upon the Antique Dials. 121 



clination less than D', is always less than the abscissal distance of points in 

 the hectemoria, and their rectilineal chords at the same declination. 



These conclusions might also have been readily established by means of 

 the differential calculus ; but that is perhaps, at present, unnecessary. 



The deviation of these latter hectemorial chords might also be investi- 

 gated, and its maximum determined. The two maxima are not, however, 

 at the same distance from the equator, though not very distant from it. 

 The better method, however, in practice, is to find the value of D for the 

 value of L already determined in the several curves ; and then find for this 

 value of D the value of L in the chord. The difference is very nearly 

 the greatest error ; which, converted into equinoxial time, gives the error 

 of such a dial reckoned from apparent time. The computations will be 

 given in the subsequent part of the dissertation. 



XXXII. 



As a proof that DELAMBRE did not even imagine the possibility of 

 finding a co-ordinate equation of the hectemoria, we may quote the last pas- 

 sage which has perhaps been penned at least the last published on this 

 subject. It is taken from the " Corrections" to the second volume of his 

 History of Ancient Astronomy. By a system of experiments he arrived 

 at some general notion of the form of the curve upon a dial for the latitude 

 of 66 30' ; and the advantages of the present system of investigation cannot 

 probably be better shewn than by a comparison with that passage *. 



" Depuis 1'impression de ce chapitre (that on the Ancient Dials), pour 

 mieux connaitre la Jigure de ces lignes, j'ai calcule un cadran pour le 

 cercle polaire ; j'en ai determine tous les points horaires pour toutes les decli- 

 naisons de degre en degre, et mmee pour quelques fractions de degre de 

 23 a 23 28' ; il en est resulte que les lignes horaires pour cette latitude 

 ont a fort peu pres la figure du signe d'integration J] c'est-a-dire que dans 

 le voisinage du solstice d'hiver, la ligne a une courbure sensible ; que pen- 

 dant la plus grande partie de 1'annee, la ligne est sensiblement droite, et 

 qu'elle acquiert de nouveau une corbure, mais moins sensiblement vers le 



* Tome ii., at the end of the Table of Contents. 



