Page:The American Cyclopædia (1879) Volume III.djvu/575

CALCULATING MACHINES CALCULI 569 ing the same problem and trisecting an angle. Some mechanical devices for assisting in arith- metical computation were also in use at a very early age ; but these were exceedingly limited in their operations, and therefore of little prac- tical advantage. The same may be said of the more ingenious contrivances devised in the be- ginning of the 17th century, Gunter's scale and Napier's bones. John Napier, who was proba- bly the first man to suggest the modern nota- tion of decimal fractions, and whose invention of logarithms was well called canon mirificus, devised two modes of mechanical computation, one by means of square rods engraved with the Arabic figures, the other by means of circular plates. Napier's discovery of logarithms was made by Edmund Gunter the basis of a very simple machine, consisting merely of a straight line graduated to logarithms, but marked with the corresponding numbers. Addition and subtraction can be performed upon this line by taeans of a pair of dividers, and the correspond- ing number by the side of the line will be pro- ducts, quotients, and factors. But Pascal, in 1642, at the age of 19, invented the first arith- metical machine properly so called. This ma- chine was improved by L'Epine and Boitissen- deau about 80 years afterward, but it never came into practical use. It consisted essen- tially of short barrels, upon whose circumfer- ence the 10 figures were inscribed, covered by a box, one figure alone of each barrel being visible through a row of little windows on the upper surface of the box. These barrels were so connected that 10 revolutions in one pro- duced one revolution in the next, the revolu- tions of the first barrel being performed by hand to correspond with the numbers to be added. Subtraction was performed by the device of having each figure on the wheels ac- companied by a smaller figure, such that the sum of the two was equal to 9. Whatever number was added to the large figures was of course subtracted from the smaller. In 1673 Leibnitz published a description of a ma- chine which was much superior to that of Pascal, but complicated in construction and too expensive for the work it was capable of performing, which was only that of arithmet- ical addition, subtraction, multiplication, and division. But the glory of Pascal and Leibnitz, as inventors of calculating machinery, has been eclipsed by Charles Babbago and by G. and E. Scheutz. The British government be- gan in 1822 to build a machine under Mr. Bab- bage's direction. Early in 1833 a small por- tion of the machine was put together, and was found to perform its work with the utmost precision. In 1834 Mr. Babbago commenced the design of a far more powerful engine, but nothing lias been done toward its construction. These machines of Babbago are enormously ox- pensive, $80,000 having been spent in the par- tial construction of the first. They are de- signed for the calculation of tables or series of numbers, such as tables of logarithms, of sines, &c., and are based upon the fact that if we make a new table consisting of the differences between the successive numbers of the first table, then a third consisting of the differences of the successive numbers of the second, then a fourth in like manner from the third, and so on, we shall at length generally obtain a table in which the numbers are all alike. If we had then given to us the first number in each of these tables, we might, beginning with the table in which all the numbers were alike, get back to the original table by a simple process of addition. Thus, by this principle of differ- ences, the computation of all tables is, in gen- eral, reduced to a process of addition. The machine prepares a stereotype plate of the table as fast as calculated, so that no errors of the press can occur in publishing the result of its labors. Many incidental benefits arose from the invention, the most curious and valuable of which was the contrivance of a scheme of mechanical notation by which the connection of all parts of a machine, and the precise action of each part, at each instant of time, may be rendered visible on a diagram, thus enabling the contriver of machinery to devise modes of economizing space and time by a proper ar- rangement of the parts of his invention. This mechanical notation of Babbage (" Philosophi- cal Transactions," 1826) is for an inventor of machinery what the notation of algebra is to the student of geometry. The machine in the Dudley observatory, Albany, N. Y., was in- vented by G. and E. Scheutz of Stockholm, and finished in 1853. The Swedish govern- ment paid $20,000 as a gratuity toward its construction. The inventors sought to attain the same ends that Mr. Babbage had attained, but with simpler means. Their engine pro- ceeds by the method of differences, calculating to the 15th place of decimals, and stamping the eight left-hand places in lead, so as to make a stereotype mould from which plates can be taken by either a stereotype or electro- type process, ready for the printing press. It can express numbers either decimally or sexa- gesimally, and prints by the side of the table the corresponding series of numbers or argu- ments for which the table is calculated. It has been employed at Albany in calculating a table of the true anomaly of Mars for each tenth of a day. CALCULI, stone-like concretions which form in different parts of the body, often about some undissolved particle in the fluid, which holds the matter of the concretion in solution, and again as a deposit upon some hard surface, as the tartar which collects upon the teeth. In the intestines the concretionary deposits are sometimes mechanical agglutinations of dry fibrous particles, as the fine down of the oat gathered about a piece of bone or stone of some fruit, and intermixed with layers of phosphate of limo. The fluids of the body may deposit concretions in most of the vessels, organs, and tissues. They are left by the blood in the arte-