[2.] G. M. Bond in a lecture delivered before the Franklin Institute, February 29th, 1884.
[3.] Report on Standard Screw Threads, Philadelphia, 1884.
[CHAPTER II]
CALCULATING MACHINES
The simplest form of calculating machine was the Abacus, on which the schoolboys of ancient Greece did their sums. It consisted of a smooth board with a narrow rim, on which were arranged rows of pebbles, bits of bone or ivory, or silver coins. By replacing these little counters by sand, strewn evenly all over its surface, the abacus was transformed into a slate for writing or geometrical lessons. The Romans took the abacus, along with many other spoils of conquest, from the Greeks and improved it, dividing it by means of cross-lines, and assigning a multiple value to each line with regard to its neighbours. From their method of using the calculi, or pebbles, we derive our English verb, to calculate.
During the Middle Ages the abacus still flourished, and it has left a further mark on our language by giving its name to the Court of Exchequer, in which was a table divided into chequered squares like this simple school appliance.
Step by step further improvements were made, most important among them being those of Napier of Merchiston, whose logarithms vex the heads of our youth, and save many an hour's calculation to people who understand how to handle them. Sir Samuel Morland, Gunter, and Lamb invented other contrivances suitable for trigonometrical problems. Gersten and Pascal harnessed trains of wheels to their "ready-reckoners," somewhat similar to the well-known cyclometer.
All these devices faded into insignificance when Mr. Charles Babbage came on the scene with his famous calculator, which is probably the most ingenious piece of mechanism ever devised by the human brain. To describe the "Difference Engine," as it is called, would be impossible, so complicated is its character. Dr. Lardner, who had a wonderful command of language, and could explain details in a manner so lucid that his words could almost always be understood in the absence of diagrams, occupied twenty-five pages of the Edinburgh Review in the endeavour to describe its working, but gave several features up as a bad job. Another clever writer, Dr. Samuel Smiles, frankly shuns the task, and satisfies himself with the following brief description:—
"Some parts of the apparatus and modes of action are indeed extraordinary—and, perhaps, none more so than that for ensuring accuracy in the calculated results—the machine actually correcting itself, and rubbing itself back into accuracy, by the friction of the adjacent machinery! When an error is made the wheels become locked and refuse to proceed; thus the machine must go rightly or not at all—an arrangement as nearly resembling volition as anything that brass and steel are likely to accomplish."[4]