ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 



391 



Fig. 16. 



xc,. 



vertically up or down, from the points of intersection of perpendiculars to 

 these two scales at the same draft. 



' If the two scales are scales of equal value, as they usually are, the 

 same result is manifestly gained by simply drawing a line at an angle of 

 45° from the maximum draft (as to XV 

 in the sketch), and dropping a vertical 

 through that line at any draft for which 

 the height of the metacentre, or centre 

 of buoyancy, has been calculated, and 

 then passing a curve through the points 

 so found. Usually, the curve of centres 

 of buoyancy is practically a straight line, 

 except at the lower part. It is difficult 

 to predicate the form of the curve of 

 metacentres, as its character varies very 

 much in different types of ships ; but for 

 ordinary modern cargo- steamers it is 

 usually concave upwards from the base 

 line, and has its greatest values at the 

 lowest drafts. It is, of course, possible 



to devise numbers of other curves which may be serviceable, but the 

 above are those which are most commonly used, and the data for them 

 are generally calculated, even when the results are not plotted down 

 graphically. 



' Stability curves (Sg. 17), in which length of righting arm is measured 

 vertically, and angle of heel is measured horizontally, are sometimes calcu- 

 lated and plotted, but by no means universally. 



XT 



Fig. 17. 



■Z/t 



O' )0' 20° 3f' 40' JO° 



An^'L& ofMe^ . 



' To be of practical utility they require to be extended by plotting 

 different curves for different positions of the height of centre of gravity, 

 corresponding with different conditions of loading. 



' Speed carves, in which indicated horse-power is measured vertically 

 and speed horizontally, are commonly plotted for large passenger and 

 mail steamers, and these are sometimes extended by plotting different 

 curves for varying drafts ; but these curves, when based upon mere hypo- 

 thesis, are not of much practical value, and, as the experimental data for 

 them cannot be obtained without a considerable outlay, they do not occur 

 in ordinary practice. 



' The curves which I have elaborated most in the foregoing memoran- 

 dum are those which are most frequently used. They are often combined 

 in one diagram, in a way which will almost naturally suggest itself, but 

 which I need not describe here, as it will be foreign to your purpose. I 



