But there are a good many general propositions, more or less trustworthy within a certain range of conditions, which cannot be methodically proved for want of a precise principle by which they may be tested; and they, therefore, depend upon Immethodical Induction, that is, upon the examination of as many instances as can be found, relying for the rest upon the undefinable principle of the Uniformity of Nature, since we are not able to connect them with any of its definite modes enumerated in chap. xiii.  Sec. 7.  To this subject we shall return in chap. xix., after treating of Methodical Induction, or the means of determining that a relation of events is of the nature of cause and effect, because the relation can be shown to have the marks of causation, or some of them.

Sec. 5.  Observations and Experiments are the material grounds of Induction.  An experiment is an observation made under prepared, and therefore known, conditions; and, when obtainable, it is much to be preferred.  Simple observation shows that the burning of the fire depends, for one thing, on the supply of air; but it cannot show us that it depends on oxygen.  To prove this we must make experiments as by obtaining pure oxygen and pure nitrogen (which, mixed in the proportion of one to four, form the air) in separate vessels, and then plunging a burning taper into the oxygen—­when it will blaze fiercely; and again plunging it into the nitrogen—­when it will be extinguished.  This shows that the greater part of the air does nothing to keep the fire alight, except by diminishing its intensity and so making it last longer.  Experiments are more perfect the more carefully they are prepared, and the more completely the conditions are known under which the given phenomenon is to be observed.  Therefore, they become possible only when some knowledge has already been gained by observation; for else the preparation which they require could not be made.

Observation, then, was the first material ground of Induction, and in some sciences it remains the chief ground.  The heavenly bodies, the winds and tides, the strata of the earth, and the movements of history, are beyond our power to experiment with.  Experiments upon the living body or mind are indeed resorted to when practicable, even in the case of man, as now in all departments of Psychology; but, if of a grave nature, they are usually thought unjustifiable.  And in political affairs experiments are hindered by the reflection, that those whose interests are affected must bear the consequences and may resent them.  Hence, it is in physical and chemical inquiries and in the physiology of plants and animals (under certain conditions) that direct experiment is most constantly practised.