A theoretical expression is derived for the first-order contribution to the Curie constant arising from cross terms between the off-diagonal parts of the magnetic moments and the interactions between the magnetic moments. In certain simple cases the contribution ΔC1 is equal to 2αθ, where α is the temperature-independent part of the susceptibility and θ is the Weiss constant. Estimates of ΔC1 show that in many cases its contribution to the Curie constant may be appreciable. A discussion is given of the danger of deducing Curie constants from susceptibility measurements over a limited temperature range, even under apparently favorable conditions, and illustrated by an analysis of some new measurements on ErCl3.