22, REPORTS ON THE STATE OF SCIENCE.—1918. 
beginning and end of the swing by the weight of the hammer. This 
result must be corrected for friction. (Fig. 8.) 
Let OA = Initial position of pendulum. 
OC = Position after free swing. 
OC’ = - . second free swing. 
0B — bs .,  Yupture of test-piece. 
OB’ = 5 ., first swing after rupture of test-piece. 
K = Energy of rupture. W = weight of hammer. 
Then— 
(Energy just before impact) — (Energy just after impact). 
A 
ll 
(Wh, — friction loss over ¢ AOX) 
— (Wh’ + friction over 7 XOB) 
But friction loss over 2 AOX = } friction loss over 7 AOC 
= 1 Wa. 
Similarly friction loss over 2 XOB = } Wb. 
“. K = (Wh, — }Wa) — (Wh’ + } Wd). 
= (Wh, — Wh’) + (— }Wa } — Wb) 
but h, =h-+ ta 
“. K = W (h — hh’) + $W (a — BD). 
a =I(cos ZCOY — Cos 2 C’OY) : b =1 (cos Z BOX — Cos Z BOX) 
where / = length of pendulum from suspension to the centre of gravity. 
By observing the decrement in the swing we may find values of a 
and 6, and hence of +W (a — b) for any value ofa. Tabulate these values 
and plot 2 BOX against the friction correction k’. 
K=W (h—W’) + 
= WI! cosa — WI cosa, + k’. 
The Direct Fall or Block Hammer. 
The type used in these tests was designed by Martens, but a recording | 
drum apparatus has been added, made by Messrs. Amsler. Various 
hammers can be used in this apparatus, but the authors, after much 
experimenting, decided to use a 36 K.G. for the more resilient steels, 
and a 12 K.G. hammer for the less resilient shell steel. The height of 
drop was 3 métres in each case. 
The hammer has a striking face with the sides inclined at 50°, and 
the ends rounded to a radius of 2 mm. The test-pieces are supported 
on specially designed steel castings, with edges rounded to a radius of 
2mm. and spaced 120 mm. apart in order to suit the 160 by 30 by 30 mm., 
oe “ 160 by 20 by 20 mm. test-pieces. The weights of the anvil are 
as follows :— 
Steels GA Ste See ae mc eek shes este m one 90 lb. 
Cast-iron anvil to which the castings are bolted 2,300 ,, 
Concrete foundations on shale rock . . . 7,600,, 
otal nveight:.. 5. ns iqon ada \o 400k BEDE 
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