryonated eggs in the concentrations of elements measured in shells (Cu, Cd, Pb, Mn, Fe, and Zn) and egg contents (Pb). Analysis of the relationships between laying order and concentrations of elements revealed a significant increase in Mg and Ca concentrations in the shells of embryonated eggs, and a significant decrease in Ni in the contents of nonembryonated eggs and in Cu, Cd, Mn, and Co in the contents of embryonated eggs. Our results indicate that laying order and the presence of an embryo are critical factors responsible for variation in some features of egg morphometry and element concentrations in eggshells and egg contents. These factors should therefore be taken into consideration in studies of the chemistry and morphometry of avian eggs.