COM 
take three points at once, and so to form 
triangles; to lay down three positions of a 
map, to be copied at once, &c. 
Compasses heam, consist of a long 
branch or beam, carrying two brass cursors, 
the one fixed at one end, the other sliding 
along the beam, with a screw to fasten it on 
occasion. To the cursors may be screwed 
points of any kind, whether steel, for pen- 
cils, or the like. It is used to draw large 
circles, to take great extents, &c. See 
Instruments, mathematical. 
Compasses, caliber. See the article Ca- 
user. 
Compasses, clockmakers’, are joined, like 
the common compasses ; with a quadrant or 
bow, like the spring compasses ; only of dif- 
ferent use, serving here to keep the instru- 
ment firm at any opening. They are made 
very strong, with the points of their legs of 
well-tempered steel, as being used to draw 
lines on pasteboard or copper. 
Compasses, elliptic, consist of a cross with 
grooves in it, and an index which is fasten- 
ed to the cross by means of dove-tails that 
slide in the grooves; so that when the in- 
dex is turned about, the end will describe 
an ellipsis, which is the use of these com- 
passes. 
COMPENSATION, in horology, is a 
contrivance in the pendulum of a clock, by 
means of which, while the expansion from 
increase of temperature depresses the cen- 
tre of gravity of some of the vibrating parts, 
other parts are made to ascend nearer the 
centre of suspension, or else to draw up 
the pendulum, so as to preserve the centre 
of oscillation of the compound pendulum at 
an invqjiable distance ; and in consequence 
to keep all the vibrations to the same time. 
Compensation pendulums have the part 
which expands upwards made either of 
brass, or zinc, or some very expansible me- 
tal, while the descending parts are usually 
iron or steel, and some of these Ijave leaves 
or machinery in their construction: in 
others, the compensation-part does not vi- 
brate, but serves to alter the length of a 
simple pendulum ; and in others a fluid is 
used, most commonly mercury. See Ho- 
rology and Pendulum. 
COMPENSATION balance. See Ho- 
rology. 
COMPLEMENT, in astronomy, the dis- 
tance of a star fium the zenith : or the arch 
comprehended between the place of the 
star above the horizon and the zenith. 
Complement, in geometry, is what re- 
mains of a quadrant of a circle, or of 90", 
COM 
after any certain arch has been taken away 
from it. Thus, if the arch taken away 
be 40", its complement is 50 : because 
50 40 z= 90. The sine of the complement 
of ail arch is called the cosine, and that of 
the tangent, the co-tangent, &c. 
Complement of the course, in naviga- 
tion, is the number of points the course 
wants of 90", or eight points, viz. of a quar- 
ter of the compass. 
Complement of life, in the doctrine of 
annuities, denotes the difference, according 
to M. De Moivre’s hypothesis, betvveen 
the age of any given life and 86 years. Thus 
the complement of a life of 45 years is 41 : 
of 30 it is 56. According to this hypothe- 
sis, the probabilities of life, through every 
period of existence, are supposed to de- 
crease in an arithmetical progression, so 
that out of 86 persons just born, one is sup- 
posed to die every year, till at the end of 
86 years, which is considered as the utmost 
limit of human life, the last survivor be- 
comes extinct. On this supposition the 
number of years that a person has an equal 
chance of surviving, is made to be the 
same with the expectation which M. De 
Moivre finds to be equal to half the comple- 
ment of life : so that if the age be 4, the 
82 
expectation will be = 41 : if the age be 
4 
82, the expectation will be - = 2 ; while 
the chance that a child aged 4 survives 41 
41 
years is — , and the chance that a person 
aged 82 survives 2 years is f. Since each 
of these fractions is z= i, it follows that the 
one has an equal chance of living 41, and 
the other of living 2 years. But by tables 
founded on observation, the expectation of 
these lives are 40f and while the chance 
of the younger living 40f years is 464, and 
the chance of the elder living 3i is 53 : that 
is, in the first instance, the chance is less, 
and in the second greater, than an even one, 
that a person lives such a number of years 
as shall be equal to his expectation, which 
proves the incorrectness of M. De Moivre’s 
hypothesis. 
Complements in a parallelogram, are the 
two smaller parallelograms made by draw- 
ing two right lines through a point in the 
diagonal : and parallel to the side of a pa- 
rallelogram. In every parallelogram these 
complements are equal. 
COMPLEX terms, or ideas, in logic, are 
such as are compounded of several simple 
ones. 
