-314 ^^. B. (^uinby on high and low pressure Boilers . 



• The thickness of the boiler in the -^tna, was f of an inch ; 

 and the thickness of a lozo pressure boiler for an engine of 

 equal power would be about } of an inch. 



From these data it is easy to calculate the comparative 

 liability of the two engines to explode ; for, by mechanics, 

 the force of steam which a high pressure boiler 30 inches in 

 diameter, and f of an inch thick is capable of resisting, is 

 equal to the thickness multiplied by the tenacity of the metal, 



divided by half the diameter f =f X '^^'^^^ =750 lbs. ; which 



15 

 is 600 lbs. more than the usual working pressure ; or 5 times 

 the usual working pressure. 



And, next, the force of steam which Sl low pressure boiler 

 90 inches in diameter, and | of an inch thick, is capable of 



resisting is =|X — !__=166| lbs. ; which is 15Gilbs. more 



. 46 



than the usual working pressure ; or 16} times the usual 

 working pressure. 



Hence, if the excesses, merely, be considered, laying aside 

 the ratio of the elastic force of the steam in the two boifers, 

 it appears that the high pressure engine is safer by 443|^ lbs. 

 per square inch, than one of the low pressure kind. But, on 

 the contrary, if the ratio of the elastic force of the steam in 

 the two boilers be considered, and the excesses be laid aside, 



* The formulai for the elastic force of steam which a given boiler will 

 sustain may be derived in the following- manner ; 



Let the circle ADB, Fig-. 6, represent an end projection of a boiler 



one inch in length. And put {te) for the tenacity of the metal; e for the 



elastic force of the steam employed ; r for the radius of the boiler ; and 



[th) for the thickness. 



2r 



Then r : '■ ■■, (the mean dis. of the semicircle ADB, from the 



3.14159 &c. 



2e 



line ACB,") : : e : , the mean elastic fqrce of the steam em- 



' ' 3.14159 &c. 



ployed, (acting upon the surface ADB,) inflected into directions perpen- 

 dicular to the line ACB. 



Hence, for the whole force of the steam employed, estimated in a 

 direction perpendicular to the line ACB, we have 



2e 



XrX3.14159 &c.=2re. 

 3.14159 &c. 

 And for the strain at A, or B, we have 2re-7-2=re. , 



in. in. 



And, now, [te) : re : : 1 : [th). Whence re^(th)X{te) ; and e: 

 (i^)><M: also, (</.)=^. 



