Through the courtesy of Mr. W. C. Cushing, Chief Engineer of Maintenance of Way, Pennsylvania Lines West of Pittsburg, S. W. System, the author is enabled to quote very largely from a paper published by him in Bulletin No. 75 of the American Railway Engineering and Maintenance of Way Association. Mr. Cushing made an investigation, with a view to determining, as closely as possible, the relative value of concrete and steel cross-ties, taking cost and prospective life into account, as compared with the wooden cross-ties at present in use. The author states that "some of the data used are costs established from actual practice and from reliable information given, while in other cases assumptions have been made after examining the most reliable information available. It is quite true, of course, that these figures cannot be considered as absolutely correct, but it is believed by the writer that they are fairly trustworthy." The author develops his values on the basis of the formula proposed by Mr. S. Whinery, in the " Railroad Gazette" for November 11, 1904. In order to eliminate any difference due to variability of tie-spacing, all results have been reduced to the cost per linear foot of track.

This annual cost per linear foot of track may be expressed algebraically thus:

Let x=the required annual cost of ties per linear foot of track; c = the first cost in the track per linear foot of track; ʋ = the value of the worn-out tie per linear foot of track; L = the useful life of the tie in years. i=the rate of interest = the interest on \$1.00 for one year; s=an annual payment into a sinking-fund which at i rate of interest for L years will amount to One dollar (s can be taken directly from tables such as that on page 16 of Kent's Mechanical Engineers' Pocket-book): Then x = ci + (c-ʋ)s.

If ʋ=0, then x = c(i + s).

On the basis of the above formula, Mr. Cushing made three tabulations which have not been copied. Table I shows the "cost delivered which a white-oak tie lasting 10 years must reach before it will be economical to use any of the ties heading the columns." The ties considered in this table were made of white oak untreated, inferior woods treated with zinc-chloride and zinc-tannin, but using no tie-plates, also ties of inferior woods using tie-plates and treated with zinc-chloride, zinc-tannin, zinc-creosote, and with creosote costing 30 and 85 cents per tie, also steel ties costing \$1.75 and \$2.50; also concrete ties costing \$1.50 and \$2.25. Table II shows "how long ties of different materials must last in order to be as economical as white oak costing 70 cents and lasting ten years." Table III shows "first cost which can be paid for different kinds of ties in order to be as economical as white oak costing 70 cents and lasting ten years." The kinds of tie considered and also their chemical treatment, if any, are the same in Tables II and III as were stated for Table I. From these various tables Mr. Cushing made the following deductions.

## Deductions From Table I

(1) With white-oak ties costing 70 cents delivered on the railroad, it is economical at the present time to buy inferior woods at a price not to exceed 50 cents, have them treated with zinc-chloride or zinc-tannin, lay them in the tracks without the use of tie-plates (except where it is necessary to use them on oak ties), and use a standard railroad spike. A life of ten (10) or eleven (11) years has been found to be a maximum for such ties without the use of tie-plates and better fastenings, and if the life of ten (10) years is not attained, there will be that much loss to the company.

(2) When a white-oak tie reaches a cost of 86 or 87 cents delivered on the railroad, it will be economical to use the zinc-creosote process, or straight creosote costing 30 cents, if the tie costs 46 cents delivered on the railroad and will last (16) sixteen years; or it will be economical to use straight creosoting costing 85 cents for treatment if the tie can be made to last thirty (30) years, which is French practice, before the oak tie reaches a cost of 80 cents delivered on the railroad. In both of these cases it is assumed that tie-plates, wood screws, and helical linings are used because ties cannot be made to last more than ten (10) or twelve (12) years without the use of proper fastenings, since, otherwise, the tie will be destroyed by mechanical wear. It is necessary, therefore, to use improved fastenings when we expect to obtain a life of ties greater than ten (10) or eleven (11) years.

It will also be economical to use a steel tie costing \$1.75 delivered if it will last twenty (20) years.

(3) When the white-oak tie reaches a cost of 90 cents delivered on the railroad, it will be economical to use either ties of inferior woods treated with zinc-tannin if a life of fourteen (14) years can be obtained, the improved fastenings being used, or a concrete tie costing \$1.50 if it will last twenty (20) years.

(4) When the price of white-oak ties reaches \$1, it will be economical to use a steel tie costing \$2.50 if it will last thirty (30) years, a concrete tie costing \$2.25 if it will last thirty (30) years, or an inferior wood tie treated with zinc-chloride if a life of twelve (12) years can be obtained.

## Deductions From Table II

(5) With ties of inferior woods costing 46 cents delivered on the railroad we must obtain a life of from eighteen (18) to twenty (20) years, whether treated with zinc-chloride, zinc-tannin, or zinc-creosote, to make them as economical as white-oak ties costing 70 cents. It is assumed, of course, that they must have the most approved fastenings in order to attain an age as great as that.

(6) With inferior woods costing 46 cents delivered on the railroad, and if the creosoting costs 30 cents, it will be necessary for us to obtain a life of twenty-one (21) years in order to make them as economical as white-oak ties costing 70 cents delivered.

(7) With inferior wood ties costing 46 cents delivered, and with the creosote treatment costing 85 cents, as in French practice, it will be necessary for us to obtain a life of thirty-six (36) years from the ties in order to make them as economical as white-oak ties costing 70 cents delivered.

(8) With steel ties costing \$1.75 each delivered, it will be necessary for us to obtain a life of twenty-eight and one-half (28«) years in order to have them as economical as white-oak ties costing 70 cents delivered. This price is a little less than the cost of the Buehrer steel ties in the tracks at Emsworth.

(9) With concrete ties costing \$1.50 each delivered, it will be necessary for them to last twenty-eight (28) years before they will be as economical as the white-oak ties costing 70 cents delivered.

(10) With steel ties costing \$2.50 delivered and concrete ties costing \$2.25 delivered, which are approximately the prices of the Seitz steel tie and the Buehrer concrete tie in the tracks at Emsworth, it is necessary for them to last over fifty (50) years each in order to make them as economical as the white-oak ties costing 70 cents delivered.

## Deductions From Table III

(11) In order to make treated inferior woods as economical as white oak costing 70 cents delivered, when the treated ties are equipped with proper fastenings in order to make them last as long as has been found practicable by experience, we can only afford to pay for the ties delivered on the railroad, 10 cents each when treated with zinc-chloride; 20 cents each when treated with zinc-tannin or creosoted at 30 cents; 23 cents each when treated with zinc-creosote, and 29 cents each when creosoted in accordance with French practice.

(12) In order to make them as economical as white-oak ties costing 70 cents delivered, we can only afford to pay \$1.48 each for steel ties which last twenty (20) years, and \$1.79 each when lasting thirty (30) years.

(13) In order to make them as economical as white-oak ties costing 70 cents delivered, we can only afford to pay, as first cost of concrete ties delivered, \$1.15 each if they last twenty (20) years, and \$1.57 each if they last thirty (30) years.

(14) We know nothing about the life of concrete ties, and it is at least very desirable to experiment with them for yard and side tracks, even though we do not use them in the main tracks, because they might lie undisturbed in yard tracks for many more years than they would in main tracks.

(15) When white-oak ties are costing 70 cents delivered (about present prices), we can afford to buy inferior oak and other hard woods at 45 to 50 cents (present prices) and have them treated with the zinc-tannin or zinc-chloride processes, and only use common spike fastenings.