584 Mr. C. A. B. Garrett on the 
Rayleigh gives the frequency in the form 
m? KU 
areenh Lee 
m for the laeeege tia being 1: 192 5 5- Our theory gives an 
m= 1 167. or 
) ? 
Second Approximation. 
Now let the bending force be applied at a point on the 
bar distant pL from the fixed end. 
In this case let y; be the deflexion of the point of applica- 
tion of the force. Then the bending moment at O, as before, 
is 
aprBAw, . | » eee 
Also the moment of the forces causing motion of the bar 
is 
a én vlees * 
~oA(ph)’y,+toAy, ‘a[t+2 —— ard da, 
40 A Ny 
where pw is the slope of the bar between z=pL and a=L. 
oy is easily seen to be oe from (1). 
-- moment of forces about O 
p?—10p+ 20 
=cAp’ Ly, 0p 1 6. 
Equating (7) and (8) we have 
Le cL ee me 
a In Le WV pP(p?—LOp+20)° °° * () 
Photographs of the Vibrating Bars. 
Instantaneous photographs were taken of a bar when 
vibrating and of the same bar when pulled aside to the same 
end displacement. The bar used was a steel strip, and the 
dimensions were: length 94 cms., breadth 1°25 ems., thick- 
ness ‘13 cm. This bar is clamped tightly in a vice and set 
