Application of the Fluxional Ratio, &c. 103 
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 I deem 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 ean 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; and if, instead 
of making the meridian line pass through the angular point, we make 
it bisect the first side, we shall arrive, as J conceive, at the highest 
improvement of which the problem is susceptible. - 
Covititions —Page 303, Vol. xxiv. 1. 11 fr. bot. for — read — 
+9 306, &é - 
Sa? 
ee _ in the diagram (Fig. 4.) fic read H.. 
2a%n 
e304; “1.8 fr. bot. for2a? Ze? read 
“<* 308, oh, 9 fr. bot. aes aa-8 read a 
