long, to crossarms of posts driven firmly in the ground. Five mercurial thermometers were suspended so that the bulb was in proximity of the wires, at the 100, 300, 500, 700 and 900 meter marks. The tension was applied by three spring balances and the distances were marked carefully on a metal plate securely fastened. In this manner ninety-nine sets of measurements were obtained, and it was possible to obtain two hundred measurements per day. The probable error in the field work was about 1:10,000,000, and the probable error arising from the comparator 1:4,000,000, making the probable error in whole work about 1:3,000,000, a degree of refinement that had never been equaled before, I think. A wooden rod, such as described by Mr. McElroy, is subject to a change of length due to a varying temperature the same as a metal tape or wire, and the coefficient of expansion is not as well known, although considerable smaller; and, as he says, its length is affected by dampness, whereas it has no effect on the steel tape except as it may cause a change in the temperature of the tape. Therefore, the tape would be preferable for measurements on a dewy night, which many engineers consider one of the best conditions for making a careful measurement. Again, no matter how carefully the rod may be clamped in position, when the forward rod is brought against the last placed rod, a slight jar is very apt to disturb the rear rod, thus causing an error. It seems to me that with the same care applied to a measurement by a steel tape as that used by Mr. McElroy with his wooden rod apparatus, that the result obtained should be more accurate, and certainly the amount of ground covered would be greater. In ordinary field work this would surely be the case with a green crowd of assistants. So it would seem that when fairly accurate, or even very accurate work, has to be done, the steel tape is the best known means as well as the most convenient, but of course, if a very high degree of refinement is required, then an apparatus such as that used by Mr. Haskell would be better. This, however, is simply a modification of the steel tape. The President: The chair might add, in supplementing Mr Wisner's discussion, that in the last two or three years some very precise measurements have been made in the neighborhood of the Straits of Mackinaw by means of steel wires. These wires have the length of one kilometer, and there are two wires, one of phosphor bronze and one of steel; they were soldered together at one end, and the comparative readings at the other end of the wire indicated the temperature, the set of wires becoming a thermometer. These wires were supported at short intervals, 25 or 30 feet, and are subjected to a dead weight pull. The weight is attached to one end of the wire, and is carried over a wheel which has a bicycle wheel center, reducing the friction to a very small amount. By this method the probable errors in measurements have been reduced to much below one in one million. ABSTRACTS OF PAPERS IN FOREIGN AND AMERICAN TRANSLATIONS AND PERIODICALS. "STATISTICS OF GAUGINGS MADE IN THE PRINCIPAL BASINS OF FRANCE." Abstract from an Article by M. BRESSE.* (Published in the Annales des Ponts et Chaussees, 1897, Third Quarter.) In this article Mr. Bresse commences by saying that his aim was not the inventing of new methods of gauging, nor the making of new experiments, but simply the compiling of the statistics of the results obtained. The author further says: In each basin we have kept separate, as particularly interesting, the information relating to the floods and to low water; further, whenever the gaugings were numerous enough at any one station, we have endeavored to establish a relation between the discharge and the height or the nearest gauge reading, and to express this relation by an algebraic formula as well as by a curve. Is is almost always possible to represent the discharge curve by the parabolic formula Q-A+B H+C H by properly disposing of the three coefficients. and this is the form which has been generally adopted. Unless otherwise indicated H represents the gauge reading; but as the discharge at low water is particularly interesting we have in most cases put our formulas under the from Q=A+B (H-e)+C (H-e), e being the positive. or negative ordinate corresponding to low water, and consequently (H-e) the height above the low water. Such formulas have no value beyond the value of the gaugings