And for inconsiderable heights (under 1,200 metres), b = 16000 h B = This simplification is extremely useful, as it enables hypsometric results to be calculated out at once, without the need of a table of logarithms. Lefroy has given a very good approximate formula, also free of logarithms: Adding or subtracting to or from the result for each degree, Fahr. Thermo., mean temperature of the air above or below 55°. The Thermometer is also employed, particularly in India, for hypsometrical purposes; and instruments for this special use are supplied in a convenient form by Casella, London. A convenient approximate rule has been given by Lefroy : Allow for each degree below 212° Fahr. that water boils in a metal vessel, in mean state of barometer (i.e. little above or below 30 inches in height) 511 feet for first degree; 513 for second 22 515 for third &c. The errors of thermometric measurements of height are always large, except in the tropics. Heights may sometimes be ascertained approximately by dropping a stone. In this case, h = 1 g t2 g= 32.1803 feet for lat. 45°; and = 32.19 feet for London. = 16.10 feet for lat. of London. Hence, g Mr. Gravatt, C.E., has lately printed, but we believe for private circulation only, a very nice little " Companion to the Barometer," in which, by the aid of an approximate formula and a table, covering only a few square inches, hypsometrical calculations may be made without logarithms. His formula is, perhaps, rather less convenient than M. Babinet's. The table was calculated and printed by Schentz's calculating machine. Chronoscopes, for the observations of t, or generally for that of any minute portions of time. The chronoscope of Bregnet, which is made by Robert, Rue de Coq, Paris, of pocket size, and at a moderate price, is better employed than a stop-watch. For very accurate purposes, the electro-chronoscope of Wheat stone, or other constructions of the instrument, must be employed. By their means T0000 of a second may be measured. To those engaged with_artillery, the electro-ballistic chronoscopes of Major Navez, and of Lieutenant Boulengé, of the Belgian Artillery, demand notice as the best instruments at present known for the determination of initial velocities, times of flight, &c. Deep-Sea Thermometers.-Since the laying of ocean telegraphic cables has come to be an established branch of engineering, ascertaining of oceanic temperatures in relation to currents, &c., at great depths, has become important to the engineer, as it has always been to the navigator. A modification of registering spirit thermometer is chiefly employed by the Admiralty, but has the serious disadvantage that the record of the instrument is liable to be disturbed by rude shakes in hauling up. In every respect preference appears due to Johnson's Patent Deepsea Registering Metallic Thermometer, the action of which depends upon the unequal expansion or contraction of two conjoined bars of different metals. In principle it is identical with the thermostad of the late Dr. Ure. The instrument is made by Mr. Hoffmann, 32, Wilmington Square, Clerkenwell. Samples of Sea Bottoms are often of greater importance to the telegraphic engineer than temperature. The spring clutching hollow pincers, which are released and close up on touching the bottom, enclosing more or less of it if soft, and known as the bull-dog clams, are chiefly used by the Admiralty. An extremely simple instrument, however (due, it is believed, to Captain Spratt, R.N.), and equally efficient, consists of about foot long of brass tubing of 1 inch or 14 inch diameter, secured, by lashing with copper wire, to one side of a deep-sea lead, below which the lower and open end projects about 6 inches; the upper end, also open, has a little leather or vulcanised india-rubber flap (like a pump valve) opening upwards, tied or otherwise secured over it. The lower end of the tube digs into the bottom when reached by the lead, and seldom fails to bring up a good plug of it to surface. Levelling Staves.-Several novel forms for the graduation of these have been devised, but we are not aware that any present much advantage over those commonly in use. The principles on which all such graduation had best proceed are very well given in Mr. Simm's "Treatise on Levelling." Scales, Graduated Instruments of Measure, Gauges.-Scales in ivory, which are triangular prisms in form, and graduated at the edges on all the angles, have been produced by Pastorelli, London. Each scale affords thus six edges (in place of two on the ordinary flat form) for graduation, and the prismatic form enables a number of scales to fit together and into a cylindrical case without looseness. These scales look extremely elegant, and seem to have no disadvantage but oneviz., when one side is laid flat on the paper, the sharp inclination of the other two sides of the prism of smooth ivory, make it rather hard to pick up by the fingers. Beam callipers with Verniers and screw fine adjustments are now supplied by Troughton and Simms to the Government gun factories, &c., which are admirable instruments in all respects. The writer has employed jointed steel callipers with reversed or back lever ends, carrying a graduated arc and Vernier, and multiplying the actual chord of the callipers as 10: 1, with satisfaction. These, as all steel instruments of precision should be, were electro gilt. Steel straight-edges, with rigidly parallel sides and edges, and either graduated or not on the edges, as also sliding beam callipers of steel for common use, as well as other steel instruments of measurement, are made in great perfection by McFarland, of Birmingham. Graduated steel tape measures, up to 50 feet in length, may also be procured now from makers at Sheffield, and for lengths not exceeding 25 feet are very useful and exact. When much longer they are liable, being tempered, to kink and break. Steel gauges for various purposes, early brought into notice by Whitworth, are now so well known as scarcely to require remark here. Curvilinear Drawing Instruments.