70 Mr Greenhill, On height consistent with stability. [Feb. 7, 



and supposing h the height OA, and c the least root of the equa- 

 tion J 3 (x) = 0, then 



c = kIv 1 , 



2„„2 



_3i?tan 2 ac : 

 16iv 



The value of c for n = 3 is 6-379 (Table B. p. 274, Rayleigh, 

 Theory of Sound, Vol. I.), and therefore 



fe = 7'63- tan 2 a. 

 to 



For instance with pine, where 



37-5 

 12 3 



h = 527380000 tan 2 a ; 



#=1500000, and w = n 



and if 6 be the radius of the base in inches, tan a = j , 



/t 3 = 5273800006 s , 

 or fe = 807-9&S, 



^, and 6 being given in inches. 



III. If the rod be in the form of a paraboloid of revolution, 

 then the differential equation of the central line 



becomes, since i ? = 4nnx, where 4<m is the latus rectum of the 

 generating parabola, 



^irn^E -t-\x~ ~\ = — ^irmwp I x dx' 

 dx\ dx) ■'Jo 



= — J.7TVUVX' 



P> 



, d 2 p _ dp w 

 or x 2 -jf+2x-/ + jp=- x~p = 0, 



d l x dx 2Em ^ 



cFp _ dp w 

 or x -f± + 2 -f + -=- ,r» = 0, 



dx* dx 2Em l 