used in establishing them. If they have been sufficiently numerous, the accidental errors are eliminated, but if there should be a systematic error, like the inaccurate rating of the meter, or wrong selection of co-efficient, these errors will affect the formula. Only an abstract will be given of the very complete and exhaustive statistics which follow, and of the methods used in obtaining the results. THE SEINE BASIN DISCHARGE AT EXTREME HIGH WATER., During the flood of 1882 and 1883 observations taken on the Seine by means of floats, the tube of Darcey or the current meter of Lagrené gave the following results: Flood of Dec., 1882. Maximum at Mantes: 7.54 m. (Dec. 8th and 9th.) *Translated for the Journal by Mr. Ralph Modjeski, Mem. W. S. E. Dec. 11, 1882: Below the mouth of the Eure (between Elbeuf and Orival, kil. 221), 2,483 cub. m. Dec. 10, 1882: Above the lock of Poses (kil. 201.8) 2,246 cub. m. Dec. 8 and 12, 1882: Below the lock of the Garenne (kil. 162.4), 2,363 cub. m. Dec. 9, 1882: Above the lock of Port Villez (kil. 143.8), 2,149 cub. m. Dec. 9, 1882: At Merincourt (kil. 120.9), 2,203 cub. m. Dec. 10, 1882: Above the lock of Meulan (kil. 95.6), 2,128 cub. m. Flood of January, 1883. Maximum at Mantes, 7.60 m: Jan. 6, 1883: At Rolleboise, 2,201 cub. m. The principal information relating to high water in the Seine at and above Paris is given in the following table: GAUGINGS AT LOW AND MEAN STAGE OF WATER. Seine: At Mantes the discharge curve has been platted from gaugings made at Triel and Manoir. These gaugings gave the following results: From these results Mr. Cheysson arrives at the following formula for the discharge curve: Q=90 √(H+I)3 (0.62+0.05H) It was suggested to replace this complicated formula by a simpler one: Q=71+110 H+25H2 (Lagrene) or Q=170+150 (H-0.80)+22 (H-0.80)' (Preaudeau) For the discharges of the Seine at Paris Mr. Preaudeau suggests the two following formulas, reduced to the gauge of La Tournelle and to be applied only for gauge readings greater than 2 metres: Q=110+180 H+9H2 and Q=70 √(H—1.80)' These two formulæ, which give practically identical results, have been arrived at from gaugings by floats in Paris during the floods of 1876, 1879 and 1882-3, and at St. Cloud in 1876, 1877 and 1882. Their correctness has been confirmed by the high water of 1889. In the parabolic formula the co-efficient of H' is relatively small. The straight line formula Q=25H gives results which are within 3 per cent. of those given by the parabolic formula. A number of other similar formulæ for different points on the Seine are cited by the author also for the rivers Oise, Aisne, Marne, etc. A number of plates accompany the paper of M. Bresse, showing the various observations and discharge curves platted as derived from the formulæ. DISCHARGE AT LOW WATER. The author cites some results of gaugings obtained at low water in the Seine, Oise, Aisne, Marne, etc. THE MEUSE BASIN. The method for this basin is here given in brief. Discharge curves for a number of stations have been drawn from direct observations made with the wheel of Woltmann. In addition to these, which we will call principal curves, a certain number of auxiliary ones were established for intermediate stations in the following manner: The discharge at the lower stages of water was obtained from gaugings at the nearest power plant; the rest of the curve was obtained by comparing the heights reached by various floods, with the discharges observed for the same floods at the two nearest principal stations. Mr. Mouton has figured by means of the discharge curves of the various stations the total discharge of the river Meuse during the flood of 1882-83, lasting from Nov. I until Jan. 15. Comparing these total discharges with the amount of rainfall in the watershed he obtains the following co-efficients or percentages of runoff: Pagny-la-Blanche-Cote (principal station).. .0.73 .0.73 0.76 ..0.73 ..0.78 ..0.83 ..0.81 0.76 ..0.83 ..0.84 ...0.81 It was since deemed necessary to modify the original curves, owing to the recent construction of sewers. This was done in the same manner as explained above with reference to auxiliary curves. The author then gives various formulæ for discharge curves of the river Meuse at different stations, similar to those of the Seine basin. THE MOSELLE BASIN. At Epinal, Mr. Denys has calculated the discharge of the Moselle by applying the weir formula at the Champs du Pin weir: Q=0.40 L h2 gh |