-Curves, both circular and of other orders, have within a few years been introduced from France, cut out of thin pear-tree, or other woods, and have added much to the draughtsman's convenience. They are liable to get injured on the edges or even split by violence, and in some parts of Germany curves of all sorts can be procured cut out in sheet zinc, which are very light, clean, and serviceable. Beam compasses of great excellence and beauty, and extremely light and yet rigid, are sold now in London by the dealers in Swiss drawing instruments. These are, in truth, the very best of the Swiss instruments. Their drawing instruments generally, though sold at wonderfully low prices and beautifully executed, are not found free from several serious practical defects in use. A special instrument for drawing spirals, such as those of the Ionic volute, has been invented by Mr. Johnson, the inventor also of the deep-sea thermometer; it is sold by Mr. Hamilton, Royal Exchange, Cornhill, London. The price is high, but the instrument works beautifully, and possesses a great range of variation in the curves it can describe. For the description on the ground of large circular curves, such as those of railways, several methods of more or less novelty have been proposed within the last fifteen years. Our limits will not admit of more than this reference to them. For instrumentally taking the areas of curved (or other) figures, two or three different instruments have been produced. One of these, the integrating totalizateur, is a very elegant instrument of French origin. A much cheaper and simpler instrument is obtainable in London. None of these appear to have come into common use, and their practical advantages are very doubtful. Minor Instruments, for the draughtsman.-Amongst these may be noticed the admirable pencils of Faber, made of the newly-discovered Siberian plumbago. We have found no pencils equal to these for evenness, firmness, and depth of line, or so free from grit. Drawing pins for laying down paper have been cheapened, but have so deteriorated in quality that a really good one is not to be had. The steel puncturing point in all those now supplied is tapered in the brass head, and riveted in. This involves making the brass head so clumsy and thick, and the edges so abrupt, that the T-square will not lie evenly over them, and its edge is continually caught and injured by striking them. The puncturing pin should (as it always was thirty years ago) be screwed through the brass head, and the latter should have a low and very flat circular segmental cross section, and be almost as thin and sharp at the edges as a table-knife. Such pins are better worth 3s. per dozen, at which price they were sold, than the existing run of rubbish called French pins, &c., is worth 6d. Photographic Instruments.-Photography has now fully taken its place as an auxiliary to engineering operations. By its use the mechanical engineer is enabled to send forth and abroad correct representations of his machinery, however complicated; and works of civil engineering have their monthly progress recorded, and the results sent home, to give ocular proof of their truth, to chiefs and directors. In addition to this, Sir H. James, R.E., and others, have made it applicable to the copying, with reduction or enlargement, of geodetic maps and plans, with immense economy of time and labour. A practical knowledge of photographic processes has hence become almost a necessary, certainly a most desirable, portion of every young engineer's education. Several special manuals in English and French are to be found. Of the apparatus itself it would quite pass our limits to treat. Two or three new forms of sketching instruments, i.e., instruments (like Jones's, made by Cary, Strand, London) for guiding mechanically the eye and hand in sketching solid objects, have been devised. None appear to answer better, if so well, as the Camera Lucida of Wollaston, described in the text. The title of this work is so extensive that we might without impropriety have noticed under it a great number of other instruments or methods; for in reality mathematical instruments mean properly all instruments relating to the objects of mathematical science, viz., the determination of quantity in any of its relations to space or time. As commonly used, however, the term means, instruments applicable to geography or navigation, astronomy, geodesy, and draughtsmanship. In such sense it was used by the author, and in that sense we have followed. R. M. DESCRIPTION OF THE IMPROVED Y LEVEL Made by GEORGE DOLLOND, Optician by appointment to the Queen, 59, St. Paul's Churchyard, London. THE tripod A screws on the staff head, and the level is fixed upon it by means of the three screws CC C, which are placed in the three Y's, c cc. By turning the locking plate, the level is held fast in its place, the spring being secured by slipping the bolt B, which effectually prevents any chance of displacement. D is the clamp screw for fixing the instrument when approximately in position, and E the tangent screw for finer adjustment. The bubble, which is fixed on the limb across the compass box, has two joints, H, h, by which it can be adjusted at right angles with the centre by the larger key, fitting to the square F. The same key also applies to the square I |