Encyclopædia americana. A popular dictionary of arts, sciences, literature, history, politics and biography, a new ed.; including a copious collection of original articles in American biography; on the basis of the 7th ed. of the German Conversations-lexicon. Ed. by Francis Lieber, assisted by E. Wigglesworth ...

CALCULUS. 395
equation finally obtained. Instead of the marked with characters, and then were
actual increments of the flowing or vari- made of wood. Calculi lusorii or latrones
able quantities, Newton introduced the were counters used in a game, something
Jfuxions of those quantities; meaning, by like backgammon. Calculus Minervx was
fluxions, quantities which had to one an expression employed to signify that
another the same ratio which the incre- the accused escaped by an equal division
ments had in their ultimate or evanes- of the votes of the judges. He was said
cent state. The fluxions of Newton cor- to be acquitted calculo Minervce (by the
responded with the differentials of Leib- vote of Minerva), because Orestes was
nitz; and the fluents of the former with acquitted by the vote of that goddess
the integrals of the latter. The fluxionary when the judges were equally divided.
and the differential calculus are therefore CALCULUS, or STONE, is the name givtwo modifications of one general method. en to all hard concretions, not bony,
The problems which relate to the naxiina formed in the bodies of animals. Calculi
and mininma, or the greatest and least val- may be divided into two classes, accordues of variable quantities, are among the ing as they are found in the gall-bladder
most interesting in mathematics. When or in the urinary bladder. The first are
any function becomes either the greatest called biliar;y calculi, the second urinary
or the least, it does so by the velocity of calculi.-Biliary calculi are of a lamellaits increase or decrease becoming equal ted structure, and are composed of a subto nothing: in this case, the fluxion which stance which is considered, by 1M. Chevis proportional to that velocity must be- reul, as a peculiar principle, which he has
come nothing. By taking the fluxion of named cholesterine (from xoXA, bile, and
the given function, and supposing it equal rs-EpEo, solid). It is described as a white,
to nothing, an equation may be obtained crystalline substance, with much lustre,
in finite termns, expressing the relation of insipid and inodorous, much resembling
the quantities when the function assigned spermaceti, but differing in being less
is the greatest or least possible. The new fusible, and in not forming a soap with
analysis is peculiarly adapted to physical alkalies. It is also converted, by the acresearches. The momentary increments tion of nitric acid, into a peculiar acid,
represent precisely the forces by which called cholesteric acid. This is slightly
the changes in nature are produced; so soluble in water, and forms soluble salts
that this doctrine seemed created to pen- with the alkalies. Cholesterine consists of
etrate into the interior of things, and take carbon 85.095, oxygen 3.025, and hydrocognizance of those powers which elude gen 11.88. It has lately been detected in
the ordinary mnethods of geometrical in- the bile itself, both in that of animals and
vestigation. It alone affords the means of man. Besides cholesterine, biliary
of'measuring forces, when each acts sep- concretions contain a portion of inspissaarately and instantaneously, under condi- ted bile, and the yellow coloring matter
tions that can be accurately ascertained. of the bile in a concentrated state, which,
In comparing the effects of continued ac- from the beauty of its hue, and its permation, the variety of time and circumstance, nence, is much valued as a pigment.and the continuance of effects after their Urinary calculi are of very variable charcauses have ceased, introduce uncertainty, acters and composition. The following
and render the conclusions vague and un- substances enter principally into their
satisfactory. The analysis of infinites composition: uric acid, urate of arlemohere goes to the point; it measures the in- nia, phosphate of lime, phosphate of amtensity or instantaneous effort of the force, monia and magnesia, oxalate of limet
and removes all those causes of uncer- silex, sometimes oxyde of iron and animal
tainty. It is by effects, taken in their matter-these being more or less pure or
nascent or evanescent state, that the true mixed, and being often diversified by meproportion of causes must be ascertained. chanical structure, so as to render it diffiCALCULUs. Little stones, anciently used cult to constitute well-defined species.
for computation, voting, &c., were called The six following species embrace the
calculi. The Thracians used to mark principal varieties of urinary calculi:-1.
lucky days by white, and unlucky by that composed chiefly of uric acid; 2.
black pebbles; and the Roman judges, at that consisting chiefly of the triple phosan early period, voted for the acquittal of phate of ammonia and magnesia; 3. the
the accused by a white, and for condem- bone-earth calculus, formed, almost enlnation by a black calculus: helnce, niger tirely, of phosphate of lime; 4. the fusi
or albus calculus, a favorable or unfavor- ble calculus, composed of the two preable vote. Sometimes the ballots were ceding intermixed; 5. the mulberry cal