21 After our tables of first review, our rejection or exclusive table, and the first vintage derived from them, we must advance to the remaining helps of the understanding with regard to the interpretation of nature, and a true and perfect induction.
We will treat of:
- Prerogative instances
- the supports of induction
- the correction of induction
- varying the investigation according to the nature of the subject
- the prerogative natures with respect to investigation, or of what should be the first or last objects of our research
- the limits of investigation, or a synopsis of all natures that exist in the universe
- the application to practical purposes, or of what relates to man
- the preparations for investigation
- of the ascending and descending scale of axioms.
22 The first prerogative instance is solitary instance.
Solitary instances are those which exhibit the required nature in subjects that:
- have nothing in common with any other subject regarding the nature in question
- do not exhibit the required nature in resembling subjects
- Those resembling subjects:
- remove prolixity
- accelerate and confirm exclusion, so that a few of them are of as much avail as many.
- Those resembling subjects:
An example is color.
Prisms and crystalline gems yield colors:
- externally on the wall, dews, etc.
These are solitary instances. They have nothing in common with the fixed colors in flowers, metals, woods, etc. except the color itself.
Hence color is nothing but a modification of the image of the incident and absorbed light, occasioned in the former case by the different degrees of incidence, in the latter by the various textures and forms of bodies.
These are solitary instances as regards similitude.
Again, in the same inquiry the distinct veins of white and black in marble, and the variegated colors of flowers of the same species, are solitary instances; for the black and white of marble, and the spots of white and purple in the flowers of the stock, agree in every respect but that of color. Thence we easily deduce that color has not much to do with the intrinsic natures of any body, but depends only on the coarser and as it were mechanical arrangement of the parts. These are solitary instances as regards difference. We call them both solitary or wild, to borrow a word from the astronomers.
2. The migrating instance
23 In these, the required nature passes toward generation, having no previous existence, or toward corruption, having first existed.
In each of these divisions, the instances are always twofold. Or rather, it is one instance:
- first in motion or on its passage, and then
- brought to the opposite conclusion.
- hasten and confirm exclusion
- reduce affirmation, or the form itself, to a narrow compass
for the form must be something conferred by this migration, or, on the contrary, removed and destroyed by it; and although all exclusion advances affirmation, yet this takes place more directly in the same than in different subjects; but if the form (as it is quite clear from what has been advanced) exhibit itself in one subject, it leads to all.
The more simple the migration is, the more valuable is the instance.
These migrating instances are, moreover, very useful in practice, for since they manifest the form, coupled with that which causes or destroys it, they point out the right practice in some subjects, and thence there is an easy transition to those with which they are most allied.
There is, however, a degree of danger which demands caution, namely, lest they should refer the form too much to its efficient cause, and imbue, or at least tinge, the understanding with a false notion of the form from the appearance of such cause, which is never more than a vehicle or conveyance of the form.
This may easily be remedied by a proper application of exclusion.
The following is an example of a migrating instance.
Let whiteness be the required nature. An instance which passes toward generation is glass in its entire and in its powdered state, or water in its natural state, and when agitated to froth; for glass when entire, and water in its natural state, are transparent and not white, but powdered glass and the froth of water are white and not transparent.
What happened to the glass or water in the course of this migration?
- The form of whiteness is conveyed and introduced by:
- the bruising of the glass and
- the agitation of the water
- But only the following have been introduced:
- a diminishing of the parts of the glass and water and
- the insertion of air.
Yet this is not progress toward discovering the form of whiteness, namely, that two bodies, in themselves more or less transparent (as air and water, or air and glass), when brought into contact in minute portions, exhibit whiteness from the unequal refraction of the rays of light.
But here we must also give an example of the danger and caution of which we spoke;
We might think that:
- air is always necessary for producing the form of whiteness, or
- whiteness is only generated by transparent bodies
These are both false.
In fact, all all bodies which are even in such of their parts as affect the sight exhibit transparency, those which are uneven and of simple texture whiteness, those which are uneven and of compound but regular texture all the other colors except black, but those which are uneven and of a compound irregular and confused texture exhibit blackness.
An example has been given, therefore, of an instance migrating toward generation in the required nature of whiteness. An instance migrating toward corruption in the same nature is that of dissolving froth or snow, for they lose their whiteness and assume the transparency of water in its pure state without air.
Nor should we by any means omit to state, that under migrating instances we must comprehend not only those which pass toward generation and destruction, but also those which pass toward increase or decrease, for they, too, assist in the discovery of the form, as is clear from our definition of a form and the Table of Degrees. Hence paper, which is white when dry, is less white when moistened (from the exclusion of air and admission of water), and tends more to transparency. The reason is the same as in the above instances.
3. conspicuous instance or coruscations, or free and predominant instances
24 This is of which we spoke in our first vintage of the form of heat.
These show the required nature in its bare substantial shape.
At its greatest power, emancipated and free from all impediments, or at least overcoming, suppressing, and restraining them by the strength of its qualities;
for since every body is susceptible of many united forms of natures in the concrete, the consequence is that they mutually deaden, depress, break, and confine each other, and the individual forms are obscured. But there are some subjects in which the required nature exists in its full vigor rather than in others, either from the absence of any impediment, or the predominance of its quality. Such instances are eminently conspicuous.
But even in these care must be taken, and the hastiness of the understanding checked, for whatever makes a show of the form, and forces it forward, is to be suspected, and recourse must be had to severe and diligent exclusion.
For example, let heat be the required nature.
The thermometer is a conspicuous instance of the expansive motion, which (as has been observed) constitutes the chief part of the form of heat;
Flame exhibits expansion. Yet its being extinguished every moment stops this progress of expansion.
Boiling water  converts into vapor. But it does not so well exhibit the expansion of water in its own shape.
Red-hot iron and the like are so far from showing this progress, that, on the contrary, the expansion itself is scarcely evident to the senses, on account of its spirit being repressed and weakened by the compact and coarse particles which subdue and restrain it. But the thermometer strikingly exhibits the expansion of the air as being evident and progressive, durable and not transitory.
Take another example. Let the required nature be weight. Quicksilver is a conspicuous instance of weight; for it is far heavier than any other substance except gold, which is not much heavier, and it is a better instance than gold for the purpose of indicating the form of weight; for gold is solid and consistent, which qualities must be referred to density, but quicksilver is liquid and teeming with spirit, yet much heavier than the diamond and other substances considered to be most solid; whence it is shown that the form of gravity or weight predominates only in the quantity of matter, and not in the close fitting of it.