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In this article we present the orbits and masses of 20 double stars discovered by P. Couteau at the Nice Observatory (France), namely WDS 01450+2703 (COU 750), 03321+4340 (1688), 03423+3141 (691), 06503+2409 (768), 12409+2708 (596),14138+3059 (606), 15390+2545 (612), 16584+3943 (1289), 17075+3810 (1291), 17221+2310 (415), 18035+ 4032 (1785), 18043+4206 (1786), 19089+3404 (1462), 19180+2012 (321), 20151+3742 (2416), 20216+1930 (327 AB), 21593+4606 (2138), 22077+2622 (537), 22307+1758 (234) and 23199+2844 (439). For two of these stars, COU 750 and COU 1289, these are the first orbits to be published other than IAU Circulars; for the others, previously published orbits are improved on by those presented here. Star masses were in fifteen cases calculated from Hipparcos parallax data, and in the other five from dynamical parallaxes; in all cases, the error is estimated. Some of the other physical and orbital properties of these stars are also discussed.

We report 312 micrometer measurements of 155 visual double stars made with the 50 cm refractor at the Côte D'Azur observatory (Nice, France) and with the 152 cm telescope at Calar Alto observatory (Almería, Spain).

The stellar three-body problem has been approached by directly integrating the equations of motion in the orbital elements. The problem is set up in a barycentric chain with the orbits as perturbed ellipses.

It is a well-known fact that the number of hours of daylight varies with the time of year, except at points on the equator. It is sometimes thought that at latitudes between the Arctic and Antarctic circles the variation takes the form of a sine curve. However there is no theoretical basis for this idea, although it is true that a sine curve may give quite a good approximation.

The idea of a probability generating function seems to be a difficult one for sixth formers, and this may well be because the formalism is introduced too abruptly. The tor zor whatever letter is used in a p.g.f. has to be explained as having “no physical significance”, to quote from a recent M.A. booklet on sixth form probability and statistics. The following gentler approach I have found to lead to better understanding on the part of ‘lower fliers’, and it has the advantage of drawing attention to an underlying structure.