At first it might be supposed that the formula of Inductive Logic need only be of this kind: 'These particulars, and all known particulars of the same kind, are exactly included in the following general proposition.' But a moment's reflection on what has just been said will show us that this is not sufficient: for the particulars are not merely _included_ in the general proposition. It is not enough that they appertain to it by enumeration. It is, for instance, no adequate example of Induction to say, 'Mercury describes an elliptical path, so does Venus, so do the Earth, Mars, Jupiter, Saturn, Uranus; therefore all the Planets describe elliptical paths.' This is, as we have seen, the mode of stating the _evidence_ when the proposition is once suggested; but the Inductive step consists in the _suggestion_ of a conception not before apparent. When Kepler, after trying to connect the observed places of the planet Mars in many other ways, found at last that the conception of an _ellipse_ would include them all, he obtained a truth by induction: for this conclusion was not obviously included in the phenomena, and had not been applied to these {111} facts previously. Thus in our Formula, besides stating that the particulars are included in the general proposition, we must also imply that the generality is constituted by a new Conception,--new at least in its application. Hence our Inductive Formula might be something like the following: 'These particulars, and all known particulars of the same kind, are exactly expressed by adopting the Conceptions and Statement of the following Proposition.' It is of course requisite that the Conceptions should be perfectly clear, and should precisely embrace the facts, according to the explanation we have already given of those conditions. 15. It may happen, as we have already stated, that the Explication of a Conception, by which it acquires its due distinctness, leads to a Definition, which Definition may be taken as the summary and total result of the intellectual efforts to which this distinctness is due. In such cases, the Formula of Induction may be modified according to this condition; and we may state the inference by saying, after an enumeration and analysis of the appropriate facts, 'These facts are completely and distinctly expressed by adopting the following Definition and Proposition.' This Formula has been adopted in stating the Inductive Propositions which constitute the basis of the science of Mechanics, in a work intitled _The Mechanical Euclid_. The fundamental truths of the subject are expressed in _Inductive Pairs_ of Assertions, consisting each of a Definition and a Proposition, such as the following: DEF.--A _Uniform Force_ is that which acting in the direction of the body's motion, adds or subtracts equal velocities in equal times. PROP.--Gravity is a Uniform Force. Again, DEF.--Two _Motions_ are _compounded_ when each produces its separate effect in a direction parallel to itself.