It will be well, in weighing the value of the book, to consider it first with reference to the purpose of its author, though a judgment based on that consideration alone would not be a fair one. These, then, are the words in which Mrs. Somerville presents the scope and purpose of her work :

'A complete acquaintance with physical astronomy can only be attained by those who are well versed in the highest branches of mathematical and mechanical science : such alone can appreciate the extreme beauty of the results, and the means by which these results are obtained. Nevertheless, a sufficient skill in analysis to follow the general outline, to see the mutual dependence of the several parts of the system, and to comprehend by what means some of the most extraordinary conclusions have been arrived at, is within the reach of many who shrink from the task, appalled by difficulties which perhaps are not more formidable than those incident to the study of the elements of every branch of knowledge, and possibly overrating them by not making a sufficient distinction between the degree of mathematical acquirement necessary for making discoveries and that which is requisite for understanding what others have done. That the study of mathematics, and their application to astronomy, are full of interest, will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at truth, whether it be the discovery of a world or of a new property of numbers.'

It cannot be doubted that Mrs. Somerville here indicates her belief in the possibility of presenting her subject in a form suited to the capacities of a large number of readers, and to some extent advocates this as her object. Whether she succeeded or failed in this purpose must therefore be the first question to engage our attention. Sir John Herschel considers that she succeeded, ' for all those parts of her subject, at least, which the work ' professes to embrace, that is to say, the general exposition of the mechanical principles employed, the planetary and lunar theories, and those of Jupiter's satellites, with the incidental points naturally arising out of them.' With the utmost respect for the authority of one who was so thorough a master of the subject which Mary Somerville endeavoured to popularise, I venture to express a different opinion. I find it impossible to come to any other conclusion than that, as respects the main purpose of her work, Mrs. Somerville failed entirely; though I hasten to qualify this statement by the remark that, in my opinion, success was altogether impossible. I believe, in fact, that neither Mrs. Somerville nor Sir John Herschel thoroughly apprehended the difficulty of conveying to the general reader clear ideas respecting even the elements of the subjects they severally endeavoured to expound. But I feel bound to add that Mrs. Somerville's failure, inevitable from the very nature of her task, would in any case have been brought about by the manner in which the task was accomplished. It will presently be seen that, in saying this, I am, in fact, touching on the most remarkable and distinguishing quality of Mrs. Somerville's mind.

There are two essential requisites in a treatise intended to introduce a difficult subject to general readers. First, there must be a clear apprehension of the position of such readers, of what they can and of what they cannot understand, and of the form in which what is written for them may most usefully be presented. It is not too much to say that if just ideas had been entertained by Mrs. Somerville on this point, the attempt to present the Mechanism of the Heavens in a popular form would never have been made. But, secondly, it is essential that in any work of the kind each statement each sentence, in fact - should be presented in terms so precise as to be absolutely unmistakable. This is not so necessary in advanced treatises-indeed, it is too well known how large a proportion of our works on advanced science are wanting in strict precision of expression. But it is absolutely necessary in works intended to popularise science. It is a somewhat remarkable circumstance that in the Mechanism of the

Heavens-the boldest attempt ever made, perhaps, in this direction-not only is precision of expression not a notable feature, but, on the contrary, the most striking fault in the work is the inexactness of the language. Even Sir John Herschel, whose perfect familiarity with the subject of the work would tend to render the fault less obvious to him, was nevertheless struck by it: 'The most considerable fault we have to find,' he wrote, 'with the work before us consists in an habitual laxity of language, evidently originating in so complete a familiarity with the quantities concerned as to induce a disregard of the words by which they are designated, but which, to any one less intimately conversant with the actual analytical operations than its author, must infallibly become a source of serious errors, and which, at all events, renders it necessary for the reader to be constantly on his guard.'

These words form the penultimate sentence of Sir John Herschel's critique. I have preferred to speak first of the subject touched on, so as to pass without reservation to a more pleasing topic-the real and unquestionable value of Mrs. Somerville's chief work. And, after all, the good qualities of the work are intrinsic, while its main fault relates to a purpose which the work never could have fulfilled, no matter how carefully the fault had been avoided.

It is in this sense-regarding the work apart from its special purpose, and judging of it only as a contribution to advanced scientific literature-that we may fairly say, with Sir John Herschel, that the work is one of which any geometer might be proud. There is, indeed, ample evidence of the disadvantage under which Mrs. Somerville laboured, in the want of thorough mathematical training; but so much the more wonderful is it that she should have completely mastered her subject. Every page indicates her appreciation of the methods employed by Laplace and Lagrange. Where she does not strictly follow the Mecanique Celeste, she evidences a clear recognition of the purposes to be subserved by adopting a different course. I would not be understood as commending all the departures thus made;on the contrary, there are cases where it appears to me that on the whole it would have been preferable to have followed the processes of the Mecanique Celeste more closely, while there are others where certain more modern processes might perhaps with advantage have been introduced. But even in such instances we recognise in the course pursued by Mrs. Somerville the decision of one perfectly familiar with the subject in hand. And many of the changes must undoubtedly be regarded either as improvements, or else as altogether desirable when the scale of Mrs. Somerville's treatise is taken into account. Amongst instances of the former kind must be classed the method employed in the investigation of the equations of continuity of a fluid; amongst instances of the latter, I would specially cite the treatment of the theory of elliptic motion, in the opening chapters of the second book.