Take for example a block Fig A block has a certain length l , width w and height h. Volumes can also be expressed in cubic decimetres dm 3 , cubic metres m 3 , etc. The volume of the water is thus 1 litre or 1 dm 3. When the bottle of water is emptied on a table, the water will spread out over the table and form a thin water layer.
The amount of water on the table is the same as the amount of water that was in the bottle; being 1 litre. The volume of water remains the same; only the shape of the "water body" changes see Fig. One litre of water spread over a table A similar process happens if you spread irrigation water from a storage reservoir over a farmer's field. All the water from the reservoir is spread over a field of 1 hectare.
Calculate the water depth which is the thickness of the water layer on the field, see Fig.
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A volume of m 3 of water spread over an area of one hectare The formula to use is Calculate the volume of the water in m 3 , with the help of Fig. Related to irrigation, the volume of water is usually expressed in litres l or cubic metres m 3 and the time in seconds s or hours h. The flow-rate is also called discharge-rate. What is the flow rate of this pump? The formula used is For larger flows, e. In relation to agriculture, the words percentage and per mil will be met regularly.
For instance "60 percent of the total area is irrigated during the dry season". In this Section the meaning of the words "percentage" and "per mil" will be discussed. A graph is a drawing in which the relationship between two or more items of information e. To this end, two lines are drawn at a right angle.
The horizontal one is called the x axis and the vertical one is called the y axis. Where the x axis and the y axis intersect is the "0" zero point see Fig. The plotting of the information on the graph is discussed in the following examples.
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A graph 1. Each week the height of the plant is measured. One week after planting the seed, the plant measures 2 cm in height, two weeks after planting it measures 5 cm and 3 weeks after planting the height is 10 cm, as illustrated in Fig. Measuring the growth rate of a maize plant These results can be plotted on a graph. The time in weeks will be indicated on the x axis; 2 cm on the axis represents 1 week.
The plant height in centimetres will be indicated on the y axis; 1 cm on the axis represents 1 cm of plant height. After 1 week the height is 2 cm; this is indicated on the graph with A; after 2 weeks the height is 5 cm, see B, and after 3 weeks the height is 10 cm, see C, as shown in Fig. Now connect the crosses see Fig. The line indicates the growth rate of the plant; this is the height increase over time. Growth rate of a maize plant It can be seen from the graph that the plant is growing faster and faster during the first week 2 cm and during the third week 5 cm ; the line from B to C is steeper than the line from D to A.
From this crossing follow the dotted line to the left until the vertical axis is reached. Now take the reading: 7. This height has not been measured in reality, but with the graph the height can be determined anyway. Graph of the growth rate of a maize plant 1. Suppose the outside temperature always in the shade is measured, with a thermometer, every two hours, starting at midnight and ending the following midnight. Now indicate with crosses the values from the table above on the graph paper and connect the crosses with straight dotted lines see Fig.
The Language of the Modhupur Mandi (Garo), Volume 1
Graph showing temperature over 24 hours; mistake 16 hour reading At this stage, if you look attentively at the graph, you will note that there is a very abrupt change in its shape around the sixteenth hour. That does not make sense, and the reading of the thermometer at the sixteenth hour must have been wrong. Most Mandi speakers in Bangladesh do not even know the older Garo numbers above the word for 'five'.
The numbers from 'one' to 'five' are used without classifiers in only two circumstances: First, classifiers can be omitted when counting: sa, gin-i, git-tam , but speakers often include classifier even then: sak-sa, sak-gin-i, sak-git-tam 'one person, two people, three people'. Since Bengali numbers are so often used in Modhupur, counting with Mandi numbers is not common, and counting for very long is impossible, but A'chik speakers count easily with A'chik numbers, with or without classifiers.
The second use of numbers without classifiers is as ordinals meaning 'first, second, third' and so forth, or 'first one, second one, third one'. These are constructed by adding gip-a to the cardinal number: sa-gip-a 'first, first one', gin-i-gip-a 'second, second one' etc. These are nouns and they can be used in all nominal constructions. In view of the limited use of the older Garo numbers, it is surprising that the system of classifiers has survived in such a healthy state. The numbers in A'chik and in Mandi are given in Table 10—1.
They are given in the table without classifiers, but in use they are almost joined to a classifier. A few older people in Modhupur still remember an alternative counting system that is based on cycles of twenty rather than ten. This, and similar systems, are heard occasionally in the Garo Hills, but they have not found their way into orthographic Garo or into the speech of most educated people, so this way of counting is probably on its way to extinction.
