172 ON AERIAL NAVIGATIOlJr. 



tliese two laminae proceed till they are themselves reflertedf, 

 when they (considered as one lamina of larger dimensions) 

 rush against the third and fourth, which together contain 

 three times the fluid in the two former laminij?, and thus re- 

 duce the dire«'tioTi of the combined mass to one fourth of 

 the angle between the axis and the line of the second re- 

 flection. This process is constant, whatever be the angles 

 formed between the surface of the actual solid of least re- 

 sistance at these points of reflection, and the directions of 

 tlje currents thus reflected. 

 Ja£er«n.ce. From this mode of reasoning, which must in some degree 



resemble what takes place, and which I only propose as a 

 resemblance, it appears, that the fluid keeps creeping along 

 the curved surface of such a so]id> meeting it in very acute 

 angles. Hence, as the experiments of the French. Academy 

 show, that the differeiice of resistance between the direct 

 impulse, and that in an angle of six degrees, on the same 

 , iurface, is only in the ratio of 10 to 4, it is probable, that 



iu the slight difference of angles that occur in this instance, 

 the resistances may be taken as equal upon every part, with- 

 out any material deviation from truth. If this reasoning be 

 correct, it will reduce the question, so far as utility is con- 

 cerned, within a strictly abstract mathematical inquiry. 

 Figur^of the It has been found by experiment, that the shape of the 

 "mDdUam'^ hinder part of the spindle is of as much importance as that 

 of the front, in diminishing resistance. This arises from 

 the partial vacuity created behind the obstructing body. If 

 there be no solid to fill up this space, a deficiency of hy- 

 drostatic pressure exists within it, and is transferred to the 

 spindle. This is seen distinctly near the rudder of a ship 

 in full sail, where the water is much below the level of the 

 surrounding sea. The cause here, being more evident, and 

 ■uniform iu its nature, may probably be obviated with better 

 success; in as much as this portion of the spindle may not 

 differ essentitdly from the simple cone. I fear however, that 

 the whole of this suV)ject is of so dark a nature, as to be 

 _ more usefully investigated by experiment, than by reason- 



ing ; and in the absence of any conclusive evidence from 

 either, the only way that presents itself is to copy nature; 

 accordingly I shall instance the spindles of the trout and 



woodcock. 



