ing magazine, but several of the most essential passages were suppressed. The reviewer says, "The charges which Mr. Keith has adduced against Mr. Bonnycastle it is not my immediate business to refute." I would ask, for what purpose then did he make his reply? He makes a most ridiculous comment on the words copying, and collecting from the Nautical Almanac. Notwithstanding which, my observations were perfectly correct, for the tables of the sun's right ascension and declination inserted in my book, were collected from the different pages of the Nautical Almanac, with the alteration of the last figures, and the arrangement was my own; whereas Mr. Bonnycastle's tables were exactly copied from my work. Now, why did Mr. Bonnycastle copy these tables from my treatise? The answer is obvious, they were copied for the express purpose of solving the various astronomical problems which he had taken from my work, for they were of no other use whatever. The reviewer next makes some remarks on two diagrams noticed in my first letter to the Editor of the Magazine; and here, it appears, he has carefully measured the figures to the greatest nicety (perhaps with the assistance of a microscope) and exults at the (supposed) advantage which he has obtained over me. In consequence of which, like a conqueror of true courage and humanity, he assumes a milder tone in the next sentence, and says, "There is in general only one way of constructing these figures; so that the cry of plagiarism on such an occasion is perfectly ridiculous, as I have no doubt Mr. Keith very well knows." I feel highly flattered that this learned reviewer will allow me to know any thing, and in return for this mark of his condescension, I beg leave to refer him to the 120th page of the second volume of Hodgson's System of Mathematics, printed in the year 1723, wherein he will find that a right-angled or quadrantal spherical triangle may be constructed, not only one way, but one hundred and twenty different ways! "How "How far Mr. Bonnycastle may judge it right" (says the reviewer)" to enter into any altercation with Mr. Keith, in consequence of the liberties he has taken with his character, is not for me to decide." If what I have charged Mr. Bonnycastle (in the Philosophical Magazine) with copying from my work, has really not been copied, and can be found in any other treatise, prior to the first publication of mine, then indeed I have accused him unjustly, and shall, undoubtedly, meet with that contempt which so base a conduct would merit. But, if, on the contrary, my charges are well founded, and the matter in question cannot be found in any other publication (however insignificant or unimportant the subjects which are copied may be); I stand upon a foundation, not to be shaken by the false assertions, and illiberal insinuations of this, or of any other critic. The reviewer concludes his letter, by paying a handsome compliment to his own superior talents and acquirements, with which he seems to be highly pleased; and, as it is my fixed determination never to notice him again, I shall take my leave of him whilst he remains in that happy state of mind. With regard to Mr. Bonnycastle, who now holds one of the first mathematical situations in the kingdom, if he can conscientiously acquit his conduct of reprehension, I envy not the happiness of his disposition, but leave him in quiet possession of the honour and emolument which he may have acquired. Norfolk-street, Fitzroy-square, London. THOMAS KEITH THE THE CONTENTS. THE NATURE AND PROPERTIES OF LOGARITHMS. THE USE OF THE TABLE OF LOGARITHMS. 1. To find the logarithm of any whole number, or mixed decimal, consisting of one, two, three, or four 5. To find the number answering to any logarithm to 11. To find the value of a quantity having a vulgar frac- 12. To find a fourth proportional to three given num- 3. To find the degrees, minutes; or degrees, minutes, and seconds, corresponding to any given logarithmical 4. To find the natural or logarithmical versed sine of 2. To erect a perpendicular from a given point in a given line, or to make a right angle 4. To make an angle of any proposed number of de- grees upon a given straight line, by the scale of chords 5. An angle being given, to find how many degrees it 4. Plane sailing, in navigation, is only the practice of 5. MERCATOR'S sailing is the application of right- THE SIDES AND ANGLES OF OBLIQUE-ANGLED PLANE TRIANGLES, &c. Page 2. Rules for solving all the cases of oblique triangles 3. Practical examples, exercising the rules in oblique- The subject continued, and more minutely considered 1. Observations on the admeasurement of a base line 2. Of the errors which occur in taking angles of ele- vation and depression with a theodolite 3. The nature of terrestrial refraction, and its effects 4. Of the reduction of angles to the centre of the station 5. Of the reduction of angles from one plane to another 6. Of the dip, or depression of the horizon at sea 7. Of the parallax of the celestial bodies '. OF THE SIGNS OF TRIGONOMETRICAL QUANTI- 1. General properties of the sines, tangents, chords, &c. 3. General properties of the sines, tangents, &c. of the |