THt: EFFECTS OF SfACHINES WHEN IN MOTION. 157 



foregoing cases, as it is easy to assign numbers for 

 the given terms, and from thence compute the va- 

 lue of d\ But as the 17th Prob. is the most com- 

 plicated with respect to the / so often mentioned, 

 and because the lever there represented is nearly the 

 form of those generally used in machines that act 

 with a reciprocating motion, I will subjoin an ex- 

 ample for determining the value of .r, both after a 

 given time, and after passing through a giveit space; 

 and then proceed to compute the greatest possible 

 effects of the steam engine, agi-eeable to the princi- 

 ples laid down in this theory. 



Example : — Let then the weight (zv) of the 

 great beam ab (see the figure in Problem I?) be ten 

 cwt. its length (2 r) equal twenty feet. The weight 

 of the two circular ends ( W) — two cwt. The weight 

 of all the braces (2iv)~one cwt. their length (v) 

 mfive feet. Then let SB (R) be twelve feet ; sd (a) 

 =. six feet, and therefore 7^— a — four feet : and make 



zz ten cwt. Now — ■■ \ — =~~, zz 8127 

 nA:, and ^-^^^zi 1,128 the p' of all the braces re- 

 duced to B. Then ao-ain -^.—3,Q7S = h,-^ — 

 3, 273, -^ = 2, 546. Therefore we have P + "^ -\- 

 ~ — l--^ + l694,7lb. =:if ; and by substituting the 



value of t thus found, in the equation \/f+tV — f, 

 will give .2^=4-]<2lb. very nearly, when its effect is 

 greatest after a ^7 WW time, and if the values of ^ and 

 P be put in the equation v/p^+^°^''+9^^ p— 3^ ^ ^^ have 



.r — 631,5lb. when its effect is greatest after passing 

 through a give?! space. Had the weight of the lever 

 not been considered, x in the first case would have 

 been 414,2, and in the second 618,04 nearly. 



Now to compute the greatest effects of the steam 

 engine on the principles here laid down, without en- 

 tering into a minute description of that machine, let 

 c be the diameter of the cylinder into which the 

 steam is conveyed, 2i\\& p the diameter of the pump. 

 Then if a denote the weight of the atmosphere on 



a 



