142 Royal Astronomical Society, 



series of arithmetical operations of extreme simplicity, only a few 

 analytical expressions of by no means a complicated character being 

 employed in the computation. 



*2. It affords the means of immediately correcting the quantities 

 employed in computing the disturbing forces for each successive in- 

 terval, and thereby leads rapidly to results of great accuracy. 



3. Since the perturbations of x,y, z are of the same order as 

 those of the polar coordinates, they serve to afford unequivocal 

 indication of the extent to which the intervals of quadrature ought 

 to be diminished. It is well known that the method of the varia- 

 tion of constants may assign enormous perturbations to the elements, 

 while at the same time the actual perturbations may be very in- 

 significant. 



The original researches of M. Encke on this subject are contained 

 in Nos. 791, 792, and 814 of the Astronomische Nachrichten. It 

 may be mentioned that a similar method had been already proposed 

 by Mr. G. P. Bond, of Cambridge, U.S. M. Encke, however, did 

 not become acquainted with this circumstance until he had completed 

 his investigation. 



Extract of a Letter from Professor Secchi to Mr. Grant, F.R.A.S. 



"Rome, May 8, 1852. 



*' Allow me, dear Sir, to present you my most sincere thanks for 

 the kind letter you addressed to me, and for the valuable present of 

 your book, which was joined with it. I would have written to you 

 sooner, but I waited a little while, to be able to inform you of some 

 researches which I have undertaken on the distribution of heat at 

 the surface of the sun, and on the constitution of the lunar geology, 

 which 1 hope will be well received by you. 



"As to the first subject, you know that it is generally admitted 

 that light is brighter at the centre of the solar disc than at the 

 edges. M. Fizeau proved that the same diminution subsisted for 

 chemical radiation, and I obtained a confirmation of it in the 

 Daguerreotypes of the sun taken during the last solar eclipse. But 

 I had no proof that the fact would be the same with heat, although 

 this was highly probable. I tried, therefore, to fill this blank, and 

 have instituted a series of researches on the temperature of the 

 diflferent parts of the solar disc. I have been thus led to some 

 interesting conclusions quite new to me ; but before exposing 

 them, I think it necessary to say something on the method of con- 

 ducting the experiments. A thermo-electric pile, belonging to a 

 very nice Melloni's apparatus, was attached to the telescope of 

 our equatoreal, and fixed on the prolongation of its optical axis at 

 a distance of about 15*=™ from the eye-piece : the image of the sun, 

 magnified by the eye-j)iece itself, was thus projected on the pile, 

 and had a diameter of 12'"" nearly. When a leaf of white paper 

 was put in the place *of the pile, the image was perfectly defined, 

 and the spots neatly terminated. By a diaphragm; the aperture of 

 which was 4'""™ broad and 15'"'" long, disposed parallel to the edge 

 of the disc, a small portion of the sun's image, which was about 

 1' of arc broad and 4' long, was allowed to radiate on the pile. 



