Then the resultant loss to the community from the latter part will be

(1 −

x) {m C2 + n [A, − (q − 1) C',']} + (1 − x') (m' C2 q + n'. A2) ;

and from the former part, at beginning of 1st year,

at beginning of 2nd year,

λm C2 + \'m'C2;

xmC2.q + x'm'C2 . q + λn {A, − (q − 1) C‚'} + X'n‚Â ;

at beginning of 3rd year,

\mÑ¿q°v + \'m'Ñ„q°v + \n {A‚q − (qv − 1) C{q} + \'n‚Âqv;

at beginning of x + 1th year,

{(\m + X'm') C2qv*-1 + (λn + X'n'v*-1) A ̧ − λn (qv*−1 − 1) C,'} (qv ̈ ̄ï)•-1. Hence, during the x+1th year, the whole possible loss of income will

be :

From expenditure of Proprietor, a {1 + 7 =-1(qv

From Capital removed or destroyed whose expended without accumulation,

profits would have been

(m + m'q) C, − n (q − 1) C',' + (n + n') A ̧ + λ {n (q − 1) C – m C, - nA2} -X' (m'C2q + n'A2).

From Capital removed or destroyed whose profits would have been accumulated,

{λ [(m C, − n C2') qv2-1 + n (Ci + A‚)] + X' (m ̊C,q + n1 A‚) v*~'} (qv)·-1. The greatest possible loss in this year, when v, l, m', n', λ', each = 1, and .. m, n each = 0, will be

a + (m + m,q) C2 − n (q − 1) C + (n + n') A ̧.

As far as the destruction of Capital is concerned the investigation, of course, applies to the case of proprietors becoming absentees, and not of their continuing so.

The general effects of absenteeism may be thus enunciated. There will in all cases be a loss to the home-revenue in those direct taxes whose payment can be evaded by absence. There will, whenever there are duties on importation and not on exportation, be a further loss of the

в в 2

import-duty paid on the foreign productions which the proprietor consumed when at home.

Beyond this there will be a diminution of the aggregate income of the community whenever the capital that is disengaged by the absenteeism is forced into less profitable employments than those it previously occupied, and in no other case. When therefore the country from which the proprietor absents himself exports raw produce, there will generally, though not necessarily, be a loss beyond the loss to the revenue, and this loss will be accompanied by a general increase of rental. When it exports manufactures, there will not in general be any loss beyond that to the

revenue.

There will however in all cases be this further and very important effect: though the income which the proprietor removes may be replaced, it must be replaced by labour, and there will therefore be substituted for the leisure class, which a part of that income maintained, a class who must by their own exertions produce the incomes on which they subsist; and there is nothing in the conditions of the problem to limit the extent to which the subdivision of income may, among the members of this class, be carried, or to fix the minimum that may be enjoyed by each.

It is necessary to the truth of these results, that the withdrawal of the proprietor should cause no removal of capital, that any part of the proprietor's income which was not expended should still be saved at home, and that no part should have been consumed without calling for the employment of capital.

In applying the result to any particular country, the first step is to decide how far, in the case of its absentees, these conditions are fulfilled; if they be not fulfilled, or if the individuals who remove had in any degree the qualities of productive labourers, the wealth of the community must be impaired by their absence; and the injury is capable of increasing with time to an indefinite extent.

CAIUS COLLEGE, CAMBRIDGE,

March 16, 1840.

J. TOZER.

XII. Demonstration that all Matter is heavy. By the Rev. WILLIAM WHEWELL, B.D. Fellow of Trinity College and Professor of Moral Philosophy.

[Read February 22, 1841.]

THE discussion of the nature of the grounds and proofs of the most general propositions which the physical sciences include, belongs rather to Metaphysics than to that course of experimental and mathematical investigation by which the sciences are formed. But such discussions seem by no means unfitted to occupy the attention of the cultivators of physical science. The ideal, as well as the experimental side of our knowledge must be carefully studied and scrutinized, in order that its true import may be seen; and this province of human speculation has been perhaps of late unjustly depreciated and neglected by men of science. Yet it can be prosecuted in the most advantageous manner by them only for no one can speculate securely and rightly respecting the nature and proofs of the truths of science without a steady possession of some large and solid portions of such truths. A man must be a mathematician, a mechanical philosopher, a natural historian, in order that he may philosophize well concerning mathematics, and mechanics, and natural history; and the mere metaphysician who without such preparation and fitness sets himself to determine the grounds of mathematical or mechanical truths, or the principles of classification, will be liable to be led into error at every step. He must speculate by means of general terms, which he will not be able to use as instruments of discovering and conveying philosophical truth, because he cannot, in his own mind, habitually and familiarly, embody their import in special examples.

