A SUBSTITUTE FOR THE ADMIRALTY FORMULA. 51 



nearly the same. If either one of these ratios vary (even but little) the value of the 

 constant will have to be adjusted or else a large error will result. 



In using the new formula the same considerations hold good but not to the 

 same extent; for example, if the displacement ratio should differ by about lo per 

 cent the value of the constant changes only a small amount, while the speed ratio 

 may vary considerably within certain limits without hardly any change in the con- 

 stant. 



In order to compare these two formulas, Table 9, Plate 43, was worked out 

 for the values of the constants in both the Admiralty and the new formula for the 

 Delaware and Utah* at different speeds. These values were plotted and curves 

 drawn as shown in Plate 32. Curves representing the mean values of these con- 

 stants for the two above-mentioned ships were then drawn. The greatest varia- 

 tion of the curves of the individual ships from these mean curves occurs at a speed 

 ratio of about .yy where it is 5.36 per cent for the Admiralty formula, while for the 

 new formula it is but 1.08 per cent. The values of the mean curve of the constant 

 in the Admiralty formula varies from 383 (at a speed ratio of .487) to 265 (at a 

 speed ratio of .952). This represents a difference of 18 per cent from the mean 

 value between these points, while the value of the constant in the new formula 

 varies between these points from 7.74 to 6.865, which is only 6 per cent. 



The data from these curves give, the writer believes, a very fair comparison 

 of the relative accuracy of the two formulas. The error due to propulsive effi- 

 ciency is done away with, while that due to difference in model cannot be very great, 

 as the two ships are very similar in shape. 



Table 10, Plate 44, shows the value of the constants in the two formulas for 

 the Marietta, Dubuque and Bancroft, from which the curves on Plate 33 were 

 drawn. Mean curves might have been drawn here but it is believed that their im- 

 portance would not be as great as in the case of the Delaware and Utah, as these 

 three ships vary considerably in model; besides this the propulsive coefficients of 

 these vessels are not known. 



VARIATION OF THE VALUE OF THE CONSTANT IN THE NEW FORMULA. 



( 1 ) For ships of the same length, but varying in displacement, the value of the 

 constant seems to be greater for the heavier ship at the lower speeds, while at the 

 higher speeds it is less than for the lighter ship; this is as shown in Plate 31. 



(2) For torpedo-boat destroyers between the speed ratios of .8 and 1.9 the 

 value of C decreases in almost a straight line as the higher speed is approached. 



(3) Between the speed ratios of .4 and .74 the value of the constant falls in 

 some cases while it rises in others as the higher value is approached. From .75 up 

 this value drops, except in the case of very light high-speed motor boats as shown 

 in Table 12, Plate 46. 



*The indicated horse-power of the Utah in this table is assumed by taking her effective horse-power at 

 various speeds, and dividing it by the propulsive coefficient of the Delaware at the same speeds. 