These numbers are rarely used, and the only ones at all likely to be heard are the even multiples of This dying system is shown in Table 10—2. In addition to the numbers, a handful of other morphemes can be used with classifiers in the position where a number would otherwise go. This can describe events happening jointly to everyone or to events that effect each one separately, but in the same way. It is likely to refer to a larger group of individuals than -prak : ak-rik-kit 'each person', do'-mok mang-rik-kit 'each goat'; a'-ba dam-rik-kit 'each field'.
This is similar in meaning to -rik-kit but it is likely to imply a smaller number, and it is more focused on individual acts and events: sal-prak 'each day'; kan-prak-ko ron'-bo 'give one of each. Gip-in, prak and rik-kit can be considered to be numbers when they are used with classifiers. Unlike the numbers from 'one' to 'five', however, these three words are used in other ways as well, so they are not always found with a classifier. Classifiers specify both the nature and the size of the unit being counted.
This is obvious in the case of measures such as ke-ji- 'KG, kilogram', mail- 'mile', and kap- 'the amount held in a cup', as in cha kap-sa 'one cup of tea'.
It not quite so obvious for the classifiers that are used for people, animals and physical objects. The natural translation for a-chak mang-sa is 'one dog' but on the analogy of cha kap-sa 'one cup of tea', we might translate the phrase more literally as 'one mang of dog'. This is made more plausible by such phrases as ma-su ju-ra-sa 'one team of cattle, one pair of cattle' in which the classifier ju-ra- specifies two animals rather than just one.
If ju-ra- is a measure for two animals it is reasonable to consider mang- to be a measure for one animal—-the amount of animal stuff contained in one animal. Similarly, Man-de sak-sa has the literal meaning of 'one sak of humanity' or 'the amount of humanity that constitutes one person'. One way to understand the role of classifiers is to realize that languages like Garo do not make such a clear distinction between "mass nouns" and "count nouns" as English does.
In English, mass nouns such as water, milk, meat, iron, and sand cannot be counted without the help of some measure word: one puddle of water, two pounds of meat, three piles of sand. Count nouns, on the other hand, require no classifier in English, but can be counted directly: one person, five animals, three stars, four songs. In Garo all nouns act like English mass nouns, and all require some unit of measurement whenever their amounts are counted.
Classifiers are not simply assigned to nouns in an arbitrary way. Rather, classifiers convey important meanings. It is often the case that a single noun can be used with more than one classifier, and each classifier contributes a different meaning: te'-rik rong-sa 'one banana, one rong- of banana', te'-rik pang-sa 'one banana tree', te'-rik gal-sa 'one hand small bunch of bananas', te'-rik ol-sa 'one arm large bunch of bananas', te'-rik ke-ji-sa 'one kilogram of bananas'. When all these are considered together, it is not unreasonable to understand rong- as specifying the amount of banana stuff held by a single fruit, just as ke-ji- specifies the amount of banana stuff held in a single kilogram.
The meanings that classifiers convey make it easy, when the context is clear, to use a numeral i.
In answer to a question about how many bananas are wanted, it would be entirely natural to say ke-ji-gin-i 'two kilograms' or rong-bong-a 'five fruits'. If the particular type of person is not known or is known so well that it need not be repeated, it is entirely appropriate to say sak-gin-i sok-ba-jok 'two people arrived', where a classifier is used, but no noun. Since sak- is used only for people, there is no possibility that this will be misunderstood as meaning two animals.
Indeed, man-de sak-gin-i is completely redundant since man-de , the noun meaning 'people', conveys no more information than sak-.
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Of course, if it is important to specify a particular kind of person one is talking about, it is necessary to use a noun: me'-chik sak-gin-i 'two women'. I will define the class of numeral classifiers to include all morphemes that can be prefixed to the numbers, and any combination of such a classifier with a number will be considered a "numeral".
This is a somewhat broader definition for classifiers than has sometimes been used for other languages, but it is convenient for Garo. Defining classifiers this way does mean that the class includes several somewhat different kinds of morphemes. Most typical of what have generally been called classifiers are those that are used when counting discrete physical objects that have enduring shapes.
These are the sorts of things that are named by count nouns in English, and it is the classifiers used for these objects that are most foreign to languages like English.
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