Application of the Fluxional Ratio, ^c. lOiS 



this problem was transmitted to him for the purpose of being com- 

 municated to the American Academy of Arts and Sciences, and 

 I have never yet become acquainted with any other method simi- 

 lar to it. But rdeem it unimportant to substantiate the claim of 

 priority in time. Who first thought of an improvement is to the 

 public a matter of trivial consequence, and even to the inventor himself, 

 provided he can bring before the public a useful invention, which he 

 can honestly call his own. The writer of the VII. Article in No. 47 

 of the Journal of Science seems to have overlooked the improvement 

 contained in the article he alluded to. It consists in making the first 

 meridian bisect the first side in the calculation, by means of which 

 the two areas of opposite values, formed by the bisection, balance 

 and destroy each other. Hence the first product vanishes, and the 

 number of products, which in the example he has given is four, is 

 reduced to three. The assumption " that the first meridian may 

 pass through any station of the field wherever it may be convenient 

 to commence either the measurement or calculation" is common to 

 both our methods, and lays the foundation for the algebraical pro- 

 cess of adding and multiplying, recommended for its '• simplicity and 

 the universality of its application." If, therefore, we commence the 

 calculation with that side which causes the meridian line to divide the 

 field into nearly equal parts, as the writer proposes j and if, instead 

 of making the meridian line pass through the angular point, we make 

 it bisect the first side, we shall arrive, as I conceive, at the highest 

 improvement of which the problem is susceptible. 



Corrections. — Page 303, Vol. xxiv. 1. 11 fr. hot. for EG read FG. 



1 s. 



« 306, " 1. 5 fr. bot. for — ^read — -. 



8a^' 8a2 



" " " in the diagram (Fig. 4.) for I read H. 



L 1 



« 307, • " 1. 8 fr. bot. for2ay read 



3 



1 1 



« 309, " 1. 9 fr. bot. for - -3 read — . 



