His observations of the great comet of January 1672 supplied the basis of modern cometary astronomy.
The prize was again awarded to Lagrange; and he earned the same distinction with essays on the problem of three bodies in 1772, on the secular equation of the moon in 1774, and in 1778 on the theory of cometary perturbations.
In the Berlin Memoirs for 1778 and 1783 Lagrange gave the first direct and theoretically perfect method of determining cometary orbits.
It has not indeed proved practically available; but his system of calculating cometary perturbations by means of "mechanical quadratures" has formed the startingpoint of all subsequent researches on the subject.
In addition to magnesium and sodium the lines of potassium, lithium and also the carbon flutings exhibited in cometary spectra, has been seen.