848 Transa ctions of the American Institute. 



other conditions that cannot be defined, they cannot be put in a mathe- 

 matical formula, and must be considered separately, and superadded. 

 It is necessary to have experiments in many branches of practical 

 mechanics, in order to have theory ; but without theory what would 

 be the value of observations ? You can grope your way by experi- 

 ment to some valuable results ; but you cannot make a system, or 

 form a safe conclusion, without theory. Mathematics does not tell you 

 everything, but what it tells you is true. The formula do not tell 

 you everything about the steam-engine, but they tell you what con- 

 ditions they assume, and the results of these conditions, and tell you to 

 look for and investigate the other conditions independently, to see h»w 

 they will modify the practical results. They are not a sole guide, but 

 they are a valuable aid; and without the aid of absolute abstract 

 science, you cannot have any practical science that is good for any- 

 thing. (Applause.) 



Mr. Emery — Every successful engineer depends on theories as a 

 basis ; but it is often necessary to make large allowances. In steam- 

 boilers, for instance, we make enormous allowances, and yet make 

 much less allowance for accident than in many other cases. In build- 

 ing a bridge we give it six times as much strength as is required by 

 calculation ; but nine-tenths of the boilers that are made allow only 

 about three and a half times. With an agent capable of causing so 

 much destruction, we tamely submit to be blown up occasionally, from 

 neglecting the precaution that we take in the beams of a house, or in 

 the construction of a bridge. If in doubling the size of an engine, 

 every part were to be doubled in size, we should make some parts too 

 heavy, and others too weak. We must observe scientific principles to 

 make the proportions correct. 



For the want of true scientific knowledge we often see in steam- 

 boilers one part capable of sustaining 500 pounds, another 200 pounds 

 while the shell itself will bear perhaps but 100 pouuds. These sub- 

 jects require investigation; and there is need of mathematics as 

 the foundation. The question before us to-night is one of pure 

 mathematics. It is a matter where there are no allowances to be 

 made. The proper weights for pistons are to be ascertained by pure 

 mathematics. It has been said that the formulas before Rankin are 

 incorrect. It is usually the case that it is only the constants in these 

 formulas that are in error; so that by substituting the proper coeffici- 

 ents they may be made accurate. In many cases it is only to multiply 

 the result by a constant quantity. In that way the old formulae are 

 used every day. Adjourned. 



