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N explaining what we understand by science, in the first number of this monthly, it was stated to consist in accurate as contrasted with lax and careless thinking. We had not then space to show how a great deal of the knowledge that is truly recognized as scientific may be still so loose and imperfect as to be misleading. Let us, therefore, briefly consider this aspect of the case.

There are two stages in the history of science, and two states of mind among so-called educated people, which correspond to them. The first stage of all science consisted simply in recognizing the properties of bodies so as to identify them. The characters were made out which distinguished this thing from that, and one kind of effect from another. The first thing was to determine the qualities of objects, and this was the work in the early or qualitative stage in the progress of each science. But, qualities being ascertained, the next and inevitable step was to bring them under the operation of mathematics, which deals with the laws of quantity. First, it was asked, What are the properties or effects? and next, What are their degrees, or what quantities are involved in given results? This implies exact measurement, and is known as the quantitative stage of science.

For example, bodies, which burn and produce heat, have the property of combustibility; but the next question is, How much heat will different bodies produce in burning? It is a quality of vinegar to unite with soda, and this was ascertained in the qualitative infancy of chemistry, but how much vinegar will combine with a given amount of soda was only determined with the development of quantitative chemistry. It is a quality of animals that they exhale carbonic-acid gas in respiration, but, when this was known, it became necessary to know the rates of exhalation in the different tribes, and the variations of these rates in sex, age, activity, sleep, and disease. It is a quality of ideas that they cohere with each other, forming groups and trains by which thinking becomes a connected and orderly process; but it is also a fact that these cohesions are of unequal degrees of strength, and this gives rise to a kind of quantitative psychology, which is only imperfect because we lack the means of exact measurement.

Now, qualitative information is the first indispensable step in the growth of knowledge, and is just as truly “science” as the knowledge of quantities; but it is not the whole of science. Qualitative chemistry must precede and underlie quantitative chemistry, and so with other departments. But, to suppose that a mere knowledge of qualities may pass for science is an error leading to the worst practical consequences. Current scientific knowledge, however, is very much of this qualitative sort. As it was first in the order of development, because it is simplest, it is also most widely diffused for the same reason. This is one of the things that is meant in saying that people think vaguely and loosely, and reason wildly, upon subjects in which science is involved. For every thing in practical and applied science turns at last on the question, How much? It is not enough to know that a given substance will produce a given effect; we must know the degree or amount of effect before we can build upon it. It is this scientific smattering with qualitative notions that exposes people to all forms