CAL 
CALCULATION, the act of computing 
several sums, by adding, subtracting, multi- 
plying, or dividing. See Arithmetic. 
An error in calculation is never protect- 
ed or secured by any sentence, decree, &c. 
for in stating accounts it is always under- 
stood that errors of calculation are ex- 
cepted. 
Calculation is more particularly used 
to signify the computations in astronomy 
and geometry, for ' making tables of loga- 
rithms, ephemerides, finding the time of 
eclipses, &c. 
Calculation, in music : many eminent 
mathematicians suppose that a good ear and 
strong hand on instruments, where the tone 
depends on the performer, are the musician’s 
best guide, without having recourse to cal- 
culation. On this subject the celebrated 
D’Alembert says, “ It is an achievement of 
no small importance to have deduced the 
principal facts to a system from one experi- 
ment, viz. the harmonies of a single string. 
Calculation may, indeed, facilitate the in- 
telligence of certain points of theory, such 
as the relation between the tones of the 
gamut and temperament ; but the calcula- 
tion necessary for treating these two points 
is so simple and trifling that it merits no 
display. Let us not, therefore, imitate those 
musicians who believe themselves geome- 
tricians, or those geometricians who fancy 
themselves musicians, and in their writings 
heap figures on figures, imagining, perhaps, 
that this display is necessary to the art,” 
See D’Alembert. 
CALCULI, biliary, in chemistry, are 
small stones found in the gall-bladder, and 
probably formed by the changes produced 
on the bile while it remains in that organ. 
These are not uniform in their appearance, 
but vaiy in colour, texture, and hardness. 
The most common are of a lamellated struc- 
ture, resembling spermaceti, disposed in 
crystalline lamin®, which have a close re- 
semblance in their properties to Adipocire, 
which see, Biliary calculi are soluble in oil 
of turpentine ; but more completely in the 
fixed alkalies, by which they ai-e reduced to 
a saponaceous state, Ammonia, unless in 
the boiling state, has little effect upon them, 
Nitric acid dissolves them, forming a liquid 
similar to the oil of camphor, which be- 
comes concrete, and without and crystalline 
structure, and is more soluble in ether, and 
CAL 
the alkalies than the original matter. This 
substance is contained in a greater or less 
degree in nearly all the human biliary cal- 
culi ; hence they partake of its properties ; 
are fusible, inflammable, and more or less 
soluble in the re-agents which dissolve it. 
Other calculi are occasionally found in the 
gall-bladders of quadi'upeds, which have 
been supposed to consist of inspissated bile ; 
they are irregular, and of various forms. 
Gall-stones in general are distinguished for 
their lightness and inflammability, few of 
them being so heavy as to sink in water, 
and when put to a lighted candle they 
usually melt like wax, and kindle with a 
bright flame, attended with an ammoniacal 
smell. 
Calculi, urinary, concretions formed m 
the kidney or bladder ; and composed in 
greater or smaller proportions, of the fol- 
lowing substances, viz. uric acid, urate of 
ammonia, phosphate of lime, phosphate 
of ammonia and magnesia, oxalate of lime , 
silex and animal albumen. These principles 
being more or less common, and in different 
proportions, give rise to numerous varie- 
ties. 
The calculi most common are those com- 
posed of uric acid ; they are generally of a 
brown or yellowish colour, smooth on the 
surface, and with a texture compact or 
radiated ; they are perfectly soluble in alka- 
line solutions, and give a red colour when 
treated with nitric acid. Dr. Wollaston 
has arranged the urinary calculi under four 
species, viz. t, The uric acid concretion , 
2. The fusible calculus, or phosphate of 
ammonia and magnesia : 3. The mulberry 
calculus, or oxalate and phosphate of lime ; 
And, 4, the bone earthy calculus, composed 
of phosphate of lime, which forms the basis 
of bone. Fom’croy and Vauquelin have 
given a different arrangement : they affirm 
that in all calculi there exists a quantity of 
animal matter wdiich appears to connect 
their particles ; but independently of this, 
which is common to the whole, they com- 
pose three genera ; the first contains three 
species, each formed of one ingredient : 
the second comprises seven species, formed 
of two ingredients each : and in the third 
there are two species, consisting of three 
or four ingredients ; this system is exhibited 
in the following table : 
