522 Sir G. Greenhill on the 



from a base o£ B yards, with a magnifying power M, the- 

 angle of parallax or convergence must be measured within S" v 

 given by 



sinS = MB^f. 



Taking the gunner's rule of one inch, or a halfpenny,, 

 subtending an angle of 1' at 100 yards, 1" at 6000 yards, 

 this makes the radian 3600', or 216000", instead of the 

 more exact value of 3138', or 206265", and is equi- 

 valent to taking 7r = 3, instead of 3*1416 ; so that 1" is 

 0-00000485 radians, 12" is 0'0000582 radians. 



Then with M=30, B = 10, R= 20,000, AR = 80, 



sin S = 3( ^^_ 8() =6 x 10 -5 ? s = 12"«96, say 13", 



or more accurately, 



S = 6 x 206265 x 10" 5 = 12"'38, nearly 12"'5. 

 (' Nature/ p. 404, July 24, 1919.) 



Whirling and lateral vibration of a bar. 



16. Take Clifford's function w = G n (x), and x n w = x n O n {x) 

 = 0- n {x) ; then 



\\jM>d*=±G- n -*(*y, 5? =c„ +3 w= J .-»- 2 c_,_ 2 (^), (i) 



9.- C 



so that the differential equation 



<HS =$<"*■• or J^ +2 S0=^ (2) 



has a solution C»(j?), with the associated functions C n (—x) r 

 D n (±x) ; it is required in problems of the whirling or 

 lateral vibration of a bar of variable cross section, such as at 

 the muzzle of a rifle-barrel, gripped at the breech ; or in the 

 reed of an organ pipe or musical instrument. 



Change the independent variable, with x = e e , and (2) 

 becomes 



