706 ___________________________________________________________________________________________________________ THE COLLIERY GUARDIAN. October 4, 1918. 8. When the atmosphere is clear, the leader shall, when passing the junction of two or more roads, clearly indicate the route by means of arrow marks in chalk. When the atmosphere is thick with smoke, the leader shall see that a life-line is led in from fresh air, and shall not allow any member of 4he brigade to move out of reach of that line; or, if that course is impracticable, he shall not proceed until every road branching from the route is fenced across the opening. 9. Before proceeding underground, the leader shall test, or witness the testing of, every rescue apparatus of the brigade. He shall check the equipment of his party, and, immediately before entering irrespirable air, make sure that every apparatus is working properly. 10. When using rescue apparatus the leader (who shall carry a watch) shall read the pr.essute of the com- pressed oxygen every twenty minues, or thereabouts, and shall commence the return journey in ample time. In travelling he shall adapt the rate to that of the slowest member. Members of Rescue Brigades. 11. Members of brigades shall in general use the pre- scribed signals in communicating to one another. 12. In travelling with rescue apparatus, each member of the brigade shall keep the place given him when numbering off. If the pace is too quick, or if distress is felt for any reason, the member shall at once sound the distress signal. 13. No person shall commence a second or subse- quent spell of work in bad air without being examined and passed by a doctor, if present, or by the rescue station instructor or other competent person if the doctor be not present. ________ Signal. CODE OF SIGNALS. (To be used when working in poisonous air.) swnallmx. of a brigade. “Distress” or ... “ Distress” or ... ONE prolonged ring, “ Help Wanted.” “ Help Wanted.” or a, prolonged suc- cession of hoots. (If NO ANSWER is given to a call, “ Distress” is to be understood.) “Not under- ... Halt............ONE sharp ring or stood” or ONE hoot. “Repeat the Message.” “ No” .......... Retire ........... TWO sharp rings or TWO hoots. THRE F. sharp rings or THREE hoots. “Yes” or “All ... Advance ........ right” or “ All’s well.” To “ring up.” ... To call attention ... FOUR sharp rings or To“ringoff.” FOUR hoots. Direction of Air Current Telephones Underground Ambulance Station (in red)... Fire Dams or Seals Doors Regulators_____________________________ Air Crossings, explosion proof (Section 42 (3), 1911) _________ ____________ Air Crossings other than the above_______ CODE OF VENTILATION SIGNS. Brick, Stone, nr Concrete Stoppings, explo- ___ sion proof (General Regulation 91)______ _.. Brick, Stone, or Concrete Stoppings other - than the above ... ___________________ ___ Intake Airways—Blue. Return Airways—Red. ____________________________ Middlesbrough Iron and Steel Shipments.—Shipments of iron and steel from the Port of Middlesbrough for Sep- tember were disappointing, and, in fact, only in one month since the commencement of the war has the aggregate fallen so low. The total clearances for September were returned at 36,317 tons, compared with 65,484 tons for August. Foreign shipments of pig iron last month were down nearly 50 per cent., being only 22,813 tons, against 41,712 tons in August, whilst only 5,749 tons of manu- factured iron and steel went abroad, as against 16,302 tons in August. The coastwise shipments of pig iron showed little variation, amounting to 6,766 tons in Sep- tember, and 6,881 tons in August. Wigan and Distri'ct Mining College.— At the last meeting of the governing body of the Wigan and District Mining and Technical College, Mr. J. T. Gee (the chairman of the college governing body) moved, and Mr. J. Brown seconded, a resolution expressing profound regret regarding the death of Mr. A. Hewlett. At the same meeting a letter was received from Mr. A. M. Lamb, J.P., chairman of the College General Purposes Committee, enclosing a cheque for £150 for providing a full-time day mining scholarship of £50 per annum for three years. This is the second scholarship of the same value given by Mr. Lamb, A letter was received from Mr. W. H. Hewlett, managing director of the Wigan Coal and Iron Company Limited, enclosing a cheque for £150 from Mr. George Bradshaw, metal merchant, of Manchester, for the award of scholar- ships to students attending the college. The donation was accompanied by a suggestion that the sum might well be utilised to enable deserving students in need of finan- cial assistance to proceed to higher courses at the college. A similar donation of £150 was subscribed by Mr. Brad- shaw same twelve months ago for the award of a full- time scholarship in the mining department. Communica- tions were received from the Lancashire County Educa- tion Committee and from the' Wigan County Borough Education Committee respectively, intimating. that the annual grant from each authority to the college would be increased in future by £500 (making £1,000 per annum). THE POWER FACTOR. n. [Specially Contributed.] Proof that