CHA 
CH A 
except in cases of charity, nor for lands un- 
der 40s. per annum. 
CHANCRE. See Surgery. 
CHANGES, in arithmetic, the variations 
or permutations of any miraber of things, 
with regard to their position, order, &c. 
The method of finding out the number of 
clianges, is by a continual multiplication of 
all the terms in a series of arithmetical pro- 
gressionals ; whose first term, and common 
difference, is unity, or 1 ; and last term the 
number of things proposed to be varied ; 
fiz- 1X2X3X4X5X6X7, &c. as 
will appear from what follows ; 
1. If the tilings proposed to be varied 
are only two, they admit of a double posi- 
tion, as to order of place, and no more. 
Thus, =2 = 1X2. 
2. And if three things are proposed to be 
varied, they may be changed six several 
Ways, as to their order of places, and no 
more. 
For, beginning with 1, there ? 1 . 2 . 3 
will be ^1.3.2 
Next, beginning with 2, there ? 2 . 1 . 3 
will be S 2 . 3 . 1 
Again, beginning with 3, it will 13.1.2 
be 5 o . 2 . 1 
Which, in all, make 6, or 3' times 2 j viz. 
1 X 2 X 3 = 6. 
3. Suppose 4 things were supposed to 
be varied, then they admit of 24 several 
changes, as to tlieir order of different 
places, 
ri.2.3.4 
For, beginning the order I 1 
with 1, it will be J 1 
] 1 
Here are 6 different changes. 1 
Ll 
.2.4.3 
.3.2.4 
.3.4.2 
.4.2.3 
.4. 3. .2 
And for the same reason there will be 6 
different changes when 2 begins the order, 
and as many when 3 and 4 begin the order ; 
which, in all, is24 = lX2X3x4. And, 
by this method of proceeding, it may be 
made evident, that 5 things admit of 120 
several variations or changes ; and 6 things, 
of 720. 
Thus, if it be required, in how many dif- 
ferent ways seven persons may be placed 
at table, the answer islx2X3x4x 
5 x 6 X 7 = 5040. The following table 
will shew the several variations and changes 
of any number of things up to 12. 
The number 
of tilings to 
be varied. 
How the varia- 
tions are pro- 
duced. 
The different va- 
riations each of 
tlie proposed 
numbers can ad- 
mit of. 
1 
1 X 1 
= 1 
2 
1X2 
= 2 
3 
2X3 
= 6 
4 
6X4 
= 24 
5 
24 X 5 
= 120 
6 
120 X 6 
= 720 
7 
720 X 7 
= 5040 
8 
3040 X 8 
= 40320 
9 
40320 X 9 
= 362880 
10 
362880 X 10 
= 3628800 
11 
3628800 X 11 
= 39916800 
12 
39916800 X 12 
— 479001600 
They may be thus continued on to any 
assigned number. Suppose to 24, the num- 
ber of letters in the alphabet, which will 
admit of 62044a401 733239439360000 seve- 
ral variations. 
Since on 12 bells there would be, by 
the table, 479001600 changes : suppose 10 
changes to be rung in a minute, that is 
10 X 12, or 120 strokes in a minute, it 
would even then require upwards of 90 
years to ring over all the changes on the 
12 bells. 
Changes of quantities, in algebra, the 
same with what is otherwise called combi- 
nation. See Combination. 
CHANNEL, in hydrography, the deep- 
est part of a river, harbour, strait, &c. 
which is most convenient for the track of 
shipping ; also an arm of the sea running 
between an island and the main or conti- 
nent, as the British Channel. 
CHAOS, in natural history, a genus of in- 
sects, belonging to the order Zoophyta. 
The body has no covering ; no joints ; no 
external organs of sensation. There are 
five species, most obtained by infusion of 
different vegetables in water, and seen 
only by the aid of the microscope. 
CHAPLAIN, an ecclesiastic who offi- 
ciates in a chapel. The King of Great Bri- 
tain hath forty-eight chaplains in ordinary, 
usually eminent doctors in divinity, who 
wait four each month, preach in the cha- 
pel, read the service to the family, and to 
the King in his private oratory, and say- 
grace in the absence of the clerk of the 
closet. Besides, there are twenty-four 
chaplains at Whitehall, fellows of Oxford 
or Cambridge, who preach in their turns, 
and are allowed thirty pounds per annum- 
each. According to a statute of Hen. VIII. 
the persons vested with a power of retain- 
