tons of stone expected was allowed. When a top shaft was in question, 1 lb. of powder ought to produce 3 tons of stone; the average over the quarries of both shafts and headings being 1 lb. of powder to 2 tons of stone. The difference between the quantity of powder, calculated in this way, and the quantity obtained with reference to the line of least resistance cubed, was the variable quantity, which was altered according to the position of the joints, &c. &c. Half the difference was taken in ordinary cases. = For example, in a lower heading-Let the line of least resistance 30 feet; the height of rock=60 feet; the average width of column = 50 feet; then taking this last check rule we obtain 30+ 50 + 60 Say 12 (the number of cubic feet to the ton). 7500 tons of expected stone. = Now, had we taken the line of least resistance as the only element in the calculation, applying the general rule for headings, we have— a difference of 1500 lbs. less than by the other method. In practice, about one-half this difference, or 750 lbs., would be added to the quantity obtained by the th of the line of least resistance 3, to enable the powder to do the work required by the position of the heading. The charge would therefore be 3000 lbs.; instead of 3750 by the one method, or 2250 by the other. The only remaining point now to be noticed is the cost of quarrying on the large scale. This I am enabled to give from a very accurate estimate which was made in November 1855 from the pay-sheets for a week, during which the quantity quarried was 23,095 tons, of which 1165 tons was debris, not deposited in the breakwater. This estimate includes quarrying, filling the waggons, and moving them clear of the face of the quarry. Total cost of quarrying 23,095 tons, £441 8 10 4.58 8.97 Total cost of stone quarried and filled, per ton, The miners' wages varied with the kind of work; in some parts of the quarry they got 25s. per foot run for driving a heading, in others only 14s.; out of which they had to pay about 2s. for the powder, fuses, &c., used in blasting. One man could drive fully 14 feet per week; the average over the quarries being 5 feet of heading for 4 men. In one case 4 men only drove 3 feet in a week, in another case as much as 10; a low average, therefore, is 5 feet. It is more than six years since I was at Holyhead, but I have no reason to suppose that the system of blasting has varied very materially from what is recorded in this paper. 211 Description of the Gold-disk Steam or Vacuum Gauge. By Mr RICHARD ADIE, Liverpool. * The gold-disk gauge originated through a liability to corrosion which was found often to spoil the gauges I was in the habit of supplying to a railway company. About sixteen years ago, M. Vidi invented the aneroid barometer and a steam-gauge, where corrugated metal disks were employed to measure changes of pressure. The patent is dated October 1844. M. Vidi's patent has expired, and I believe that his invention is open to be applied to other forms of steam-gauges, although there are two subsequent patents still in force where the claim is made: in the first, to a chamber covered with any elastic material; in the second, to a chamber covered by an elastic metal. Of the value of these rival patents I am unable to give an opinion; but if the claim to the general principle had to be discussed, I doubt if even M. Vidi would be allowed the priority. The late Mr Macnaught of Glasgow having so many years before introduced steam into a chamber, where he measured its pressure by its action on a spiral steel spring. Among the noble metals I sought for a corrugated disk to measure pressures which would not be destroyed by water, my thoughts were long turned to platina; but the metal of an old gold pen happening to be near me, I was struck with the manner in which it had retained its form through a long period of service, and where the ink, as an agent for corrosion, must have been as active as oxygenated water to which steamgauges are exposed. The opinions of two friends who had had much experience in working the alloys of gold, confirmed me in the selection of this alloy for a guage of vacuum or pressure. The accompanying woodcut represents the front view of a gauge where steam pressure is introduced into a small chamber by a pipe at the back. * Read before the Society, and instrument exhibited, on 9th January 1860. AA is a corrugated disk of an alloy of gold which covers the front of the small chamber. BB is a stout ring of gun-metal. CC are a series of six strong screws, which make the ring of gun-metal bind down the disk thoroughly steam-tight to the chamber. DD is a piece of brass in the form of a dish, which is fitted tightly on the edge of BB, and secured in its place by a series of screws not seen in the drawing. The outer part of DD, where the dishing ceases, is used as a plate for graduating the scale of pressure upon. EE A groove is turned in DD to receive a glass face, which, after careful fitting, is sprung in with heat. F is a cock to carry one end of an axle H. G is a cock to receive the other end of the axle H, also to carry another cock I, in which the finger turns on a vertical axis. H is an axle stretching across the face of the disk, carrying on it a portion of a crown-wheel K. A spur from the axle H is in connection with the centre of the gold disk; a knife edge, similar to those used in balances, communicates the motion of the disk to the axle and crown-wheel. The finger in the drawing carries on its axle a pinion which pitches into the crown-wheel K, so that any motion of the disk is shown by the finger on the dial. In order to prevent what is termed "drop" in the pitching of the wheel and pinion, there is applied to the vertical axle a cylindrical spring of brass or gold wire. A bent tube, in the form of the letter U, is used to connect the chamber of the gold disk-gauge to the boiler; this tube is filled with water. The use of this connection is to prevent steam reaching the chamber, and so to keep the disk at a moderate temperature, which ought never to exceed blood-heat. A subsequent improvement in the box or chamber of this gauge is, to bind firmly together the two inside surfaces by a spiral spring of gold in the centre. The requisite strength in the disk is thus attained with less weight of gold, and the degree of elasticity is higher. * ** On a Method of Constructing Life-Annuity Tables by means of an Instrument, without the use of Logarithms. By JARDINE HENRY, Esq., F.R.S.S.A.* In the construction of Life Annuity and Assurance Tables the use of logarithms has hitherto been held indispensable, on account of the many arithmetical operations in multiplication and division required. The effect of the use of logarithms is to substitute addition for multiplication, and subtraction, or addition of complements, for division. The benefit derived is very great, therefore, and the obligation the calculator owes to the illustrious inventor, Napier of Merchiston, near this city, has been acknowledged by all who, since his time, have had to perform extended series of numerical operations. By the use of logarithms extensive tables in various applications of science have been constructed, more particularly in connection with astronomy and navigation, and great assistance has also been derived from them in life annuity and assurance calculations. In the outset of a proposal by the reader to furnish a complete set of life-annuity tables, it occurred to him that the requisite tables might be formed by making use of an instrument operating so as to produce, by a simple movement, the multiplications required. The method adopted was, to form a right angled triangle of seasoned wood, of 100 inches to the side, and with its margins divided each into 10,000 equal parts. Lines were then made, formed of small threads, and extended from the left hand corner, where zero stood, to the numbers on the perpendicular side, * Read before the Society, and instrument exhibited, 23d January 1860 |