1816.] Royal Institute of France. 149 
or orthogonal route, but that which takes place in the direction of a 
meridian or parallel. In the first case we cut all the parallels at 
right angles, in the second all the meridians. Every other route 
would traverse both under angles almost always oblique. The 
spiral considered by M. Legendre had been already analyzed by 
M. Duscjour, who had given the formula of the variable angle, 
and remarked further, that this curve would cross the equator in 
different points at each demi-revolution which it made round the 
spheroid. It was from this singular property, as well as from the 
continual variation of the angle, that it appeared to us to merit the 
name of Loxodromic. ‘The Loxodrome of sailors, on the contrary, 
makes a constant angle with all the meridians which it crosses, and 
it is not the shortest road between two given points. Here, then, 
are two striking differences between the two curves. Hence they 
ought not to be confounded. But the danger is not great, as the 
one is only employed in navigation and the other in geodesy; so 
that the difference of the problems points out sufficiently the choice 
of the formulas. For the Loxodromic of sailors, see the 36th 
chapter of our Treatise on Astronomy. 
Precipuarum Stellarum imerrantium Positiones medi ineunte 
Seculo 19, ex Olservationibus habitis in Specula Panormitana ab 
Anno 1792 ad Annum 1814, ex regia Tygographia Mititart.—This 
new work of M. Piazzi is dedicated to the Institute of France, of 
which the author is one of the oldest correspondents. In this new 
edition, in which the number of stars is 7646, without counting 
those whose positions have not yet received the greatest degree of 
precision, M. Piazzi has not chosen to adopt any thing which he 
had not himself verified. He determined the right ascension of the 
fundamental stars by a direct comparison with the sun. The others 
have been deduced, as usual, by the difference of their passage over 
the meridian, observed a great number of times, and the mean 
result has been taken. Unfortunately, the size of the volume, and 
unfavourable circumstances, have obliged him to suppress all these 
comparisons, and even the observations on which they are founded. 
The declinations suppose the mean refractions of the fifth book of 
the work on the observatory of Palermo, the latitude 38° 6’ 41”, 
and a total precession of 58°388”, which leaves 50:2066” for the 
precession in longitude. 
The annual motions comprehend the proper motions, whenever 
it was possible to find in the ancient catalogues positions sufficiently 
certain. 
The notes which accompany this catalogue offer many curious 
remarks on the stars, whose motions had not yet been observed, or 
of which the brilliancy appears to increase and diminish periodi- 
cally. 
This extract, which we have been obliged to abridge, will be 
sufficient to show how precious this new catalogue must be to astro- 
homers, who already made constant use of the first edition. 
The following memoirs have been approved by the Class :— 
