PREFACE, BY THE AMERICAN EDITOR. THE last English edition of Hutton's Course of Mathematics, in three volumes octavo, may be considered as one of the best systems of Mathematics in the English language. Its great excellence consists in the judicious selection made by the authors of the work, who have constantly aimed at such things as are most necessary in the useful arts of life. To this may be added the easy and perspicuous manner in which the subject is treated a quality of primary importance in a treatise intended for beginners, and containing the elements of science. The third volume of the English edition having been but lately published, is scarcely known at present in this countryit is but justice to its excellent authors to state, that they have collected in it a great number of the most interesting subjects in Analytical and Mechanical Science. Analytical Trigonometry Plane and Spherical, Trigonometrical Surveying, Maxima and Minima of Geometrical Quantities, Motion of Machines and their Maximum Effects, Practical Gunnery, &c. are among the most important subjects in Mathematics, and are discussed in the volume just mentioned in such a manner as not only to prove highly useful to pupils, but also to such as are engaged in various departments of Practical Science. As the work, after the publication of the third volume, embraced most subjects of curiosity or utility in Mathematics, it has been thought unnecessary to enlarge its size by much additional matter. The present edition however, differs in several respects from the last English one; and it is presumed, that this difference will be found to consist of improvements. These are principally as follows: In the first place, it was thought adviseable to publish the work in two volumes instead of three; the two volumes being still of a convenient size for the use of students. Secondly, a new arrangement of various parts of the work has been adopted. Several parts of the third volume of the English edition treated of subjects already discussed in the preceding volumes; in such cases, when it was practicable, the additions in the third volume have been properly incorporated with the corresponding subjects that preceded them; Vol. I. 1 and, and, in general, such a disposition of the various departments of the work has been made as seemed best calculated to promote the improvement of the pupil, and exhibit the respective places of the various branches in the scale of science. And thirdly, several notes have been added; and numerous corrections have been made in various places of the work: it were tedious and unnecessary to enumerate all these at present; it may suffice to remark the few following: In pages 169, and 263, vol. 1, are given useful notes respecting the degree of accuracy resulting from the application of logarithms;-these notes will appear the more necessary to beginners, when we observe such oversights committed by authors of experience. In page 173, vol. 1. a new definition of surds is given, instead of that by the author of the work. In the English edition, a surd is defined to be "that which has not an exact root." In Bonnycastle's Algebra, it is "that which has no exact root." And in Emerson's Algebra, it is "a quantity that has not a proper root." But notwithstanding the weight of authority thus evidently against me, I do not hesitate to assert, that the definition, just stated, is altogether erroneous. According to their definition, the integer 2 is a surd, for it "has not an exact root." In the mensuration, page 411, vol. 1, a remark is added respecting the magnitude of the earth. Dr. Hutton has commonly used a diameter of 7957 English miles, merely because it gives the round number 25,000 for the circumference in a few places he has used a diameter of 7930. Having some years ago discovered the proper method of ascertaining the most probable magnitude and figure of the earth, from the admeasurement of several degrees of the meridian, I found the ratio of the axis to the equatorial diameter, to be as 320 to 321, and the diameter, when the earth is considered as a globe, to be 79187 English miles. In the additions immediately preceding the Table of Logarithms in the second volume, a new method is given for ascertaining the vibrations of a variable pendulum. This problem was solved by Dr. Hutton, in his Select Exercises, 1787, and he has given the same solution in the present work, see page 537, vol. 2. The method used by the Doctor appears to me to be erroneous; but in order that such as would judge for themselves on this abstruse question, may have a fair opportunity of deciding between us, the Doctor's solution is given as well as my own. It may be proper to observe, with respect to the new solution, as well as Dr. Hutton's, that the resulting formula does not not shew the relation between the time and any number of New-Brunswick, New-Jersey, ROBERT ADRAIN. CONTENTS |