Cosine Measures the Power Factor. For the purpose of proving that cosine actually measures the power factor, we have again to employ the conventional diagram, an extension of that given in fig. 2 (Colliery Guardian, August 23, 1918, p. 389). In fig. 3, the radius again sweeps out the angle, from 0 to 180 degrees, the successive values of the angle meaning successive increments of time; thus wlfen the radius reaches the perpendicular YYj, the angle is 90 degs., and the time is one quarter of a cycle, or period, 1/200 of a second with a 50 cycle service; when it has reached the line OXT half a period has elapsed, and the angle is 180 degs. OA represents the radius that is sweeping out the angle in time, correspond1 ng to the current; and OV is the radius corresponding to the pressure. It will be noted that the current is behind the pressure, or, as it is usually expressed, it is lagging; and the angle VOA is the angle of lag, the angle . For the argu- ment that follows, it is usual to call the angle VOX, which represents the pressure a, and the angle AOX which represents the current /?'; it will be noticed that the angle is the difference between the angles a and p, or (a.— P). OAj is the radius representing the current, 90 degs., a quarter of a period beyond OA in time; and OVt represents the pressure a quarter of a peri- d U*y« nd O V. X YT Fig. 3. AP, VPj AjP2, and VjP3 are perpendiculars dropped from the points A,V, A1? and Vi on the base line XOXj; and they represent the values of the sines of the angles of the current and pressure at the different points of the cycle, corresponding to the. positions of the radii, If, say, OA is 15 degs. from OX, and OV is 60 degs. from it, the angle of lag VOA will be 45 degs.; also the value of the sine of the current, as represented by A will be 0*258, and that of the pressure will be 0 866; and the value of the cosine of (a - P) will be 0*707. One or two points had better be mentioned before passing on. It will be remembered that both pressure and current rise gradually to a maximum, in accord- ance with the variation in the value of the sine of the angle swept out by the radii representing respectively, the current and pressure ; both are at their maximum value—i,e., unity, .when the angle is 90 degs., and in the second half of the cycle at 270 degs., when a quaTter, or three quarters of the cycle have been passed through. When the angle is 90 degs., or 270 degs., the perpen- dicular which measures the sine, coincides with, and is equal to the radius. The maximum value is sometimes called crest value, because in occuis at the highest por- tion of the well,known curve representing alternating currents; the radius, wherever it comes m, represents crest value ; it is important to remember this in connec- tion with the argument which follows. It will be remembered also that the effective, or virtual, or working value of the pressure or current, is found by taking a very large number of values of each, squaring each of the values, taking the mean of all the squared values ; and then taking the square root of the mean so obtained; this is the root mean square value that is referred to in the text books; it is the value corres- ponding to the continuous current that will perform the same work. Further, it will be remembered that the effective values of the pressure and current are equal to the crest value divided by V 2, or the crest value divided by 1*414 or multiplied by 0’707. It will be noted that the triangles OAP and . are what are called in trigonometry similar triangles, and that the triangles OVPj and OV1P3 are also similar triangles. Further, the two triangles dealing with the current are complementary to each other, and the two representing the pressure are also comple- mentary to each other. It will be noted that the angle AOP and the angle OA!?., are equal, and both are equal to the angle /?; also that the angle VOP2 and OVTP3 are equal—both representing the angle a- It will be understood again, that for a complete proof that cosine equals the power factor, a very large number of values of current and pressure would have to be taken. In the proof that follows, two pairs, in the two first quarters of the cycle, are taken, and what is proved of them is correct of any number of similar pairs. The writer has chosen the pairs 45 degs. apart, and 15 degs. from the base and perpendicular respectively, because they lend themselves more readily to the proof that follows—and the angle of lag 45 degs. is common in colliery working. Any number of pairs could be taken, tracing out the successive positions of current and pressure, as repre- sented by their respective radii, right throughout the cycle. Each pair of pairs would be treated in the manner in which those in the diagram are. It will be remembered that the power deliveied to any electric circuit at any instant is measured by the product of the pressure between the ends of that circuit and the current flowing in it at the instant when the measurement is taken. In the first quarter of the cycle, the current and pressure are represented by the lines AP and VPt ; and in the second quarter of the cycle, a quarter of a period further on in the cycle, they are represented by the lines AiP2 and VTP.