484 POPULAR LECTURES AND ADDRESSES, 



diameter, that is, with the wake of the ship or 

 with the line of progression of the ship. 



A little more as to the law of this diagram, 

 Fig. 48. The echelon waves consist chiefly of the 

 very steep waves at a cusp. The theoretical 

 formula gives infinite height at the cusp ; but 

 that is only a theoretical supposition, though it 

 gives an interesting illustration of mathematical 

 " infinity." Blur it, or smooth it down, precisely 

 as an artist does when he designedly blurs a 

 portion of his picture to produce an artistic effect ; 

 blur it artistically, correctly, and mathematically, 

 and you get the pattern. It will be impossible 

 to realise that perfectly ; but I have endeavoured 

 to do it in the model, necessarily with an enormous 

 exaggeration, however, as you will remark. While 

 every other dimension is unchanged, you must 

 suppose each wave to be reduced to about a fifth 

 part of its height shown in this model ; thus you 

 will get the steep " steamboat waves," so much 

 enjoyed by the little boys who, regardless of 

 danger, row out their boats to them every day 

 at the Clyde watering places. Theoretically these 



