This study analyzes the interpretive activities of scientists related to familiar and unfamiliar graphs. The analyses show that when scientists were familiar with a graph, they read it transparently and thereby leapt beyond the material basis to the thing the graph is said to be about. In contrast, when scientists were less familiar with the particular graphs, their reading turned out to be a complex iterative process. In this process, scientists linked graphs to possible worlds by means of complex inferences. They checked whether an expression referred to the actual properties of the worldly things the graphs are speaking of. They also checked graphical expressions themselves on the basis of certain circumstances. In a few instances, the scientists abandoned all attempts in interpreting the graphs and classified them as meaningless. Grounded in the data, a 2-stage model is proposed. This model accounts for different levels of reading graphs observed in this study.