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 1 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 18s. 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

revenue from all house property was just over 20/- per supply per

annum.

In many towns special consideration is not given to the poor or small consumers. In Portsmouth a trade consumer, who takes by meter 30,000 gallons per quarter, is charged 1/6 per 1,000 gallons; a customer who takes 500,000 gallons per quarter is charged 11d. per 1,000 gallons, the former being 50 per cent. higher than the latter. In Germiston many customers take less than 600 gallons per month, for which they pay the minimum charge, 8/- (being 6/6 for water per 1,000 gallons and 1/6 meter rent), whilst a customer taking 4,000 gallons per month is charged 27/6. The former rate is 1/4, and the latter 81d. per 100 gallons, i.e., the former is about 100 per cent. higher than the latter.

The

It will be advisable first of all to look into the ordinary expenditure, to see what the revenue must be made to cover. expenses may be given as :

Interest on Capital borrowed.

Redemption.

Management.

Secretary.

Accountant.

Collectors.

Stationery, etc.

Maintenance.

Water Rights.

Rents.

Rates and Taxes.

Engineering.

Reservoirs.

Mains.

Pumping.
Filtration.

In valuing Waterworks undertakings, which already have had a long life, it is customary to consider that such a sum is being spent annually on maintenance, as will keep the works in first-class order, so that not only repairs, but also renewals, are included. The maintenance is consequently high. Depreciation and Redemption are then not considered, as the works are taken to be at any time of full value for earning revenue. A new undertaking is, however, different, and it is right that Redemption should be allowed for, as during the first few years maintenance is likely to be small. In the Pretoria published accounts, Depreciation is included, but on the Capital Expenditure interest only is paid, and not Redemption.

How the revenue to cover these expenses is to be obtained, and from whom it is to be collected, is the matter under discussion. long as the money is obtained, it is immaterial to the Corporation from whom it comes, and the easier it is to collect the lower do the Management costs drop, and the less has to be collected. The payer

So

generally prefers to think of his money going for pumping or filtration rather than for clerical or office expenses.

The proportion that these different items bear to one another is of interest, and some actual cases are given in Table I., and shown diagramatically on Figure No. 1.

To obtain the necessary revenue, Corporations have different systems of charging their customers and different opinions as to who the customers are. In some cases the consumer is the customer, and is made to pay; in some cases the owner of the property supplied is charged. Payment, too, may be exacted :

(a) According to the quantity of water used.

(b) According to the opportunities of using it.

(c) According to the value of the premises where the supply is taken, or

(d) Any combination of those systems.

Before discussing these different systems in detail, it is worth while considering who use the water, who benefit by it, and who pay for it.

I. The greatest user is generally the Municipality, which draws heavily for street water, sewer flushing, and fire extinguishing. In Johannesburg, street watering takes 30 per cent. of the whole supply, and in Pretoria 12 per cent. (see Table II. and Figure No. 2). The beneficiaries in this case are:

(a) All inhabitants of the town, who live in more healthy surroundings on account of the Municipality's action, and

2.

(b) All landlords, on account of the increased value and safety of their property. This Municipal water is generally paid for by a tax, which may be a general assessment rate, falling on the landlords, or a public water rate, paid partly by tenant and partly by landlord. In some cases a general charge is not made, with the result that those who pay for water pay not only for what they use, but for a share of what the Municipality uses. The next users to be considered are the townspeople, the house occupiers, who use water for domestic purposes, garden watering, etc. In this case the beneficiaries are the users. The payment is made sometimes by user, sometimes by landlord. It is a common practice to charge the user in good class property, which has a valuation above a certain limit, but to charge the landlord in the case of property of lower value. It is a convenience to the seller to deal only with landlords. There are not so many bad debts, there are fewer landlords than there are householders, and consequently it is less trouble to collect the money, and the landlord may be trusted to take his equivalent out of the tenant.

3. Business people who require large quantities of water for trade purposes. This includes all cases where the amount used on any premises is greater than is required for ordinary domestic purposes. These may be looked on as wholesale purchasers, in contrast to