2.4.7 The Spring Balance

cision, and accuracy. Linear spring balances, such as those used for weighing fish on a boat, also have built-in friction from the parts that rub on the scale face.

Despite their general lack of accuracy, their popularity is understandable. Their limited accuracy and reliability are more than sufficient, however, for the demands of grocery stores or bathroom scales. To use anything more complicated or expensive when the need is not justified is a waste of time and money.

There is an interesting story, from the gold rush days, about people taking advantage of the inaccuracies peculiar to the spring balance. As you go from the north or south pole toward the equator, the centrifugal force caused by the earth spinning increases, which counter-effects the force of gravity. In addition, the earth is somewhat oblate (due to centrifugal force) and the effects of gravity are somewhat less at the equator because the earth's surface is farther from the earth's center. Thus, using a spring balance, an object weighs less at the equator than it does at a pole. During the California gold rush, some people would purchase gold in California, using a spring balance for weight measurement, and sell the same gold in Alaska using the same balance. Because the gold weighed more in Alaska, it was worth more. Thus, a (good) living was made by buying and selling gold at the same price per ounce. Such a practice would not be possible with a two-pan balance.

Some highly accurate spring balances are typically made out of fused silica (quartz glass) and used in vacuum systems. The use of fused silica has two advantages. For one, the material is extremely nonreactive. Thus it is unlikely to corrode as a metal might when in contact with acids and/or oxidizers. In addition, glass is considered perfectly elastic until the point of failure. Thus, there are no hysteresis problems.

These balances simply are a hanging coil of fused silica with a glass basket on the bottom. An optical device with a calibrated vertical measurement system sights on a point on the glass basket. A calibrated weight is placed within the basket, and the optical device is moved down so the system can sight on the same point and the new calibration is noted. Several more weight measurements are made to verify linearity. By observing the amount of spring travel for a given amount of weight, very accurate measurements can be made. Unfortunately, the amount and type of supporting equipment for this type of spring balance are expensive.

2.4.8 The Lever Arm Balance

The lever arm balance compares the mass of an object to the mass of calibrated weights. There are two major types of lever arm balances. The equal arm balance [see Fig. 2.23(a)] works by directly comparing a known weight to an unknown weight, both of which are placed an equal distance from the fulcrum. Once in balance, there is a one-to-one ratio (of the weights) between the unknown and known weights. A well-made balance of this type is capable of high accuracy and preci-

Fig. 2.23 Two basic lever arm designs.

sion. The disadvantage of this type of balance is that many standard weights are needed to provide the balance with its full range of weighing capabilities.

The unequal arm balance [see Fig. 2.23(b)] compares an unknown weight to the distance a known weight is to the fulcrum. When weighing an object, the further the balance weight is moved from the fulcrum, the heavier the object. The primary advantage of the unequal arm balance is that it needs only a limited number of calibrated weights. The disadvantage of this type of balance is that its accuracy is limited by how many divisions can accurately be defined between the units on the balance arm.

Another problem of the equal arm balance is ensuring that the weight is directly under its pivot point. This alignment is important because the pivot point helps define how far the weight is from the fulcrum. As the unequal arm balance demonstrates, variations in the distance a weight is from the fulcrum can change its effective weight. In the 17th century, a mathematician named Roberval devised a balance arm that guaranteed that weights would act as if they were under the pivot point, regardless of how far they were placed from the fulcrum. The basic configuration of a balance utilizing the Roberval principle is shown in Fig. 2.24, and the

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Fig. 2.24 The Roberval principle balance. From The National Bureau of Standards Handbook 94, Figure 5, "The Examination of Weighing Equipment" by M.W. Jensen and R.W. Smith.,U.S. Printing Office, 1965, p. 155. Reprinted courtesy of the national Institute of Standards and Technology, Technology Adminstration, U.S. Department of Commerce. Not copyrightable in the United States.