6. THE METHOD OF RESIDUES.
(1) Principle stated.
As stated by Mill the principle of residue is this: “Subtract from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.”
In simpler form the notion is this: Subtract from any phenomenon those parts of it which are known to be the effect of certain antecedents, and what is left of the phenomenon is the effect of the remaining antecedents.
(2) Principle symbolized.
| Antecedent | Consequent |
| A | x |
| B | y |
| C | z |
The total cause of the phenomenon xyz is ABC.But it is known that the cause of x is the antecedent A; whereas the cause of y is the antecedent B; hence it is concluded that the cause of z is the antecedent C.
(3) Concrete illustrations.
Problem: To find the weight of coal.
| Antecedents | Consequents | ||||||
| Weight of driver, |  | = | 4200 lbs. | ||||
| Weight of wagon, | |||||||
| Weight of coal. | |||||||
| Weight of driver, | | = |  | 200 lbs. | | = 2200 lbs. | |
| Weight of wagon. | 2000 lbs. | ||||||
Hence we may conclude that the weight of coal is 4200 lbs. − 2200 lbs., or 2000 lbs.
Perhaps the most noted instance in history of the application of this method, was the one which resulted in the discovery of Neptune. In calculating the orbit of Uranus, it was found that the combined attractions of the sun and the known planets did not account for the path which Uranus took. There was some unknown influence at work. Assuming that this unaccountable attraction was due to the presence of another planet beyond the orbit of Uranus, an Englishman by the name of Adams, and later the Frenchman Leverrier, were able to indicate by the principle of Residues, the spot where this planet should be. By directing the telescope toward this point, Neptune was discovered.
(4) Distinguishing features:
The phenomenon always occurs,
The antecedents are usually invariable,
Some of the antecedents are known to be the cause of a part of the phenomenon.
(5) Advantages and disadvantages.
The Method of Residues gives three distinct results: First, it tells what is left over after all the other parts of the phenomenon have been explained. Second, it tells how much is left over, and third, it calls attention to the unexplained parts of the phenomenon. For example, in the first concrete illustration, by subtracting the known quantities from the total quantity, what is left over is found to be coal; not only so but we are able to calculate the exact amount of coal. This illustrates the first and second results of the Method of Residues. (Like concomitant variations it is seen that residues is serviceable in given definite quantitative values.) The discovery of Neptune illustrates well the third result of this method; i. e., after accounting for every other force, it was found that there was yet a force at work which had never been explained. It is this third feature of unexplained residues which has placed “Science in its present advanced state.” “Most of the phenomena which nature presents are complicated; and when the effects of all known causes are estimated with exactness, and subducted, the residual facts are constantly appearing in the form of phenomena altogether new, and leading to the most important conclusions.” So says John Herschel. Almost all of the discoveries in astronomy have come about in this way. If a heavenly body does not behave as it should according to the established theory, then either thetheory is wrong or there is some residual phenomenon which needs to be explained. Its suggestiveness is, therefore, the most important function of this method, though this very feature is the one which makes evident its greatest disadvantage. The unexplained residual phenomenon may be very complex and, therefore, a careless observer is apt to overlook a lurking element which in reality is the true cause.