As I have shown previously, 6 the probability of the overlapping of images of nebulae is considerable. The gravitational fields of a number of "foreground" nebulae may therefore be expected to deflect the light coming to us from certain background nebulae. The observation of such gravitational lens effects promises to furnish us with the simplest and most accurate determination of nebular masses. No thorough search for these effects has as yet been undertaken. It would seem, perhaps, that if the masses of field nebulae were, on the average, as great as the masses of cluster nebulae obtained in section iii, gravitational lens effects among nebulae should have been long since discovered. Until many plates of rich nebular fields taken under excellent conditions of seeing have been carefully examined it would be dangerous, however, to draw any definite conclusions.
The mathematical analysis of the formation of images of distant nebulae through the action of the gravitational fields of nearer nebulae will be given in detail in an article to be published in the Helvetica physica acta.