Digital libraries such as the NASA Astrophysics Data System \citep{2005JASIS.tmp....2K} permit the easy accumulation of a new type of bibliometric measure, the number of electronic accesses (``reads'') of individual articles. We explore various aspects of this new measure.

We examine the obsolescence function as measured by actual reads, and show that it can be well fit by the sum of four exponentials with very different time constants. We compare the obsolescence function as measured by readership with the obsolescence function as measured by citations. We find that the citation function is proportional to the sum of two of the components of the readership function. This proves that the normative theory of citation is true in the mean. We further examine in detail the similarities and differences between the citation rate, the readership rate and the total citations for individual articles, and discuss some of the causes.

Using the number of reads as a bibliometric measure for individuals, we introduce the read-cite diagram to provide a two-dimensional view of an individual's scientific productivity. We develop a simple model to account for an individual's reads and cites and use it to show that the position of a person in the read-cite diagram is a function of age, innate productivity, and work history. We show the age biases of both reads and cites, and develop two new bibliometric measures which have substantially less age bias than citations: SumProd, a weighted sum of total citations and the readership rate, intended to show the total productivity of an individual; and Read10, the readership rate for papers published in the last ten years, intended to show an individual's current productivity. We also discuss the effect of normalization (dividing by the number of authors on a paper) on these statistics.

We apply SumProd and Read10 using new, non-parametric techniques to rank and compare different astronomical research organizations