1130 THE COLLIERY GUARDIAN. May 30, 1913. greater number of molecules than any other speed being taken as 1, then, on a proportional scale, the mean square speed G is represented by 1*22. 12, the mean speed, is represented by 1'128. These numbers repre- sent the proportion which the mean square speed bears to the mean speed. Therefore £2 «= G X = G x 0'923. 1'22 We have seen that for oxygen G = 461 m. per second. Therefore Q, = 425 m. per second. £2 is what would be called the arithmetical average, or mean of the speeds, and is the value that would be got by adding together the speeds of the molecules and dividing by their number. It is used whenever we are making calculations dependent simply on the relative motions of the molecules. When, however, we are dealing with their energy the mean square would be employed. 0 L MM Fig. 10. Y X I I 100 200 300 *00 500 METRES Fig. 11. L j—L . i-zkM Fh II 1 I I I I I 600 700 PER SECOND. The application of the calculus of probabilities to physics may at first sight seem fanciful ; but whenever groups of causes having an average distribution co-operate to produce effects, there the calculus applies producing uniformity amid diversity, order out of apparent chaos. When a mob of people crowd into a theatre there are great diversities between the speed and strength of individuals, but inasmuch as they jostle one another, on the average the great majority take the same time to get to the door. So it is with gaseous molecules. The practical method of drawing a curve of molecular distribution of velocity for oxygen is as follows :— 4 First draw the curve y = —— l2e~l&. To do this, s/tt prepare a table of relative values of I and y. This can be done by means of a table of common logarithms, for log y = log 4 — J log 7T 4- 2 log I - I2 log10e = 0'35348 + 2 log Z - 0'43426 x Z2. By giving Z various values, a table may be constructed as follows:— 1 4 y = V2e~12 I 4 y = J2e-Z2 1'0 0'8320 IT 0’8143 0'9 0'8123 1’2 0’7702 0'8 0'7442 1’3 0’7036 0'7 0’6774 1’4 0’6231 0'6 0’5663 1’5 0’5356 0’5 0’4423 1’6 0'4426 0'4 0’3076 1’7 0'3624 0'3 0T856 1’8 0'2864 0'2 0’0867 1-9 0'2204 0'1 0’0109 20 0T832 From this table the curve may be drawn. The mean speed £2, as represented on this curve, corresponds to a value of Z = 1'128, as has already been shown. This represents a velocity of Q = 425 metres. Knowing this, the values of various other velocities can be marked off along the line O X. The areas bounded by the ordinates and the curve then give the proportional numbers of molecules which have velocities between the limits of the corresponding abscissae. They will in general have to be determined by measurement, as the integrals necessary to calculate them are difficult. They will be valued on the assump- tion that the whole area of the curve = 1. Thus the two centre ones are 0'214 and 0'202 respectively. This means that the proportion of molecules of oxygen that have a velocity between 300 and 400 metres per second is 0'214 of the whole number. By adding up the areas it is easy to see that 0'93 of the whole number of molecules have velocities under 700 metres per second, and that the number of molecules having velocities much above or below the mean velocity is relatively very small. It may next be asked how it comes about that if 425 metres per second is the mean velocity, that the curve evidently shows that the velocity possessed by the greatest number of molecules is not 425, but is less than 400? This velocity would evidently be the most probable velocity; in the sense that if any molecule were selected it would be more likely to have that definite velocity than any other definite velocity. The answer is, that though there are more molecules with that velocity than with any other velocity, yet that the mean involves the general average velocity, not the velocity of the favoured few, and that though around that most probable velocity a comparatively numerous group is gathered, yet that the numbers rapidly fall away, and that the true concentration is not a narrow concentration round a high velocity, but a wider con- centration round a slightly smaller velocity. If there were a bag of marbles, verging in colour from black through all shades of grey to white, though the black might be more in number than any other particular shade of grey, and thus the “ most probable ” colour would be black, yet the average tint would be a shade of grey—a shade of which it would be quite possible that the actual number might be very^ few indeed—but so surrounded by other kindred shades of grey that the average was round that shade, and not round the black. (To be continued). LABOUR ABD WAGES. North of England. In order to provide work for the 87 coal hewers and also for the datal men who have been laid off at Heworth Colliery on account of an inrush of water into one of the seams, the management have offered to reinstate the men if they will consent to work four shifts. This, however, the men have refused. Three shifts are being worked at present. The annual meeting of the Northumberland Miners Council was concluded last Friday at the Burt Hall, Newcastle, Mr. Joseph English again presiding. It was resolved unanimously that the executive committee take up the case of the night workers and comply with any requests for the holding of meetings to assist propaganda effort for the better organisation of the night workers. After considerable negotiations a settlement of the claim of the Cleveland mines deputies for an advance of wages has been arrived at. The men originally asked for 6d. advance on base rates, and the matter was con- sidered at a conference between the mineowners and the miners’ representatives held at Middlesbrough, when it was decided to increase the wages by 3d., and that the advance should commence from March 31. On Saturday the Wages Committee of the North- umberland Miners’ Association met the coalowners of the county at the Coal Trade Offices, Newcastle, for the consideration of an application on behalf of the miners for an advance of wages. Mr. Tom Taylor presided. The miners of Northumberland received four advances in wages in 1912, amounting in all to 11£ per cent. At the end of February this year a further increase of 3J per cent, was granted, making their wages 42| per cent, above the basis of 1879 in the case of underground workmen and banksmen, and 34 per cent, in respect of other classes of surface labour. The meeting lasted about