Machines that handle information as measurements of physical quantities are called _analogue_ machines, because the measurement is _analogous_ to, or like, the information. A common example of analogue machine is the _slide rule_. With this we calculate by noting the positions of ruled lines on strips that slide by each other. These strips are made of fine wood, or of plastic, or of steel, in such fashion that the ruled lines will hold true positions and not warp. If we space the rulings so that 1, 2, 3, 4, 5, 6 ··· are equally spaced, then the slide rule is useful for addition (Fig. 3). But if we space the rulings so that _powers_ (for example, powers of two—1, 2, 4, 8, 16, 32 ···) (Fig. 4) are equally spaced, we can do multiplication. The spacings are then according to the _logarithms_ of numbers (see Supplement 2). Multiplication is more troublesome than addition, and so more slide rules are made for multiplication than for addition. [Illustration: FIG. 1. Measurement by doorpost.] [Illustration: FIG. 2. Measurement by string.] [Illustration: FIG. 3. Slide Rule for adding.] [Illustration: FIG. 4. Slide Rule for multiplying.] During World War II, the aiming and firing of guns against hostile planes was done by machine. After sighting a plane, these machines automatically calculated how to direct fire against it. They were much better and faster than any man. These _fire-control instruments_ were analogue machines with steel and electrical parts built to fine tolerances. With care we can get accuracy of 1 part in 10,000 with analogue machines, but greater accuracy is very hard to get. PHYSICAL QUANTITIES Suppose that we wish to make an analogue machine. We need to represent information by a measurement of something. What should we select? What physical thing to be measured should we choose to put into the machine? Different amounts of this _physical quantity_ will match with different amounts of the measurement being expressed. In the case of the doorpost, the string, and the slide rule, the physical quantity is distance. In many fire-control instruments, the physical quantity is the _amount of turning of a shaft_ (Fig. 5). Many other physical quantities have from time to time been used in analogue machines, such as electrical measurements. The speedometer of an automobile tells distance traveled and speed. It is an analogue machine. It uses the amount of turning of a wheel, and some electrical properties. It handles information by means of measurements. The basic physical quantity that it measures is the amount of turning of a shaft. [Illustration: FIG. 5. Measurement by amount of turning of a shaft.] DIFFERENTIAL ANALYZER