PRACTICAL EXAMPLES EXPLANATORY OF THE FOREGOING STATEMENT. 1st, Let it be required to determine the expense of working a four-horse coach over the line of road from to, at a velocity of ten miles an hour. Suppose the instrument has been run over the road, and that it has been found that the average power required to draw a fourhorse coach over the whole line amounts to 350lbs., and the distance equal to twelve miles. Let the average power which a horse should exert for eight miles a day, with a velocity of ten miles per hour, be assumed equal to 60 lbs., then 60 × 8=480 lbs., raised one mile in the day; and taking the daily expense of a horse equal to six shillings, we have 480 lbs. 6s.:: 1 lb.: 15, the expense of horse power, exerting a force of one pound over one mile. Thence, 350 x 15 x 12 miles = 630 pence, or 21. 12s. 6d., the expense of horse power required to work a four-horse coach per day over such a road. 2dly, Suppose it be required to determine whether it is more expensive to work a coach over the stage from A to B, or over the stage from C to D, both stages being exactly ten miles, and horse keep the same in both districts. Let the instrument be run over both stages, and suppose the average power thus determined to be 280 lbs. on the stage from A to B, and 320 lbs. on the stage from C to D, the difference is 320-280-40 lbs.; and this difference will amount to 40 × 10 × 15=5 shillings in horse power, in favour of the stage from A to B. Again: suppose the stage from A to B, which is ten miles in length, to be compared with the stage from E to F, which is only eight miles in length, but more hilly, or having a worse surface. Let the instrument be run over each stage as before, and suppose the average power from E to F to be found equal to 500 lbs., whilst the average power over the stage from A to B is only 320 lbs., as this stage is ten miles in length, the expense of working over it will be 320 × 10 × 15=576 pence; and the expense over the stage from E to F will be 500 × 8 × 15=600 pence; from which it will be seen that less expense will be required to draw the carriage from A to B than from E to F, although the distance from E to F is two miles shorter than from A to B; and that the difference of expense will be 600576=24 pence, or two shillings per day for a four-horse coach. 3dly, Suppose it be required to determine the best surface on different parts of a road, which has been constructed on different principles or repaired with different descriptions of road materials. Let the instrument be run. over each portion of the road, and the average power noted - also the rates of inclination, as shown by the instrument, or a spirit level then reduce the average draught over each rate of acclivity to what it would be if it was horizontal; the comparison of the corrected draughts will show the friction arising from the surface in each case. Thus, suppose the average draught over a portion of the road, which has been repaired with gravel, and which rises 1 in 20, to be 250 lbs. The correction for 1 in 20 is 39 2 lbs. The friction of the surface and axles is therefore 250— 39 2, or 210 8 lbs. (See 7th Report of Parliamentary Commissioners of the Holyhead and Liverpool Roads, published by order of the House of Commons, January, 1830.) In the same way, suppose the draught over another portion of the road which rises 1 in 10, but which has been repaired with granite, is found to be 260 lbs. The correction for 1 in 10 is 78 4 lbs., therefore the friction of the surface, or what it would be if it was horizontal, would be 260-78 ̊4, or 181 6 lbs. only; the difference between this and the gravel surface will therefore be 210 8—181 ̊6, or 29'2 lbs., which is equal to a saving of 4 pence for every horse drawing over a mile of such a road, as compared with the other. 4thly, The most important and useful application of the instrument is, perhaps, that of being able to ascertain with accuracy and precision the state of any road, from time to time, as regards its surface; and the state of repair in which it has been kept. The following table, or yearly register of a quarter of a mile of road, will show this more clearly. The numbers in the column represent the draught or horse power, taken at every ten yards. Thus, in the first column of the year 1829, the draughts were in summer 20, 30, 25, &c., and in the second, or winter column of the same year, the corresponding draughts on the same identical part of the road are found to be 35, 35, 30, &c.: these columns added up, and divided by the number of observations, give 44 ̊5 lbs. for the mean summer draught, and 49 45 lbs. for the mean winter draughts, over this quarter of a mile. By following the same process in the following year, viz. in 1830, the mean summer draught was found to be 35 ̊6 lbs., and the mean winter draught 40 36 lbs., showing that the road had been improved in the course of the year very considerably; and by a reference to the numbers in the columns on the same horizontal lines with each other, it will be found the improvement has been general, throughout the whole distance. In the next year, 1831, it will be seen that the average power in summer is 40 52 lbs., and in winter 465 lbs., which shows the road is not so good as it was in the preceding year, 1830, but better than it was in the first year, 1829. Again, in the year 1832, it is found that the average summer draught is 53'6 lbs., and the winter draught 63 18 lbs.: by comparing these numbers with any of the preceding years, it will at once be evident that the road has become worse; and by a reference to the figures in the column, it will be seen that it is defective in every part as compared with the preceding years, but more especially so near the end, where the draught in summer varies from 60 to 85 lbs., and in winter from 75 to 95 lbs.; whereas, in 1830, two years before, the draughts in summer, over the same part of the road, varied from 35 to 38 lbs. only, and in winter from 40 to 46 lbs. The instrument, therefore, shows not only that the road has been getting generally worse, but it points out the particular parts, and the exact amount of deterioration; thus enabling the proper authorities to say that the road has become worse, the amount of the deterioration, and the exact part of the road where such deterioration has taken place. The public advantages to be derived from such a system of road inspection would probably be very great. It would show not only where the best plan of repairing roads has been followed, and point out where there are good and bad surveyors, but it would also show if the money of the trust is improperly applied or wasted on any line of road; and it will enable trustees, who let the repairs of their roads by contract, to determine whether or not the contractors have done their duty, and kept the road in the same state of repair as at first, or whether they had improved it, or suffered it to become defective. There are many other uses to which the instrument may be applied, but the foregoing are the principal ones. 1 |