314 A, B. Quinby on high and low Pre Boiiers. 
The thickness of the boiler in the A.tna, + was 2 3 ofan inch ; 
and the thickness of a dow pressure boiler for an engine of 
equal power would be about + of an inch 
_. From these data it -is. easy to calculgte the comparative 
liability of the two engines tovexplode; for, by mechanics, 
the force of steam ls oy a high pressure boiler 30 inclien m 
- diameter, and } of an inch thick is capable of resisting, is 
equal to the clencae multiplied - the tenacity of the metal, 
divided by half the diameter ;* = x Be aa = 150 Ibs. ; which 
is 600 Ibs. more than the usual so pressure ; or 5 times 
the usual working pressure. 
And, next, the force of steam which a low pressure boiler : 
90 inches in diameter, and + of an inch thick, is capable of 
resisting is =} x 30,000 166) Ibs. ; which is 1564 lbs. more 
than the 7 bela pressure ; or 164 times the usual 
working pressu 
Hence, if the Bacestes; merely, be considered, laying aside 
the ratio of the elastic force of the steam in the two boilers, 
it appears that the hich pressure engine is safer by 443} Ibs. | | 
per-square inch, than one of the dow pressure kind. But, on i | 
the contrary, if the ratio of the elastic force of the steam in ‘ rd 
the two boilers be considered, and the excessés be laid aside, 
* = The formule for the elastic fores of steam which a given boiler will 
sustain may be derived in os ee pe 
Let the circle ADB, Fig. 6, rep d projection of a boiler 
one inch in length. And mut (te) for a eee of the metal;'e for the 
elastic force of the meh employed ; r for the radius of the boiler ; and 
(th) for the ate Z 
Then r: , (the mean dis. of the semicircle ADB, from the 
% it, Ke. 
oy 
line ACB.) : sis ae the mean elastic force of the steam em-~ 
ployed: Wie ae the surface ADB,) inflected into directions perpen- 
dictlar to the line ACB. 
Hence, or the whole force of the steam — estimated in a 
direction perpendicular to the line ACB, we hav 
‘ XrX3.14159 &e.=2re. 
_ B.14159 &e. 
And for the strain at A, or ES we have 2re+2==re. 
Pe ov rama le) ives: 11: (th). Whence re=(th)X(te) sand e= 
te , 
Wx) ald, ( (=e. ? 
\ 
