fbi os 1 a ae aad 
John Francis Encke. 13 
Encke has also, as already mentioned, devoted special atten- 
tion to the subject of the perturbations of the Minor Planets 
In the Appendix to the Berliner Jahréuch for 1837 and 1838, 
he expounds in detail the method of calculating these perturba- 
tions which had been long used by himself and other German 
astronomers, and which was originally given by Gauss. In this 
method the perturbations of the six elements of the orbit are 
computed for successive equal intervals of time by means of 
mechanical quadratures, and from the values of the elements 
thus found for any given time, the co-ordinates of the body at 
that time are determined. 
Now this method, although a very beautiful one in theory, is 
attended with the disadvantage of requiring the determination 
of double the number of unknown quantities that are really 
wanted, and the calculations which must be gone through con- 
sequently come excessively long. 
As the number of the known minor planets became larger, 
the want of a readier method of computing their perturbations 
became more and more pressin 
Encke was thus impelled to ‘devise a mode of applying the 
method of integration by quadratures directly to the differentia 
equations of motion of the a body, and he published an 
account of this new method in the Proceedings of the Berlin 
Academy for 1851. In this hunt he refers the place of the 
body to rectangular co-ordinates, and he determines the ur- 
bations of its movements during anes short intervals of 
time by a direct computation of the changes — in the 
three co-ordinates by the action of the disturbing plane 
He estimates that the labor of computation is jaca by the 
new method to i see one-half of that Meer by the method 
this paper when he published his own Memoir, —_ — 
he introduced into the Berlin Ephemeris. The history Be astro- 
nomical ephemerides is not a little varied and curious; a concise 
ag of it will be found in the fourth volume of the Memoirs 
yal Astronomical Society, on the occasion of the coun- 
cil of the Society presenting Eackn. through their eames: 
