ON STEAMSHIP PERFORMANCE. 133 
Example of Analysis of the Royal Mail Paddle Steemer ‘ Atraio,’ 
according to Professor Rankine’s method. 
1. L, length on load water-line, in feet.......... 336°5 
2. G, mean immersed girth, in feet, as calculated 
from the girths at twenty-five equidistant 
cross-sections by Simpson’s multipliers .. 52 
The girths are measured for the purpose of calculating an integral, viz. 
G'dz, where G’ is any girth, and dx an element of the length; the use of 
Simpson’s multipliers gives a more accurate value of the true mean girth, 
than is given by merely adding together the girths and dividing by their 
number. In practice, however, where the cross-sections are very numerous, 
there is scarcely any difference between the ordinary arithmetical mean 
and the mean as found by Simpson’s multipliers. Where there are few 
cross-sections, the use of Simpson’s multipliers becomes necessary. 
3. @, area of immersed midship section, in square feet...... 653. 
4. m, ratio in which virtual length of afterbody is less than least proper 
length for speed by the wave theory. 
5. m’, ratio in which virtual length of forebody is less than length of soli- 
tary wave for speed by the wave theory. 
The virtual lengths here referred to are those deduced from the displace- 
ment and dimensions by Mr. Scott Russell’s method; that is to say, the 
lengths of waye-line afterbody and forebody, which would give the same 
displacement. 
These two quantities are to be calculated only when less than 1; for 
when equal to or greater than 1, they have no influence on the results. 
6. y’, mean of squares of sines of angles of obliquity of stream-lines of 
afterbody at their points of inflexion ..............00000s ‘0611. 
Calculated thus :— 
Sines of Squares of 
Water-lines. obliquity. sines. 
1 ‘0871 ergs -0075 
2 1391 omet 0193 
3 1736 mheltehs °0301 
4 2079 Sieve 0432 
5 *2588 arene “0669 
6 5 eae 3090 AD ot 0954 
Wie ca. 4067 nono 1654 
Sum -4278 
Mean -0611=y? 
