discrepancies between the present tables and observations are not uncommonly outside that limit. The cause is doubtful. Errors of observation to such amount they cannot be; and therefore they can only arise from some wrong method of reduction, or wrongly assumed elliptic elements or masses of the planets, or insufficiently developed formulæ of perturbation, or else they point to some disturbing cause, which still remains obscure, and has not yet been reached by the light of theory. But it ought surely to be deemed the highest problem of astronomy, to examine with the utmost diligence into that which has been often said, but not as yet in every case sufficiently established, whether theory and experience do really always agree. When the solution of this weighty problem shall have been most studiously made trial of, in all its parts, then either will the theory of Newton be perfectly and absolutely confirmed, or else it will be known beyond all doubt that in certain cases it does not suffice without some little change, or that besides the known disturbing bodies there exist some causes of disturbance still obscure." And then after some technical remarks, less connected with our present subject, Bessel goes on to say, “To me, considering all these things together, it appears to be of the highest moment (plurimum valere) towards our future progress in the knowledge of the solar system, to reduce into catalogues as diligently as can be done, according to one common system of elements, the places of all the planets observed since 1750, than which labour, I believe that no other now will be of greater use to astronomy" (..quo labore nullum credo nunc majorem utilitatem Astronomiæ allaturum esse). Such is the opinion of Bessel; but such is not the opinion of an anonymous censor, who has written of us in a certain popular review. To him it seems a matter of little moment that old observations should be reduced. Nothing good, he imagines, can come from the study of those obsolete records. It may be very well that thousands of pounds should continue to be spent by the nation, year after year, in keeping up observatory at Greenwich; but as to the spending 500l. in turning to some scientific profit the accumulated treasures there, that is a waste of public money, and an instance of misdirected influence on the part of the British Association. For you, gentlemen, will rejoice to hear, if any of you have not already heard it, and those who have heard it already will not grudge to hear it again, that through the influence of this Association, what Bessel wished, rather than hoped, is now in process of accomplishment: and that, under the care of the man who in England has done most to show how much may be done with an observatory, that national disgrace is to be removed, of ignorance or indifference about those scientific treasures which England has almost

the

unconsciously been long amassing, and which concern her as the country of Newton and the maritime nation of the world. For the spirit of exactness is diffusive, and so is the spirit of negligence. The closeness, indeed, of the existing agreement between the tables and the observations of astronomers is so great, that it cannot easily be conceived by persons unfamiliar with that science. No theory has ever had so brilliant a fortune, or ever so outrun experience, as the theory of gravitation has done. But if astronomers ever grow weary, and faintly turn back from the task which science and nature command, of constantly continuing to test even this great theory by observation, if they put any limit to the search, which nature has not put, or are content to leave any difference unaccounted for between the testimony of sense and the results of mathematical deduction, then will they not only become gradually negligent in the discharge of their other and more practical duties; and their observations themselves, and their nautical almanacs, will then degenerate instead of improving, to the peril of navies and of honour; but also they will have done what in them lay, to mutilate outward nature, and to rob the mind of its heritage. For, be we well assured that no such search as this, were it only after the smallest of those treasures which wave after wave may dash up on the shore of the ocean of truth, is ever unrewarded. And small as those five seconds may appear, which stir the mind of Bessel, and are to him a prophecy of some knowledge undiscovered, perhaps unimagined by man, we may remember that when Kepler was "feeling" as he said, "the walls of ignorance, ere yet he reached the brilliant gate of truth," he thus expressed himself respecting discrepancies which were not larger for the science of his time:- "These eight minutes of difference, which cannot be attributed to the errors of so exact an observer as Tycho, are about to give us the means of reforming the whole of astronomy.' " We indeed cannot dream that gravitation shall ever become obsolete; perhaps it is about to receive some new and striking confirmation; but Newton never held that the law of the inverse square was the only law of the action of body upon body; and the question is, whether some other law or mode of action, coexisting with this great and principal one, may not manifest some sensible effect in the heavens to the delicacy of modern observation, and especially of modern reduction. It was worthy of the British Association to interest themselves in such a subject: it was worthy of British rulers to accede promptly to such a request.

