72 APPENDIX. 



miles per hour, and she consumes 8'3 bushels of coals per horse power per hour, or about 

 20 tons per day. She is capable of carrying 360 tons of coals, or sufficient for 18 days, and 

 consequently of making a voyage of 3370 miles. 



Let us inquire what will be the capabilities of another vessel of the same model, and of 

 1670 tons in point of distance ; supposing, 1st, her power to be increased proportionally to 

 tonnage ; and 2ndly, that it is increased proportionally to the sectional area or resistance. 



To double the tonnage of a vessel preserving the same model, her linear dimensions will 

 be increased as - 100 to 126 



Consequently, her section or area of resistance - 100 to 158 



And her stowage as 1 00 to 200. 



Now, in the first case, the power being as 200, and the resistance to which it is opposed 

 being only as 158, the increased force per square foot of the section will be as 158 to 200, 

 and the resistance being as the cube of the velocity, the speed will be increased in the ratio 

 of 158-J- to 200i, of 1 to 1'08, or, which is the same thing, 1 to 2^ ; and the capabilities of 

 the vessel for distance will be increased in the same proportion, viz. from 3370 to 3640 

 miles. 



In the second case, viz. increasing the power of the engine only in proportion to the 

 section, the velocity will remain the same as in the former vessel ; but proportional consump- 

 tion of coal will be less in the ratio of 200 to 158, and consequently the length of the voyage 

 will be increased as 158 to 200, or from 3370 to 4266 miles. 



The splendid steam ship, Victoria, now being built by Messrs. Curling, Young, and Co., 

 for the American voyage, is 1825 tons' burden, and has engines of 76 inches cylinders, or 

 nominal power of 412 horses. The speed of this vessel, if the engines bore the same pro- 

 portion to the tonnage as the Medea's, viz. 481 horse power, would be increased in the ratio of 



1 to ( -ggg- \i, or 1 to 1-091, or from 7 ! 8 to 8'5 knots per hour ; but as the engines are but of 



412 horse power, her actual speed will be reduced in the ratio of the cube root of 481 to 

 the cube root of 412, or from 8'5 to 8'08, being an actual increase of velocity above the Medea 

 from 7-8 to 8-08 knots. 



Or we may arrive at the speed differently, as follows : to give the Victoria the same speed 



as the Medea, the power must be increased as 1 to ( V, or 1 to 1' 684, or from 220 to 370 



\ 835 ' 



horse power ; but as the actual power is 412, the speed will be increased above the Medea 

 as the cube root of 370 to cube root of 412, or from 7-8 to 8'08 knots per hour, the same 

 as before. 



The Victoria is estimated to carry 750 tons of coals in addition to her cargo : allowing 

 8-3 Ibs. per horse power per hour, or 36| tons per day, to be her consumption of fuel, she 

 is well able to perform a voyage of 20| days, and traverse a distance of 3960 miles without 

 a fresh supply of coals. Now as the voyage from Cork does not exceed 3000 miles, and 

 will be accomplished in average weather in eighteen days, she will have above 2^ days' fuel 

 to spare. 



In this calculation I have assumed the same consumption of fuel per horse power as in the 

 Medea, making no allowance for the economy of the larger engines ; besides which the Victoria 



