190 Mr Sharjic, On the BcfJccHoii of SoiDid at a Paraboloid. 



Wo shall take the two lj\st cases tii-st. In (98) put v = A/x and 

 suppose both v and A large, and /t nearly = 1. 



And tirst we shall suppose fi<l, equation (98) then becomes 



d'V dV 



^,^,^^u:-'''^''-''^' ^''''- 



With the above suppositions, a solution (68) is given of this 

 equation in Art. 26. [It must, however, be admitted that (68) 

 fails if jLi be too near 1. For this ea^e and for the ciise of yu, 

 being actually = 1 another solution nnist be sought.] The solution 

 (68), however, answei"s very well if say ^ is near h. It will be 

 further observed that the solution (68) is of an exponential 

 character, so it seems to follow by reasoning similar to that used 

 before that (for points for which /.kI, but v and A both large) 

 the air-velocity curve is exponential. It is important to observe 

 that this result agrees very well with the latter part of Art. -iS. 



45. Next, with the above suppositions, we shall suppose ^ > 1. 

 In this case it is better to write the equation for V thus 



d'V dV 



A solution (70) of this equation is given in xlrt. 27. 



[As before, we must admit that this solution fails when /x is 

 very near 1 or actually =1. but it answers very well if yti is near 

 or = L] It will be further observed that the solution (70) is of a 

 trigonometrical or periodic character, so it seems to follow as 

 before that (for points for which /u,> 1, but v and A both large) the 

 air-velocity curve is wavy and cuts the axis. Again it will be 

 observed that this agrees very well with the latter part of Ai-t. 42. 



46. According to the beginning of Art. 44 it would now be 

 our duty to examine the value of i" when u does not ditier much 

 from A in excess or defect. In (99) put u = A/ll, and suppose u 

 and A both large, then (99) becomes 



''!?'+!?;: +-^'^'^^ +'''=» (1"^'^- 



As fi is supposed nearly = 1 this equation does not ditier much 

 from 



d'U , dU , , ,,„ , 

 '^ d/x- dfi 

 Put '2A-/X = i: Then 



d'U dU „ , 

 dv- dj' 



