Mr DE morgan, ON THE GENERAL PRINCIPLES, &c. 



291 



nature, one ingredient of which is the assumption*, on grounds of pure thought, that the will- 

 be shall agree with the has-been, and it shall be impossible that a stone shall refuse to fall to 

 the ground. But the impossibility is no more than the impossibility of simultaneously obeying 

 our law and disobeying it. These remarks are not out of place in an age in which we are 

 told on high authority that we ought to set out in all physical investigations with a clear view 

 of the naturally possible and impossible. We cannot do this even in logic and mathematics, 

 the only true fields of the possible and impossible. A clear view of the usages of nature must, 

 of course, existing up to a certain point, be augmented by reflexion, or further experiment, or 

 both, up to a higher point : but no length of usage gives any odds in favour of the impossi- 

 bility of the contrary. I am now setting out on a species of physical investigation not 

 merely without a clear view of the possible and impossible, but by reason of the absence of 

 that view, and with no other object than its attainment. The question is, a certain law of 

 physics being given, to lay down the postulates on which it is founded, and to decide whether 

 any contradiction of them be possible in thought, or whether all contradiction be impossible. 



There are two subdivisions of our subject. In the first are all the cases in which actions 

 are distinguished by magnitude and direction, as in the cases of translation, velocity, rotation 

 about axes passing through one point, pressures producing either equilibrium or motion, 

 moments of rotation producing either equilibrium or motion. In the second are rotations, &c. 

 about parallel axes, pressures applied at diff'erent points in parallel directions, &c. In both 

 these subdivisions there is a common form, with much variety of matter. In order to separate 

 the common form, it will be necessary to invent terms which are independent of the material 

 distinctions of the different cases. 



By a tendency I mean anything which has both magnitude and application. By appli- 

 cation I mean anything which, not giving the notion of magnitude, or of more and less, but 

 containing the notion of opposition, makes the following postulates intelligible and true. In 

 one of the subdivisions above named, different applications mean different directions : in the 

 other, different points of application of the same direction. But it may be that there are yet 

 other aggregations in which the word application has other meanings. Again, by the aggregate 

 of two tendencies, I mean a third tendency which is singly equivalent to the first two acting 

 jointly : and by equivalence I mean any notion which, subject to the condition that things 

 equivalent to the same are equivalent to one another, also makes the four postulates intelligible 

 and true. And, so long as the postulates exist, it is not necessary that the two tendencies 



• All our perfect knowledge of the future is comprised in the 

 certainty that it will, in due time, become the past, if existence 

 continue, or, taking the Kantian doctrine, if intelligent exist- 

 ence continue. We add to this our mental conviction that 

 what always has been will continue to be ; nor can 1 deny that 

 those who thus think have been justified by the result up to 

 half-past eleven a.m. on the 9ih of February, 1859. And if the 

 laws of nature should continue unaltered till noon, the addi- 

 tional half hour will add a trifle to the^brce of their data. But 

 the theory of probabilities, the only protector from false con- 



clusions in such a case as t'^e present, gives it as an undoubted 

 result that, no matter how many our observations of per- 

 manence from moment to moment may be, so long as they are 

 finite in number, we cannot, from these observations alone, 

 draw any probability, however small, in favour of an unlimited 

 continuance. Except by knowledge of continuance ab infinito, 

 we cannot acquire any well grounded faith in continuance ad 

 infinitum, from any observation and reasoning grounded on 

 tliat observation alone. 



