150 × 100 × 1200=150 × V2 × 1800,
Or,120,000=1800V2,
Reduced,1200/18=V2,
AndV=√66.66 = 8.15 knots.

From the foregoing easily intelligible formulæ we can ascertain with approximate certainty the large quantity of coal necessary to increase speed, the large saving of coal in reducing speed, as well as the means of accommodating the fuel to the voyage, or the voyage to the fuel. It is not necessary here to study very closely the economy of fuel, as this is a question affecting the transport of freight alone. When the mails are to be transported, economy of fuel is not the object desired, but speed; and, consequently, we must submit to extravagance of fuel. This large expenditure of coal is not necessary in the case of freights, as they may be transported slowly, and, consequently, cheaply. But one of the principal reasons for rapid transport of the mails is that they may largely anticipate freights in their time of arrival, and consequently control their movements.

I recently had an excellent opportunity of testing the large quantity of fuel saved on a slight reduction of the speed, and give it as illustrative of the law advanced. We were on the United States Mail steamer "Fulton," Captain Wotton, and running at 13 miles per hour. Some of the tubes became unfit for use in one of the boilers, and the fires were extinguished and the steam and water drawn off from this boiler, leaving the other one, of the same size, to propel the ship. An intelligent gentleman who happened to know that we were using only one boiler, and consequently, but half the power, remarked to me that it was very strange that the ship was still going about eleven miles per hour, without any sail. He said: "It is strange, sir; two boilers of equal size drove us thirteen miles per hour; and here now but one boiler drives us nearly eleven miles, or nearly as fast; when common-sense teaches that the one boiler would drive us only six and a half miles per hour. How is that?" I then explained to him very clearly the natural law relative to power and speed, (See [Rule II.], page 68,) which he at once comprehended and admitted, but with the remark: "Indeed, sir, I would have testified that she ought with one boiler to have gone at only half the speed; or that going at six miles with one boiler, she would go twelve with two."

As it will be interesting to the general reader to examine the details of the increased consumption of fuel at increased rates of speed, I present the following elaborate table recently prepared by Mr. Atherton for his new edition of "Steamship Capability," according to the formula above noticed, and the performance of the best type of vessel in the Royal Navy, the steamer "Rattler." Mr. A. found a higher efficiency in this vessel per horse power than any other in the Navy, and consequently based the consumption of coal in the table on the assumption that the mail and passenger vessels generally should be of as good contractive type as "Rattler." I shall present also another table showing a much larger consumption of fuel by an inferior type of vessel. I use these tables because they are thoroughly correct, and quite as perfect as any that I could construct on the same formula; and because they carry with them the weight of probably the highest authority in Great Britain.

COAL TABLE: No. I.

Displacement,[B] Speed, and Fuel consumed per Day, for Mail, Passenger, and Freight Steamers, whose locomotive performance is equal to that of the best class of ocean steam vessels; assuming the consumption of fuel to be 41/2 lbs. per indicated horse power per hour, equal to 33,000 lbs. raised one foot in one minute. The quantity consumed is expressed in tons per day of 24 hours.

[B] Displacement refers to the number of cubic feet of water displaced by the hull; allowing thirty-five cubic feet to the ton.

SHIP'S
DISPLACEMENT.
SPEED PER HOUR.—NAUTICAL MILES.
67891011121314151617181920
TONS.TONSTONSTONSTONSTONSTONSTONSTONSTONSTONSTONSTONSTONSTONSTONS
1001.041.652.473.514.826.418.3210.613.216.319.723.728.133.038.5
1251.201.922.864.075.597.449.6612.315.318.922.927.532.638.344.7
1501.362.163.234.606.318.4010.913.917.321.325.931.036.843.350.5
1751.512.403.585.107.009.3112.115.419.223.628.734.440.848.056.0
2001.652.623.915.577.6510.213.216.821.025.831.337.644.652.461.2
2501.923.044.546.478.8711.815.319.524.329.936.343.651.760.971.0
3002.253.445.137.3010.013.317.322.027.533.841.049.258.468.780.1
3502.403.815.688.0911.114.819.224.430.537.545.554.564.776.288.8
4002.624.166.218.8512.116.221.026.733.341.049.759.670.883.397.1
4502.844.506.729.5713.117.522.728.836.044.353.864.576.690.1105
5003.044.837.2110.314.118.724.330.938.647.557.769.282.196.6113
6003.435.468.1411.615.921.227.534.943.653.765.178.192.8109 127
7003.816.059.0212.817.623.530.438.748.459.572.286.6103 121 141
8004.166.619.8714.019.325.633.342.352.965.078.994.6112 132 154
9004.507.1510.715.220.827.736.045.857.270.485.4102 122 143 167
10004.837.6711.416.322.429.838.649.161.375.591.6110 130 153 179
12505.608.9013.318.926.034.544.857.071.287.6106 127 151 178 208
15006.3310.015.021.429.339.050.664.480.498.9120 144 171 201 234
17507.0111.116.623.732.543.256.171.389.1110 133 159 189 223 260
20007.6612.218.225.935.547.361.377.997.4120 145 174 207 243 284
25008.8914.121.130.041.254.871.290.5113 139 169 202 240 283 329
300010.016.023.833.946.561.980.4102 128 157 191 228 271 319 372
350011.117.726.137.651.568.689.0113 141 174 211 253 301 354 412
400012.219.328.841.156.375.097.3124 155 190 231 277 329 386 451
500014.122.433.547.765.487.0113 144 179 221 268 321 381 448 523
600015.925.337.853.873.898.3128 162 203 249 302 363 431 506 591
700017.728.141.959.681.8109 141 180 224 276 335 402 477 501 654
800019.330.745.865.289.4119 155 196 245 302 366 439 522 613 715
900020.933.249.570.596.7129 167 215 265 327 396 475 564 663 774
1000022.435.653.175.6104 138 179 228 285 350 425 510 605 712 830
1250026.041.361.787.8120 160 208 265 330 406 493 592 702 826 963
1500029.446.669.699.1136 181 235 299 373 459 557 668 793 933 1088
2000035.656.584.4120 165 219 285 362 452 556 675 809 961 11301318
2500041.365.697.9139 191 254 330 420 525 645 783 939 111513111529
3000046.674.0111 157 216 287 373 474 592 728 884 1060125814801727

By the inspection of this table we can see in condensed form the coal-cost of any speed as high as twenty miles per hour, and for any size of vessel from one hundred tons to thirty thousand tons. Let us find in the left hand column a vessel of 2,500 tons displacement. Pursuing the line along to the right we find in the second column 8.89 tons of coal, which a steamer of this displacement would burn in 24 hours, if running, as indicated at the head of the column, 6 Nautical miles per hour.