The substance of the following paper was delivered as a lecture before the scientific section of the Physical society of Groningen on 14 October 1916. It was meant as a popular exposition of the investigations contained in two more extensive papers published by the Astronomical Laboratory at Groningen, the first of which (by J. C. Kapteyn) appeared in 1903, the second (by J. C. Kapteyn and M. }. van liven) in 1916 'j. In what follows I will refer to these papers as first and second paper. In writing my part of the second paper — and as a matter of fact even already in the first — I tried, as much as was in me. to avoid any superfluous mathematical development. I found however, that, if we wish to develop the theory in as rigourous a form as possible, it is not well possible to avoid some, to the general reader very formidable looking formulae. As I know very well that this fact will be much in the way of a somewhat extensive application of the theory, I resolved, even at the time of writing the second paper, to work out also a popular exposition of the theory in which all such mathematical development should be altogether banished.