Acting upon such views, I have already laid before the Philosophical Society of Cambridge essays on such subjects as I here refer to; especially a

memoir "On the Nature of the Truth of the Laws of Motion," which was printed by the Society in its Transactions. This memoir appears to have excited in other places, notice of such a kind as to shew that the minds of many speculative persons are ready for and inclined towards the discussion of such questions. I am therefore the more willing to bring under consideration another subject of a kind closely related to the one just mentioned.

The general questions which all such discussions suggest, are (in the existing phase of English philosophy) whether certain proposed scientific truths, (as the laws of motion,) be necessary truths; and if they are necessary, (which I have attempted to shew that in a certain sense they are,) on what ground their necessity rests. These questions may be discussed in a general form, as I have elsewhere attempted to shew. But it may be instructive also to follow the general arguments into the form which they assume in special cases; and to exhibit, in a distinct shape, the incongruities into which the opposite false doctrine leads us, when applied to particular examples. This accordingly is what I propose to do in the present memoir, with regard to the proposition stated at the head of this paper, namely, that all matter is heavy.

At first sight it may appear a doctrine altogether untenable to assert that this proposition is a necessary truth: for, it may be urged, we have no difficulty in conceiving matter which is not heavy; so that matter without weight is a conception not inconsistent with itself; which it must be if the reverse were a necessary truth. It may be added, that the possibility of conceiving matter without weight was shewn in the controversy which ended in the downfall of the phlogiston theory of chemical composition; for some of the reasoners on this subject asserted phlogiston to be a body with positive levity instead of gravity, which hypothesis, however false, shews that such a supposition is possible. Again, it may be said that weight and inertia are two separate properties of matter: that mathematicians measure the quantity of matter by the inertia, and that we learn by experiment only that the weight is proportional to the inertia; Newton's experiments with pendulums of different materials having been made with this very object.

I proceed to reply to these arguments. And first, as to the possibility of conceiving matter without weight, and the argument thence deduced, that the universal gravity of matter is not a necessary truth, I remark, that it is indeed just, to say that we cannot even distinctly conceive the contrary of a necessary truth to be true; but that this impossibility can be asserted only of those perfectly distinct conceptions which result from a complete developement of the fundamental idea and its consequences. Till we reach this stage of developement, the obscurity and indistinctness may prevent our perceiving absolute contradictions, though they exist. We have abundant store of examples of this, even in geometry and arithmetic; where the truths are universally allowed to be necessary, and where the relations which are impossible, are also inconceivable, that is, not conceivable distinctly. Such relations, though not distinctly conceivable, still often appear conceivable and possible, owing to the indistinctness of our ideas. Who, at the first outset of his geometrical studies, sees any impossibility in supposing the side and the diagonal of a square to have a common measure? Yet they can be rigorously proved to be incommensurable, and therefore the attempt distinctly to conceive a common measure of them must fail. The attempts at the geometrical duplication of the cube, and the supposed solutions, (as that of Hobbes) have involved absolute contradictions; yet this has not prevented their being long and obstinately entertained by men, even of minds acute and clear in other respects. And the same might be shewn to be the case in arithmetic. It is plain, therefore, that we cannot, from the supposed possibility of conceiving matter without weight, infer that the contrary may not be a necessary truth.

Our power of judging, from the compatibility or incompatibility of our conceptions, whether certain propositions respecting the relations of ideas are true or not, must depend entirely, as I have said, upon the degree of developement which such ideas have undergone in our minds. Some of the relations of our conceptions on any subject are evident upon the first steady contemplation of the fundamental idea by a sound mind: these are the axioms of the subject. Other propositions may be deduced from the axioms by strict logical reasoning. These propositions are no less necessary than the axioms, though to common minds their evidence is very different. Yet as we become familiar with the steps by which these ulterior truths are