matter of dispute between the members of it, or between some of them and the minister himself; which appeared more likely to excite their disgust and inflame their passions than to do them or himself any real good.. It is matter of great delicacy for ministers to introduce, as some are ever prone to do, their own personal or domestic concerns into the public devotions, or to speak of themselves at all. And it is not more disgusting to hear ministers use any expressions which savour of vanity, self importance, or self-interest; than it is, with all judicious persons, to hear them apply to themselves (whether from an affected or a real humility) such degrading terms as "thy unworthy servant-thy poor worm-thy sinful dust-the meanest of all thy instruments," &c. which some pious and even sensible men have not seen it improper to adopt. For want of this' (prudence) we have sometimes heard cases of so peculiar, so trivial, and even indelicate a nature, brought into the public intercessions, as (if at all fit matter for prayer) ought to be confined to the closets of the persons themselves." We forbear to notice the injudicious and indecent expressions, and the indelicate allusious to certain passages of scripture, which may sometimes be heard in extemporary prayers; since they are chiefly confined to illiterate preachers, of the lowest order, of whom too many rank with dissenting ministers; whose indiscretion and vulgarities cause men to abhor the offering of the Lord.", Other articles of accusation are exhibited; but we need not transfer to this place any larger portion of that one ingredient in which the work itself has by far its best chance of being read. Now we repeat, that this professedly well-wishing lecture of reprehension is made in a manner which exempts the dissenters from all manner of obligations of gratitude. There may indeed be found such a sentence as this: we are far from charging our brethren in general, especially those of a liberal education, with the improprieties which we have noticed. A very few expressions like this might have been enough for complaisance amidst the freedom and confidence of fraternity, if in composing a book for publication they could have been addressing the dissenters exclusively of all other listeners. In the slight generality and brevity of their commendatory expressions they might then have been understood as saying, in effect,- We have met one another, not to establish the proof or celebrate the praise of our excellences; a very superfluous thing indeed at any time, as we none of us need an increase of our self-complacency; at any rate we have a different business just now, the specific business of taking account of our faults in order to correct them. We may rely on mutual good opinion and the firm partiality of all of us to our class, enough to waive compliments for the present, and deal about only a little wholesome and not very palatable truth.' But these candid reformers well knew, that in writing a book which should expose whatever could be found of most defective or absurd in the dissenting worship as conducted by the inferior class of its performers, they were writing what would be read by nobody with so much avidity as by the enemies of nonconformity, and by the enemies of religion; of whose extremely slight knowledge, in general, of the religious services of the dissenters they were also aware. They well knew that a civil expression or two, affecting to acquit the main body of the arraigned class of the charges exhibited with such elaborate aggravation, would not have the smallest effect on such readers; who would be sure to congratulate themselves on having obtained at last, from very good authority, a description comprehensively applicable to the class, and just such a description as it is gratifying to believe. This consequence could not be even in part prevented, these authors well knew, without the most explicit, and even repeated and amplified declarations, that such a conversion of particular charges against a portion of the class into a general estimate of its qualifications collectively, would be to incur a complete imposition on the judgment, that there is, in the whole amount, an extremely large and continually augmenting measure of intelligence and propriety displayed in public extemporary prayer,--that there are many dissenting ministers distinguished for their excellence in the practice,-that a very great proportion of them maintain a respectable propriety,that a considerable number really show their faculties to the most advantage in that employment, that some who are chargeable with some of the faults alleged, manifest, nevertheless, a considerable share, on the whole, of sense and devout sentiment, and that the very gross offenders form but a small proportion of the class. This is what these gentlemen have not done. And the impression which, through this omission, will be made on uninformed and prejudiced readers, will be confirmed by the universality of the terms in which the remedy is proposed: no minister, it would seem, is held competent to perform the public devotional services quite satisfactorily without the auxiliary expedient. Such an impression may be further confirmed by the curious sort of caution with which these writers have ventured to assert the possibility, the bare possibility, of excellence in extemporary prayer. In hazarding the assertion they have thought it necessary to look abroad into history for examples; and they have found in the last age (something less than the number of splendid comets) two examples, Dr. Watts, and Mr. Hugh Farmer! Whatever, therefore, the dissenters may think of the plan itself, we should suppose they will feel much contempt of the spirit and manner in which the benevolent service has been performed. The authors are to look for their thanks from another quarter. And they may have perceived already, in the most marked act of public attention with which they are likely to be honoured, how gladly and kindly they will be received by the avowed and consis tent enemies of nonconformity in all its parts, as witnesses against their brethren, and hopeful pupils of the higher school;-still objects of condescending, compassion, nevertheless, on account of that dimness of incipient sight which as yet but perceives men as trees walking.' Having said thus much, as honestly due, we think, to the dissenters, and as fairly within those limits of our office which exclude ecclesiastical polemics (and we are glad of the exemption conferred by this exclusion) we should be deficient in benevolence toward the fraternity so ungenerously treated in this performance, if we