An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

CORRECTIONS
To be made in the PRINCIPLES of thse DIFFERENTIAL CALCULUS.
t'age
9, line 4 from bottom, for log (4), read by (4).
12,.. 2 from bottom,for 4-rr-.AN=47rIP2, reaed2xrA N=7rAP 2.
17,... 15 from top, for Intranscendental, read Interseendental, and the same in
line 6 from the top of the next page.
d3U h2 dnu f2
89,... from top, foar a, read &C. l
d x3.2.3 xn IL1.3 c. i
read diith3_ +&. + /i
WP T. 1~2.3 axnn 1. 23.3. &. n
89,, 2 from top, for ax, read e + 7~'.
d2P d2P
134,... 7 from top, for a read u (
a "(12 a~~
(IdX2 aX2
195,... 10 and 13 from top, Cubical and Semi-cubical miust change places.
19.5, L.. 4 from bottom, for AT=-,,x, read A T - (m +1) x, and in the
next two lines, for AW= (m + 1) y, read AW 1 y, and for
LW= —mny, read L W
200,... 2 from bottom, for x = 0, read x'= 0, and for, axis of x, read axis of y.
224, l.. 1 from top, for Orders of Contact, read Contact and Osculation.
233,... 9 from bottom, for even read odd, and in the next line but one, for odd
read even.
267,... 1 from top, for a9, read a2.
270,... 2 from top, for P x 7-SP cos SPG, read P x = SP cos SPG.
X 1
383,... 5 from top, for 2- read y and in line 3 from bottom for
3; / X'- 2 1 "-~
-- sec, read -C sec2
409,..~ 4 from top, for 24, read 2'6.
417,.. 8 from bottom, for be- ag, read a g - be.
429,... 6 from bottom, for x z and y z, read yz and xz.
442,... 7 from bottom, for XA M l- and Z/P =@, read XAM (p and Z A P -;
and in the next line but two, for r d p, read r dO, and fin' ~ sin O dO0, read
g sin G d p.
447,.. 2 from top, Jbr 1 + P2 + (z'- y) R, read 1 + P 2 + (z'- y) R = 0.
489,... 10 from top, for mm-4, read Xm-4.
493,... 5 from top, for cos 50, read sin 50.
496,... 6 from top, for (a tan 0 + b2), read (a tan 0 + b)2.
d it du
499,... 3 from top, for d-, read
519,... 10 from bottom, for Cube, read Parallelopiped, and the same throughout
the Article.
524,... 7, from bottom, for tangent, read normal, and tie same in tie next line.