{. Calling Wt the power at the instant represented bv the radii OA and OV, we can write Wt = VPX x AP ; and calling the power at the second instant, a quarter of a period further on. W2, we can write W2 = V\P3 x AXP2. It will be remembered that in every right-angled triangle the sine of any angle is equal to the perpendicular opposite the angle, divided by the VP hypcthenuse. In the triangle VOPj,sin VOPj = -Qy1 Multiplying both sides of the equation by OV, we get VP, = OV sin. VO?!, or OVsin cc; similarly, it will be found that AP = OA sin. p. And so we can, write, in place of VP, multiplied by AP, Wj $= OV sin a x OA sin. p. In the other two triangles AOP2 and VOP3, the angles at A, and Vi correspond to an 1 are equal to the angles a and P. Again, we take _____ but it equals the cosine of OVjP3 or a, and aga:n by multiplying both sides , by OV, we get VjP^OV, cos- a. Similarly, in the other triangle, we find that AjP2 = OAj cos. p. We may write, therefore, W2 = QVt cos. a x OAj cos. p. Tuese two expressions are usually written Wj = OV sin. a. OA sin. p, Adding the two amounts of power together, at the two instants chosen, we get WT + W2 = OV sin. a. OA sin. p + OVT cos. a. OAX cos. p. As explained above OV, OA, OV1? and OA! represent the maximum values of the pressure and current at the instants represented by the radii. ’The maximum values of the pressure and current are usually repre- sented by E and C; and if we use these letters to express these values in this case, we can write W + Wj_ = EC (sin a sin. P -f- crs. a cos. P). It will be remembered that the expies-ion within the brackets is the expansion of the expression cosine (a — p) ; therefore we may write W 4- WT = E C cosine {a, — p~); and as the difference between the angles a and P is the angle , the angle of lag, we may write W-f Wx = EC cosine , where E and C are the maximum, the crest values of the pressure and current in the cycle. As explained above, in order to obtain the average value of the power through the cycle, which we will call W, we should have to take a very large number of pairs of radii, one of each pair representing current, and the other representing pressure ; and we should then have twice the value that we require, as each is taken twice over. We may therefore write W = I E C cos. <£. However, as explained above, the value of the E effective or virtual pressure is -7--; and the value of the effective or virtual current is----= where E and C , V 2, are the maximum or crest values of the piessure. and current. It follows, therefore, that W will equal 'EC a/T X X COs* eQuals 4 E C cos - If we write the effective pressure and current as e c, effective W will equal ec cos. ; or the power in any alternating current circuit is measured by the product of the effective pressure, into the effective current, into the cosine of the angle of lag or lead. The proof that the power factor, where the current leads the pressure is equal to cos. is obtained in the same manner. __________________________ The Fuel Wood Order.—The London Gazette contains the text of the Fuel Wood Order, 1918, dated September 27. Fuel wood is defined as the waste lop, and top of felled timber exceeding 2 in. in diameter, and any other timber unsuitable for conversion into sawn timber or pitwood, and waste produced at a sawmill or factory. All fuel wood is to be held at the disposal of the Board of Trade, and it must first be offered for sale to the dis- trict divisional officer of the Coal Mines Department. Training of Industrial Chemists.—The Salters’ Company is initiating a scheme for an institute called the Salters’ Institute of Industrial Chemistry, under the charge of a director whos^ principal duties will be to make arrange- ments with universities to enable students to obtain facili- ties for research and technical training, and to give advice and information to those who intend to become industrial chemists. The company will establish two types of fellow- ship, for which post-graduate students of any university will be eligible. Mineral Transport Facilities in Ireland.—The opening up of the Wolfhill Collieries is being pushed forward as rapidly as possible. Last week the first train ran between Athy and Gracefield on the new railway, but as the spur line is not yet completed, the coal raised from the mines has to be carted about 400 yards from Gracefield to the new line. It is expected that the spur line will be com- pleted in a couple of months. Provided that the Ministry of Munitions gives the permit for the necessary machinery to pump out the Modubeagh pit, it is anticipated that in six months’ time the two pits at Gracefield and Modu- beagh will be yielding about 500 tons per day and employ- ing over 1,000 men. At a sitting of the Irish Sub-Com- mittee on Inland Transport, last week at Belfast, evidence was given as to the absence of transport facilities at the Ballycastle (County Antrim) coal mines, the nearest sea- port (Portrush) being twenty miles distant. These mines are now working fairly, but want of transport is greatly handicapping them.