did not earnestly recommend to their perusal the part of it that deserves this very charge. They must not be allowed to fancy that there is not great room for amendment in the manner of the extemporary devotions of many among them. The faults which these worthy friends of theirs have depicted, as if just for a show to entertain the Philistines, do certainly exist among them to a considerable extent. We have now and then ourselves, in straying into some of their meetinghouses had for a short time some sensations awakened, akin to those that seem to have been prolonged into a continual qualmishness in these delicate divines: but we happened to have more knowledge than they choose to own, as well as more candour than they possess, respecting the general and collective quality of the dissenting public services. That quality, however, estimated collectively, might, we submit, be very materially improved in consequence of a serious and impartial attention to the first and third part of this same New Directory.' With regard to the Remedy,' as our authors denominate it, we have shewn that it will not be adopted; but if it would, we can see no great good it would do, though it is set forth in nearly the usual confident terms of the projector, or the advertiser of a panacea. Forms are to be composed of passages of scripture, drawn together according to the minister's judgement of their adaptedness to combine. A number of these are to be written or printed, and read as a part of the public prayer, the other portion being still extemporary. It seems not to have occurred to these projectors, that the length of this extemporary portion would remain completely at the discretion of the person performing it, and that the weak and ill-judging man will be very sure to make it long enough to admit all the faults from which it is the very purpose of the contrivance to save him. Indeed such a man will be extremely likely, as we have before observed, to reject the assistance altogether, with peculiar disdain. The reformers should either, on the one hand, have aimed at precluding all possibility of the evils complained of by recommending an entire liturgy, which, considering the habits and opinions of the dissenters, would have been as hopeful a proposal as the one they have actually made,or on the other, have been content to urge the improvement by all possible means, of extemporary prayer, exposing, of course, its most prominent existing imperfections. This exposure they have made; and we would warn the dissenters not to suffer the ungracious manner in which it is made, to provoke them into the folly of rejecting the benefit they may derive from it. Art. IV. A Treatise on Algebra in Practice and Theory, in two volumes, with Notes and Illustrations; containing à va ety of particulars relating to the Discoveries and Improvements that have been made in this Branch of Analysis. By John Bonnycastle, Professor of Mathematics in the Royal Military Aca demy, Woolwich, pp xxxvi. 834. Price 1. 4s. boards. London, Johnson and Co. 1813. NEARLY thirty years ago, the author of these volumes published a little book on Algebra, intended merely as an elementary work on this branch of science. It has been introduced with advantage into many schools; and is frequently employed as a convenient exercise book for undergraduates at Cambridge in their first year. During the interval which has elapsed since that compendium was laid before the public, Mr. Bonnycastle has (at least so far as we can judge from his published performances) devoted his attention almost exclusively to matters of pure mathematics, and has here presented the matured fruit of his labours to the world. This enlarged or rather new work (mathematically considered) is by no means unworthy of its author; though it is not altogether such, we think, as might have been expected at his hands. The first volume is devoted to "the practice" of algebra, containing rules for the different processes, and a great variety of examples, some of them very excellent. The order into which the materials are thrown, does not, of course, deviate widely from that which has been usually adopted. But it is natural that the author should pursue some of the subjects to a greater length than in his former Introductory work, as well as that he should here introduce some, which were there altogether omitted. Hence we find tolerably copious directions VOL. XI. M.m W respecting the management or solution of reciprocal equations, binomial equations, equations with equal roots, exponentials, indeterminate coefficients, vanishing fractions, figurate and polygonal numbers, continued fractions, indeterminate and diophantine analysis, recurring, logarithmic, and other series. The volume commences with a brief history of algebra (in great measure avowedly abridged from Dr. Hutton's well-known elaborate history in his Dictionary and Tracts); and terminates with a miscellaneous collection of 87 algebraical questions, several of which will be extremely interesting to students. Many of the subjects in this volume are treated with great perspicuity, and most of them sufficiently at length. But we could have wished to see more on the practice of exponential equations, as well as a greater variety of rules for the summation of series. From such a book it is difficult to quote detached pieces; and in many cases it would be as useless as exhibiting a brick or a beam of timber as a specimen of what may be expected in a building: we shall, however, venture upon one or two extracts. The following is a useful rule in the doctrine of surds, which we do not recollect to have found so well expressed in any other treatise on algebra. To find such a multiplier, or multipliers, as will make any binomial surd rational. RULE. 1. When one or both the terms are any even roots; multiply the given binomial, or residual, by the same quantity, with its sign changed; and repeat the operation as long as there are surds, when the last result will be rational. In like manner, a trinomial surd may also be rendered rational, by changing the sign of one of its terms for the multiplier; and a quadrinomial surd by changing the signs of two of the terms, &c. 2. When the terms of the binomial surd are odd roots, the rule becomes more complicated; but for the sum, or difference, of two cube roots, which is the most useful case, the multiplier will be a trinomial surd consisting of the squares of the two given terms and their product, with its sign changed. EXAMPLES. 1. To find a multiplier that shall render 5 + √3 rational. Given surd 5+ √3 Product 25-3= 22 2. To find a multiplier that shall make √5 + √3 rational. |
