Chemical Computations and Errors

Chemical Computations and Errors

Chemical Computations and Errors

Chemical Computations and Errors

Excerpt

When you can measure what you are speaking about and express it in numbers, you know something about it, and when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. It may be the beginning of knowledge, but you have scarcely in your thought advanced to the stage of a science.

--LORD KELVIN.

A physical quantity is measured in terms of an arbitrarily chosen standard unit. The measurement is expressed as the ratio of the magnitude of the quantity to the magnitude of the standard unit. It is interesting and often highly entertaining to choose at random several commonly used units of measurement and trace their formulation, as well as the etymology of their names. (See Chapter VI for some examples.) It is only in this way that one can grasp the rôle that fate or chance has played in fixing for us our scientific heritage that must serve as the unconsciously perceived background of all scientific thought and action.

The conception of number to express a ratio is very old compared with our civilization. The system of numerical symbols which we use was taken from the Arabs. The early Arabic mathematicians had formulated rules for combining these numerical symbols to obtain quickly and easily other ratios that could have been apprehended by the senses through the tedious processes of counting with the fingers and toes. Meanwhile, our less sophisticated ancestors were fumbling with the awkward and inadequate set of Roman numerals that hinder even the simplest addition or subtraction. The rules for combining numbers to deduce other ratios have been reduced to concise form and were taught to us in grammar school under the name of arithmetic.

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