78 The Comd of\S21. 



of heat, attraction, and other phaenomena, has just finished a 

 discovery of the greatest unportance in the mathematics. It 

 is well known that Newton and succeeding mathematicians have 

 extended their inquiries merely to fluxions and fluents or dif- 



_L.j _i_2 j-3 j-.j, 



ferentials and integrals of the form rf— , d— , d— , d^ , &c. 

 with indices in whole numbers only ; and to functions of the 



same form ^— , ^— , &c. regarding others, with even sim- 

 ple rational fractions, as transcending the powers of analysis. 

 Mr. Herapath has however discovered a method of great sim- 

 plicity and beauty, which is applicable to differentials, integrals, 

 and fimctions of every possible form ; whether the indices be 

 whole, fractional, rational, irrational, or even functional, and 

 imaginary. It has besides the advantage of not being confined 

 to any particular species of calculation ; but is investigated on 

 those general principles, that it extends itself with equal facility 

 to every kind of calculus that is or appears likely to be disco- 

 vered ; and if the direct calculus be possible, it always makes 

 the inverse or any real function of it equally possible. 



THE COMET OF 1822. BY M. NICOLLET*. 



The comet discovered at Marseilles on the 12th of May 

 last, by M. Gambart, was observed at Paris for the first time 

 on the 1 8th of the same month. Since that time the astrono- 

 mers of the Royal Observatory have never ceased to watch its 

 course. The fine weather having permitted us to make a great 

 number of observations, I have been able to calculate and to 

 deduce the parabolic orbit as follows : 



The course by the perihelium 6th May 1822, at 3 hours 

 5 minutes and 1 1 seconds in the morning. 



Distance of the perihelium ... ... 0.504'220 



Inclination of the orbit 53° 34' 3" 



Longitude of the ascending node ... Ill" 30' 50'" 

 Longitude of the perihelium in the orbit 192° 48' ^S" 

 The heliocentric movement — retrograde. 

 This comet does not resemble in its elements either the 

 comet of 1204, or any of the comets that have been observed 

 up to the present time. It is very small, and has very little ap- 

 pearance of a tail. Its distance from the earth increases every 

 day. On the 18th of May this distance was nearly equal to 

 that of the sun; but on the 3 1st of that month it was one-half 

 of the distance further from the eardi. Tlie comet is not vi- 



* Annalrs dc Chiinic for May 18-22. 



sible 



