172 
MINUTES OE PROCEEDINGS OF 
Let 1 be the density, for barometer 30°, thermometer 60°, 
S a a at the time of the experiment, 
R a resistance found, 
R' n corrected resistance. 
1 
: S :: JR ’: JR; 
8. Resistance expressed in Terms op the Differences 
of the Times. 
(Article 64.) 
This article begins by proving equation (A), and then finds another 
value for “ Mx+ni” by Taylor's theorem, which must be taken for granted 
by those who have not read the calculus. They should, however, study 
the article, or, at any rate, the concluding paragraph of it, as it forms 
the connecting link between Mr. Bashforth's experiments and theories. 
/\ / }/ / 
The symbol means the limit of when l is diminished, 
and n 
n 
n 
A hi x 
II 
6. 
u xH i = u x + nAu x + 
n — 1 
1 . 2 
A?u x + 
i — 1 . n — 2 
1 .2.3 
. (4 
Also by Taylor's theorem, 
Ux+nl — u x + 
7 d 2 u x n 2 l 2 , 
nl + !Zr 0 + 
dhi x nH 3 
' TX "3 
+ &c. 
(*) 
Equate co-efficients of “ n ” in these identities. 
I ^ - JA H* + JA- &c„ . (ff) 
ax 
P = A \u, - A .*#, + ^A *u. - if A H, + if fA«M, - &c. (It) 
6. This is made more convergent by putting (< x — l” for “ x” in (e). 
AUx-l —” U x ^x—l) 
ii x == u x ~i -f* An x -i, 
A%*= A?u x ~i + A?u x -i, &c. } &c., 
= A^-i-^A^.; + -&A+ & c.,.(//) 
by simple substitution* 
