Remarks on Several Subjects. 131 
This arrangement seems preferable to the glass rods used 
in the great English trigonometrical surveys. 
Brown University. March 20th 1824. 
Arr. XI.—Remarks on several papers published in former 
volumes of this Journal, (Communicated by the Author 
to the Edtior.) 
1. Remarks on the “New Algebraical Series,” given by 
Prorrssor imac 9 in page 278 of this Journal for the 
month of February, 1824. 
These series can hardly be called new. since they are noth- 
ing more than the usual expansion of the binominal quan- 
b 
a 
tity 1—kz to the negative fractional power — k ee 
arum Imperialis Pisbionauna” about fifty years since: 
Mr, Wallace supposes, 
fa=1-+-a. —+a(a+h). <5 +a(a-+k) (a+2k). =t+ 
&c. and as the series in the second number of this 
equation is equal to(1—‘z) — 3 expanded into a series by the 
binominal theorem, if we for brevity: put F=(1—éz) * 
it will become riley to F+, whence 
=F 
+5), 
which is ie Tie ato theorem of Mr. Wallace, Yotind by 
the actual multiplication of the series corresponding to 
those functions. In like manner his formulas I], Ul, IV, 
become respectively, 
