1826.] Col. Beanfoy's Astronomical Observations, 247 



March, page 173, says, "The fallacy of Mr. Herapath's 

 attempt to prove k = -h- n to be admissible, lies in his 

 erroneous assumption of the * mutual independence ' of the 

 numerator and denominator in the value of d in the present case," 

 that is, of 



{b + c)" 

 2 a (cos. TT + 1)* 



Now in the above-cited Number, p. 328, my words are, using 

 J for the sign of differentiation, " because 8 c and S 5r are 

 mutually independent, this value 



may be any thing." It is, therefore, the differentials of the 

 functional roots of the numerator and denominator which I have 

 called independent, and not, as Mr. Horner attributes to me, the 

 numerator and denominator themselves. 1 have thought it neces- 

 sary to notice this, because Mr. Horner has neither quoted the 

 passage he criticises, nor even once alluded to the place or work 

 where it is to be found. Had he done either, I should have left 

 the simple evidence itself of wliat I have advanced to answer 

 Mr. Horner's positive and groundless charge of " fallacy " and 

 error. I am. Gentlemen, your obedient humble servant, 



J. Herapath. 



Article III. 



Astronomical Observations, 1826. 

 By Col. Beaufoy, FRS. 



Sushey Heath, near Stanmore. 

 Latitude 51o 3T 44'3" North. Longitude West in time 1' 20-93". 



Occultation by the Moon. 

 Feb. 17. Immersion of a small star 7h 2T 30-8" Sidereal Time. 



Eclipses of Jupiter's satellites. 



Feb. 26. Immersion of Jupiter's second j S^ 06' 44" Jlean Time at Bushey. 



satellite ( 8 08 05 ]\Iean Time at Greenwich. 



March 3. Immersion of Jupiter's third ] 1 34 15 Mean Time at Bushey. 



sateHite ) 1 35 36 Mean Time at Greenwich. 



