Length of seconds' pendulum =39.1393 inches;

log 39 1393=1.5926130.

No. of cubic in. in 1 gal. = 277.274; log 277 274-24429091; wt. of 1 cub. in. of water=252-458 grs.; log. 252.458=2·4021892.

Table of the Squares, Cubes, Square and Cube Roots, Reciprocals, Logarithms and Logarithms of Reciprocals of the natural numbers from 1 to 20.

1

10000000 10000000

0909090 10413927 2.9586073

0833333 1.0791812 2 9208198

10 100 1000 3.1622772-154434 11 121 1331 3.316624 2.223980 12 144 1728 3:464101 2.289428 13 169 2197 3.605551 23513350769230 11139434 2 8860566 14 196 2744 3.741657 2:410142 0714285 1.1461280 2 8538720 15 225 3375 3.872983 2.4662120666666

1·1760913 2.8239087

1.2041200 2-7958800 0588235 12304489 2-7695511

0555555 1.2552725 2-7447275

19 361 6859 4.358898 2.6684020526315 1.2787536 2.7212464

20 400 8000 4:472136 2.714417 05

1-3010300|2.6989700

USEFUL ALGEBRAICAL FORMULE.

(x+y)2=x2+2xy+y2; (x+y)3=x3±y3+3xy (x+y).

-

(x+y)(x − y)=x2—y2 ..(x2+xy + y2) (x2 —xy+y3) = x+x2y2+y1.

(x2- xy + y2) (x + y) = x3 + y3.

(x2+xy+y2) (x—y) = x3—y3.

(x + a) (x + b) = x2 + (a + b) x + ab.

2” —y" is integral when n is an even number.

x + y

n

l= a + (n−1)d; s= "2 (a+1)="{2a+(n−1)d};

A.M. = (a + b); G.M. = √ab; H.м. =

2ab

a + b

No. of shot in a square pile of n courses =

12+22+ 32+.

=

+ n2....

n (n + 1) (2n +1) ̧

1.2.3

No. of shot in a triangular pile of n courses =

No. of shot in a rectangular pile of n courses =
(1+m)+2 (2+m) + 3 (3+m) +....n (n+m) =
n (n+1)(2n+1+3m)
1.2.3

No. of permutations of n things taken r at a time =
| n

n-r

No. of combinations of n things taken r at a time=

General term of the expansion of
(α2+α1x+α2x2+azx3+....)" is

log MN = log M + log N; log M÷N = log M-log N;

}

1

; Ma =

loge a

Compound Interest. A=P (1 + r)' = p(1 +

interest is payable n times a year.

Amount of an annuity of a £ in n years =

Present value of same annuity =

=

Sin (90° + A) = cos a ; cos (90° + a) =

sin A; cos (180° + A)

tan (180° + A) = tan a.

sin A; cos (360° — A)

tan A.

Sin A = sin {n + ( − 1)" a} ; cos A = cos (2 nñ ± a} ;

Sin (A + B) = sin A cos B + cos A sin B;
Cos (A + B) COS A COS B sin A sin B.