Skating on Thin Ice. 7 



length Z (100 inches), breadth b (10 inches), thickness e 

 (4 inches). 



Working with the inch as unit of length, the bending 

 moment equation is 



BAK s g=/>A(Z-*)i±^, .... (1) 



from which the cross section A = be divides out, and where 

 K 2 =— e 2 ; so that with E/p = k, inches, 



h^S-K'-H .... (3) 



and if d denotes the droop at the end, where # = Z, 



d**-^-^-^ <-£■ • • < 5 > 



Thus with Z = 100, e = 4, k = 25 million, inches, we find 



d = 0-625, say § inch (6) 



And conversely, this value of d measured would lead to the 

 value of k above. 



8. The skin stress on the top or bottom of the ice, given by 

 an equivalent length h as ph, is such that the bending moment 

 is due to an average tension or pressure ^ph, acting over \be, 

 the upper or lower half of the cross section, at a distance \e 

 from the neutral mean line, and is therefore 



lphx^bex^ex2 = ^phbe 2 = ~phAe=l 2 pA(l 2 ^^), (1) 



Z 2 — x 2 3Z 2 



li = 3 , a maximum — at 0; . . (2) 



e e 



so that in the experiment 



h = ^^ = 7500 inches, or 625 feet, . . (3) 



as of an icicle of uniform cross section ; and it is not likely 

 the ice could stand it without breaking. 



