Gen Relativ Gravit (2007) 39:1047–1052 DOI 10.1007/s10714-006-0355-5 GOLDEN OLDIE On the definition of distance in general relativity: I. M. H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933)) George F. R. Ellis Published online: 24 October 2006 © Springer Science+Business Media, LLC 2006 Editor’s note The reciprocity theorem for null geodesics is of fundamental importance for observations in astrophysics and cosmology. The first general proof of this result was given by Etherington [1]; that paper is deservedly reproduced here as a Golden Oldie. The core of the reciprocity theorem is the fact that many geometric properties are invariant when the roles of source and observer in astronomical observa- tions are transposed. In the simplest case, it states that for two observers at rest relative to each other in an arbitrary static spacetime, objects of identical size at each observer are seen by the other observer to subtend identical solid angles. When there are relative motions, as in the case of cosmology, allowance for redshift effects must be made, as follows: let the observer area distance r 0 be defined by dS 0 = r 2 0 d 0 , where a (past directed) bundle of null rays subtending a solid angle d 0 at the observer at time t 0 has cross sectional area dS 0 at the object observed (notionally a galaxy). Similarly let the galaxy area distance r G be defined by dS G = r 2 G d G , where a (future directed) bundle of null rays subtending a solid angle d G at the galaxy has cross sectional area dS G at the observer at the same time t 0 . Then these two area distances are related by r 2 G = r 2 0 (1 + z) 2 (1) G. F. R. Ellis (B ) Department of Mathematics, University of Cape Town, Rondebosch, Cape Town 7701, South Africa e-mail: ellis@maths.uct.ac.za