Marbles in a jar

Elemental Solids The other elements are solids in their elemental forms at 25 °C. The solid metals contain large numbers of atoms packed together much like marbles in a jar (see Figure 3.13). 

Two kinds of numbers are encountered in scientific work exact numbers (those whose values are known exactly) and inexact numbers (those whose values have some uncertainty). Most of the exact numbers we will encounter in this book have defined values. For example, there are exactly 12 e s in a dozen, exactly 1000 g in a kilogram, and exactly 2.54 cm in an inch. The number 1 in any conversion factor, such as 1 m = 100 cm or 1 kg = 2.2046 lb, is an exact number. Exact numbers can also result from counting objects. For example, we can count the exact number of marbles in a jar or the exact munber of people in a classroom. 

For example, consider a jar of marbles and the probability that you ll pick a red one. Or you look at the seats in an airplane and determine the probability of your getting a particular seat. Or how about the number of boys in a family How does a number of boys become a probability problem (Well, boys can be a problem — I don t know about the probability part.)... 

The Problem You have a jar that contains 10 red, 20 yellow, and 50 green marbles, and you take a marble out of the jar and put it in your right pocket without looking at the color. Now you draw another marble out of the same jar and put it in your left pocket. What is the probability that both marbles are red ... 

Right away, you should be thinking about how unlikely the probability is that both marbles are red. The red marbles are the fewest in the jar. The probability should be pretty low. To do the problem, first find the probability of drawing a red marble out of the 80 marbles, and then find the probability of drawing another red marble out of the 79 remaining marbles. 

In other words, atoms are the basic stuff of nature, the primary and most foundational, and all of matter was built up of these primordial germs. The suggestion that the structure of atoms was hard (since they were indivisible) implied that atoms could not fill all space and there had to be regions that did not contain atoms. This would be like filling a jar with marbles. Where Aristotle and Plato objected to the very idea of a void, the Epicureans were comfortable with the idea, and it provided an easier way to describe motion. Since the void could not oppose motion, atoms were free to move about, while a universe filled with matter suggested that motion was unnecessarily complicated or might even be impossible. Lucretius went on to say ... 

Many perfumers prepare this soap in iron kettles with a double bottom, heated by steam some use siLyer kettles, which are preferable, because in them the soap will retain its whiteness. The engravingPig. 26 represents a jacket or kettle with a donble bottom, heated by steam. This kettle is of tinned copper, and may be also used to purify tallow and greases. The operation lasts in all ftom seven to eight hours. When the soap is entirely cooled dowl pour it into large stone jars, in which it is kept for use. Soft soap, as obtained by the saponification of fatty matters by potash, has not that bright nacreous pearly) appearance required for the toilet. To obtain it in this state it is ground in a marble mortar and aromatised with oil of bitter almonds. 

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