Counts of Stars or Galaxies vs. Magnitude

The Structure of the Galaxy, as determined by William and John Herschel: The most influential early study of the structure of our Galaxy was the "star gaging" exercise made by William Herschel in 1785. The method he used was remarkably simple. He assumed that our Galaxy was homogeneously filled with stars out to its boundary, and was surrounded by empty space outside. Under these assumptions, the distance to the Galaxy's boundary in any given direction is indicated by the number of stars seen in that direction. As the distance to the boundary grows, the number of stars seen will grow with the cube of that distance, since that is how the volume of the Pyramid of Vision scales. So Herschel counted stars in over 600 directions, then took the cube root of each count to find a number proportional to the distance in each case.

The star gages were published in the Philosophical Transactions of the Royal Society, LXXV, 213-66. Most of this article is reprinted in the very valuable book by Michael A. Hoskin, William Herschel and the Construction of the Heavens. But the star counts themselves were deleted to save space, so one needs to seek out the original article, or its reprinting in Herschel's Collected Works.

In this VR world, the gray and red pyramids indicate the results of his survey; each points in the direction of one of his fields, and has a length proportional to his star counts in that direction. Although William Herschel published his entire set of counts, the only visualization of them that he provided was a cross sectional diagram that has been immortalized by being reprinted in nearly every astronomy textbook. The fields used to construct the cross section are shown in red; the other fields that only appeared in his table are the ones shown in gray.

The structure of the Galaxy is actually remarkably hard to discern from these pyramids. Part of the problem is that Herschel's sky coverage was haphazard, due at least in part to a telescope mounting that in 1785 could not point near the Pole. Herschel's choice to emphasize a single well selected slice through his data was sound, as well as being suited to the scientific visualization technology of his day.