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Chapter 1: Problem 51

Historically the English had a doubling system when measuring volumes; 2 mouthfuls equal 1 jigger, 2 jiggers equal 1 jack (also called a jackpot); 2 jacks equal 1 jill; 2 jills \(=\) 1 cup; 2 cups \(=1\) pint; 2 pints \(=1\) quart; 2 quarts \(=1\) pottle; 2 pottles \(=1\) gallon; 2 gallons \(=1\) pail. (The nursery rhyme "Jack and Jill" refers to these units and was a protest against King Charles I of England for his taxes on the jacks of liquor sold in the tavern. (See A. Kline, The World of Measurement, New York: Simon and Schuster, 1975, pp. \(32-39 .\) American and British cooks today use teaspoons, tablespoons, and cups; 3 teaspoons \(=1\) tablespoon; 4 tablespoons \(=1 / 4\) cup. Assume that you find an old English recipe requiring 3 jiggers of milk. How many cups does this represent? How many tablespoons? You can assume that the cups in the two systems represent the same volume.

Short Answer

Expert verified
3 jiggers of milk is \ \frac{3}{8} \ cups and \ 6 \ tablespoons.

Step by step solution

01

- Convert Jiggers to Cups

Start by converting the given 3 jiggers to cups. Use the provided conversion factors: \[ \text{2 jiggers} = 1 \text{ jack} \ 2 \text{ jacks} = 1 \text{ jill} \ 2 \text{ jills} = 1 \text{ cup} \]
02

- Set Up the Conversion Ratios

Convert 3 jiggers to jacks using the ratio \[ 1 \text{ jack} = 2 \text{ jiggers} \] So, \[ 3 \text{ jiggers} = \frac{3}{2} \text{ jacks} \]
03

- Convert Jacks to Jills

Next, convert the value from jacks to jills: \[ 1 \text{ jill} = 2 \text{ jacks} \] Given we have \[ \frac{3}{2} \text{ jacks} \ \text{we need to find jills,} \frac{3 \text{ jacks}}{2 \times 2 \text{ jacks}} = \frac{3}{4} \text{ jills} \]
04

- Convert Jills to Cups

Now convert the value from jills to cups: \[ 1 \text{ cup} = 2 \text{ jills} \] Given we have \[ \frac{3}{4} \text{ jills} \] The conversion gives us: \[ \text{cups} = \frac{3}{4} \text{ jills} \times \frac{1 \text{ cup}}{2 \text{ jills}} = \frac{3}{8} \text{ cups} \]
05

- Convert Cups to Tablespoons

To convert cups to tablespoons, use the conversion factor of the modern system: \[ 1 \text{ cup} = 4 \times 4 \text{ tablespoons} = 16 \text{ tablespoons} \] So, converting \[ \frac{3}{8} \text{ cups} \ \text{ gives us,} \ \frac{3}{8} \text{ cups} \times 16 \text{ tablespoons} = \frac{3 \times 16}{8} = 6 \text{ tablespoons} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Historical Volume Units
In historical English measurement systems, volume measurement was not as straightforward as it is today. Back in the day, they used a doubling system. This means each higher unit of volume was twice as large as the previous one. For example, 2 mouthfuls equaled 1 jigger, and 2 jiggers equaled 1 jack. This pattern continued up through larger units like jill, cup, pint, quart, pottle, and gallon. Understanding these historical units can give us insight into the past, as well as a touch of appreciation for the simplicity of our modern measurements.
The well-known nursery rhyme 'Jack and Jill' even refers to these units of volume, which hints at their familiarity and ubiquitous usage at the time.
Unit Conversions
Unit conversions are a powerful tool that helps us translate quantities from one measurement system to another. When doing conversions, it's crucial to know the exact conversion factors. In our exercise, we start with jiggers and need to convert them to cups and tablespoons. Here's how the conversions work step-by-step:
  • First, convert jiggers to jacks. Since 2 jiggers equal 1 jack, 3 jiggers equal 1.5 (or 3/2) jacks.
  • Next, we convert jacks to jills: 2 jacks equal 1 jill, so 1.5 jacks equal 0.75 (or 3/4) jills.
  • Then, convert jills to cups. Since 2 jills are 1 cup, 0.75 jills equal 0.375 (or 3/8) cups.
  • Finally, convert cups to tablespoons. Since 1 cup equals 16 tablespoons, 0.375 cups equal 6 tablespoons.
These conversions show not only how interconnected different units are but also emphasize the importance of understanding and correctly applying conversion ratios.
Measurement Systems
Measurement systems have evolved significantly over time. Ancient systems, like the English doubling system, were often based on practical, everyday tasks and trades. Today, we predominantly use the metric and imperial systems. These modern systems are standardized and universal, making it much easier to share and compare measurements around the world.
  • The metric system is based on powers of ten, making conversions simpler and more intuitive. For example, 1 liter equals 1000 milliliters.
  • The imperial system, used more commonly in the United States, includes units like gallons, quarts, pints, cups, and tablespoons. Despite being less straightforward than the metric system, it is deeply entrenched in cooking and daily life. Understanding these measurement systems and their conversions enables better cross-cultural communication and precision in various tasks, from cooking recipes to scientific research.

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Most popular questions from this chapter

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