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in projection an imaginary circle of 360 degrees through the diameter joining 90 degs. and 270 degs. This line is the surveyors' north and south axis, whilst, by co-ordination, all points of survey must be referred to an origin which lies at the intersection of an east and west axis drawn at right angles to the north and south axis or to a parallel thereto. The reference of the points of survey to this origin is by means of ordinates and abscissæ, having sign values in accordance with the direction of their projection on to the axis of co-ordination. We should thus cease to speak of a line bearing N 40 deg. E,” and say that it is a line“ whose angle of direction is 130 degrees.” The writer maintains that this is no pedantic distinction, but is a true mathematical expression, and in accord with the practice of the Land Surveyors of this Colony, who fix the north direction as go degrees.

After such a free criticism of other people's methods, it would be invidious of the writer not to proffer both a method of procedure and a method of calculation. But, in criticising, the writer has in many cases made clear what he considers the best practice should be, whilst, at the same time, he recognises that he is but criticising information supplied to him, and not a method with which he has been actually in touch. Therefore, it is possible that in putting forward the following forms he may be including much which he has failed to find in the copies of the six systems included in this paper :

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24'26

Inst. 2'45
Dist.

Pb. 1.61 Tr. 560 NOTE: R.C., L., etc., denotes whether station is right, right centre, centre, left centre, or left of drive, cross-cut, etc. Inst. = height of instrument below station plug in hanging of drive. Pb. = length of plumb line at foresight. Tr. = height of track from rail level to station plug at foresight. “A” “B” mean A and B verniers.

The date of survey is recorded. The instrument is clamped at any point of circle, thus avoiding wear in the clamps, etc., when always set at zero. If the booking be consecutive with the procedure of observation, there can be no mistake about which is the angle measured in the right direction. Thus, the reading at 931, being the foresight, is subsequent to the travel of the telescope from the reading at 929, being the backsight. Subtracting the first reading from the second gives the angle measured in the right-hand direction. Now, to check this, the telescope is transited, and the operations repeated. But rather than check this angle, measured in the right direction by again subtracting the first reading from the second, the writer prefers to take out the angle measured in the left direction, i.e., subtracting the second reading from the first (vide calculation), and thus ensure that the sum of the two shall equal approximately 360 degrees. All the numerical work that is required at the instrument when observing is mentally to determine that the readings, when the telescope is transited, are 180 degrees from the first readings.

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+ 25'13

+ 14936

+ 25 136

+ 875-24
+ 890'17

- 298:43
- 273-30

+ 875-24
+ 890'17

298.43
273-30

(931)

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NOTE : The writer prefers to do the calculations in a foolscap book, square sectional paper, rather than on loose sheets of paper.

The date and reference to page and number of field book should always precede the calculations.

x is a symbol, meaning "the angle of direction of.”

X 930-929 and x 929–930 are both copied down from final calculation for 929, the two angles differing by 180 degs. By adding the right angle to the one, and subtracting the left angle from the other the new angle of direction is obtained in two ways, differing by 180 degs. The check on taking out the angles from the field book is that they add to approximately 360 degs. allowing for the errors in reading. The mean is taken out to the nearest 10 secs., the extent to which the logarithmic tables are used.

Dips are worked out first; an angle of dip of less than i deg. is negligible for cosine. Elevations are carried out at once by bringing forward reduced level of starting point. If it has been necessary to work out horizontal distance, then logarithm so obtained is brought forward for calculation of latitudes and departures, the logarithmic calculations of which always decide the value in preference to decimal points of check.

The writer is of opinion that this method of calculation will ensure that mechanical check of accuracy so necessary in results of this importance. From long practice he has found that the calculation of any one point takes about ten minutes. The method of procedure takes a varying amount of time, according to the amount of accessory data the surveyor may find necessary to note down. On the average, ten minutes at any one station, is about an average time, when native assistants are hanging plumb bobs whilst surveyor is levelling the instrument.

The writer cannot conclude without hoping that, though he has made free use of information which several individual mine surveyors have supplied at the request of their Consulting Engineers, it will be felt that he is grateful for the trouble taken in forwarding this information. As several have asked that no names might be mentioned, the writer can only tender his thanks collectively to both the Consulting Engineer of the Group and the individual surveyors.

To the members of this Association his apologies are due for bringing to their notice so much that savours of text-book work. The writer feels, however, that by placing these deductions on record, the attention of many mine surveyors may be called to the want of coherence in their work, which may result in some practical good.

By G. W. HERDMAN, M.INST.C.E.

There is much difference of opinion as to the proper method of charging consumers for water. All must have water, and must pay for it, either directly or indirectly, and, consequently, it is of some importance that the public should know for what the payment is made and how it is exacted.

It is assumed in this paper that the water is not supplied by a private money-making company. The number of these is gradually being reduced, and Waterworks for the supply of large communities are being taken over by Municipalities or Water Boards. Many of the old Companies have been compelled by Act of Parliament to limit the amount of their dividends, and if the profit is more than sufficient to pay that dividend, the consumers have to get the benefit, and the price of the water is reduced. Municipalities generally consider that the water supply is one of the first undertakings which it is their duty to control for the public benefit, and the Municipal Corporations which have recently come into being in the Transvaal have not been slow to accept their responsibilities. Many of them are now either proposing or carrying out works, and as all citizens have the double interest in the system of rating that comes to them as consumers or purchasers, on the one hand, and as voters or sellers on the other, this is a subject which Councillors must carefully look into before drawing up a new tariff.

In some towns the revenue from water not only pays all the expenses chargeable to that account, but supplies a balance for other Municipal purposes. Pretoria is an example of this. In the published accounts for the year 1904 the balance is £10,687 185. 6d. At the same time the public health of the community is so dependent upon the water service that in some cases a Municipality would be justified in carrying out a water works project, even though the purely water revenue did not equal the expenditure. The deficiency would be made up by indirect returns, due to increased prosperity.

On account of this universal necessity for water, the charges for it are frequently drawn up on entirely different lines from the charges for some other public services, such as electric light, or tramways.

These latter are taken as luxuries, which individuals may indulge in or not as they please. The water service is more frequently classed with drainage works, street paving, street lighting, and such like, which are necessities to all, and for which the revenue should be obtained from the citizens in as equitable a manner as possible. On that account it is sometimes considered good policy so to regulate the charges that the burden falls less heavily on the poor than on the rich.

In the poorer parts of London this is so. The East London Water Works Company supplied house property by assessment, and large manufactories, taking millions of gallons of water per diem, by meter. In the latter case the rate charged was almost double that in the former. Nearly 20 per cent. of the houses supplied paid less than 10/- per annum,

while the average

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