I have been drawn into too much length by the consideration of this instance of the external effects of our Association, to be able to do more than allude to the kindred instance of the publication of the ob

servations on the tides in the port of Brest, which has, I am informed, been ordered by the French Government, at the request of M. Arago and the French Board of Longitudes, who were stimulated to make that request by a recommendation of the British Association at Edinburgh. Many other topics, also, connected with your progress and prospects, I must pass over, having occupied your time so long; and in particular I must waive what, indeed, is properly a subject for your general committee-the consideration whether anything can be done, or left undone, to increase still more the usefulness of this Association, and the respect and good will with which it is already regarded by the other institutions of this and of other countries. As an Irishman, and a native of Dublin, I may be suffered in conclusion to add my own to the many voices which welcome this goodly company of English, and Scottish, and foreign visitors to Ireland and to Dublin. We cannot, indeed, avoid regretting that many eminent persons, whose presence we should much enjoy, are not in this assembly; though not, we trust, in any case, from want of their good will or good opinion. Especially we must regret the absence of Sir David Brewster, who took so active a part in forming this association: but I am authorized, by a letter from himself, to mention that his absence proceeds entirely from private causes, and that they form the only reason why he is not here. Herschel, too, is absent; he has borne with him to another hemisphere his father's fame and his own; perhaps, from numbering the nebulæ invisible to northern eyes, he turns even now away to gaze upon some star, which we, too, can behold, and to be in spirit among us. other names we miss; but great names, too, are here: enough to give assurance that in brilliance and useful effect, this Dublin meeting of the Association will not be inferior to former assemblings, but will realize our hopes and wishes, and not only give a new impulse to science, but also cement the kindly feeling which binds us all together already.

And

REPORTS

ON

THE STATE OF SCIENCE.

Report on the Recent Progress and Present Condition of the Mathematical Theories of Electricity, Magnetism, and Heat. By the Rev. W. WHEWELL, Fellow and Tutor of Trinity College, Cambridge.

THE trophies of Miltiades would not let Themistocles rest. The trophies of Newton, won at the end of the seventeenth century, made it impossible for the physical philosophers of the eighteenth not to attempt new victories in the application of mechanical principles to the phenomena of the material world. Newton himself had pointed out this as the business of his successors. "I have deduced," says he, at the end of his preface to the Principia, "the motions of the planets by mathematical reasoning from forces; and I would that we could derive the other phenomena of nature from mechanical principles by the same mode of reasoning. For many things move me, so that I somewhat suspect, that all such may depend on certain forces by which the particles of bodies, through causes not yet known, are either urged towards each other and cohere according to regular figures, or are repelled and recede from each other: and these forces being unknown, philosophers have hitherto made their attempts on nature in vain. But I hope that the principles here laid down may supply some light either to this mode of philosophizing or to some one which is more true."

It is usually assumed that Newton's anticipations and wishes have been fulfilled. Several mathematical and mechanical Sciences have since his time made their appearance in the world, claiming to be the younger sisters of Physical Astronomy; like her, fed by exact facts, formed by rigorous principles. Yet their birth and reception have never excited so much general notice as such events might be expected to produce; they have gradually become known to a limited circle of mathematicians, and have not, 1835.

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like the first-born of their race, filled the civilized world with the noise of their fame. Moreover, it is allowed, or rather boasted, that it is only very recently that the mathematical train of reasoning which belongs to several of these new sciences has been rendered complete. It may therefore be of service to examine the claims of these parts of knowledge so far as they profess to be mathematical and mechanical sciences. I hope the undertaking will lose all appearance of presumption, when it is recollected that, in executing it, my main task will be, to study certain mathematical theories and calculations, to look at the recorded facts which are alleged to confirm these theories, and to describe as distinctly as possible the result of the comparison. Such an employment will not lead the writer to trespass on the domain of any one whose business is with new classes of facts, nor tempt him to judge any theory which does not profess to depend entirely on mathematical calculation from measured observations.

The Sciences to which I shall at present direct my attention are those of Electricity, Magnetism, and Heat. These sciences have sufficient connexion, both in the mathematical reasoning by which they have been established and the philosophical principles on which they depend, to make them a fit group to be treated of together. Though they have several features in common, I shall give a brief account of each separately.

Electricity.-Electricity, after being brought under distinct conceptions by Franklin and his contemporaries, was formed into a mathematical science by pinus; the theory of Æpinus was reformed by Coulomb; the calculations which Coulomb could not execute, Poisson in our own time has performed: such are the main steps in the history of electricity as a mathematical science. The theory of electricity of Epinus assumed one electric fluid only it invested this fluid with these two properties, that its particles repelled each other with forces increasing with a diminution of their mutual distance; and that its particles attracted the particles of all other bodies with a force following the same law. On these suppositions (assuming also the difference of conductors and electrics with respect to the easy transfer of the fluid) a great part of the facts of electricity by induction, and of electrical attraction and repulsion, could be explained in a manner strictly mechanical.

But taking the whole of the experimental facts, a third supposition was found to be necessary;-that the particles of all bodies repel each other with the same force with which they attract the electric fluid. For, without this addition to the theory, how could two negatively electrified bodies repel each other with the same force as two positively electrified, since by supposition