two hours. At the close it was officially stated that wages had been advanced 6J per cent., making the wages 48if per cent, above the basis of 1879 in the case of underground workers and banksmen, and 39percent, in respect of other classes of surface labour. The advance takes effect as from Monday first. A largely attended meeting of the Newbiggin miners was held on Saturday, to consider the dispute in con- nection with which notices were tendered over a week ago, to resist the joint committee’s award for a reduc- tion of 5d. per ton in hewing prices. Subsequently notification was sent to the management of the colliery by the lodge officials of their intention to withdraw the notices, and it was not expected that any obstacle would be placed in the way of that being done. It was also stated that the men intend to continue their efforts for the abolition of the joint committee. A conference on the question of the abolition of the three-shift system in Northumberland was held on Tuesday at the Coal Trade Offices, Newcastle. Repre- sentatives of the Miners’ Federation of Great Britain were present at the conference, over which Mr. Tom Taylor presided. The meeting lasted for three hours, and at the conclusion it was announced that the owners were not able to agree to the proposal for the abolition of the third shift. They were, however, prepared to consider any proposal which might be put before them by the workmen’s representatives with a view to modifi- cation. In all probability a further meeting will be held. A meeting of the Conciliation Board associated with with the Cumberland Brick workers was held at the Coalowners’ Association Offices, Workington, last week, Mr. Lloyd Wilson presiding. Mr. G. A. L. Skerry wrote accepting the position of neutral chairman. The Board discussed the men’s demands for a 10 per cent, advance, and eventually postponed its further considera- tion until next Tuesday, on the understanding that any advance that may be given is to date from April 28. Federated Area. After a five hours’ conference on Wednesday, at Leigh, between representatives of Bickershaw, Bedford and Westleigh colliery companies, Leigh, and the Miners’ Federation officials, representing 4,000 Leigh miners, it was agreed that the wages of the surface workers engaged in manipulating coal be increased 15 per cent., the first payment to be made on June 12. Boys aged 13 now getting Is. 6d. daily will receive Is. 9d.; boys of 17, 3s.; and men aged 21 years, 4s. 9d. a day. Moreover, all those working over nine hours a day will be paid overtime. The resumed conference between representatives of the Midland Counties Coalowners’ Association and the Notts Miners’ Association took place at the Victoria Station Hotel, Nottingham, on Friday, May 23, with regard to the hours, wages, and conditions of labour of surface workers other than those who manipulate coal at the Silver Hill, Teversail, and Brierley Hill collieries. Mr. J. T. Todd, general manager of the Blackwell Colliery Company, presided over a representative attendance of owners and miners’ officials, the meeting being one which was adjourned from May 2 to hear the owners’ decision on matters then brought forward. The owners intimated that they had decided not to consider the enginemen’s and firemen’s hours and wages at these particular collieries, explaining that they considered that these were outside the jurisdiction of the Notts Miners’ Association. They were not prepared to give a uniform rate of wages to those classes of labourers under consideration. They were, however, prepared to discuss each individual case on its merits at the respective collieries, and to fix a minimum rate of wages for the general labourer. The workmen’s repre- sentatives took strong exception to the owners’ action in regard to the enginemen and firemen, maintaining their right to deal with any question affecting any member of the Notts Miners’ Association, irrespective of their position. It was agreed that further meetings should be held at the particular collieries affected. The Lancashire and Cheshire Miners’ Federation continues its campaign against non-unionists. Unless the non-union men employed at Messrs. R. Evans and Co.’s extensive pits in the Golborne and Hay dock districts of southern Lancashire join the Federation, notices to cease contracts were to be tendered on Thurs- day this week. Similar action is to be taken at other firms’ collieries in the Wigan area. Altogether between 7,000 and 8,000 men and youths are affected. Although the whole of the clay miners in the Cradley Heath, Lye, Halesowen and surrounding districts who came out on strike in consequence of the employers’ refusal to pay the 5 per cent, advance have resumed work, there appears to be a likelihood of further trouble arising. The miners’ agent (Mr. Samuel Ed ivards) inter- viewed the whole of the employers in the Black Country area upon the matter, and the miners returned to work upon a promise being made by the colliery owners that the increase would be paid by them. Last week-end, however, Mr. Edwards was informed that the employers had reconsidered the question, and were not prepared to pay the 5 per cent, to the clay miners, their conten- tion being that this class of worker cannot be regarded in the real sense of the word as “ miners ” who come under the ruling of the British Conciliation Board. Mr. Edwards proposes to bring the position of this class of worker before the Miners’ Federation, so as to obtain an important decision with regard to the point raised by the employers. There are between 500 and 600 clay miners in the whole of the area, and their wages vary from 4s. to 6s. Id. per day. With the obiect of securing a more uniform rate of wages Mr. Edwards has made a suggestion to the employers for the forma- tion of a wages board to apply solely to the clay-mining industry. This is a matter which is at present under the consideration of the Colliery Owners’ Association. Scotland. A meeting of the members of the Musselburgh and District Branch of the Scottish Colliery Firemen’s and Shotfirers’ Association was held on the 23rd inst. Mr. William Stein, secretary, reported that he had repre- sented j to the management of the Edinburgh Collieries Company Limited, and to the management of the Niddrie and Benhar Coal Company Limited, that the local firemen were dissatisfied with their wages, and wished the establishment of a minimum wage of 7s. 3d.