Polytechnic Association. 847 



exactly so much to stand. The difficulty is that the formulae do not 

 provide for the contingencies in practice. For instance, a block of 

 wood catches in the bottom of the gate ; and tliere is no formulse 

 under heaven that provides for that case. Again, this wall is built 

 of the exact thickness required by the books ; but a bad navigator 

 comes along, perhaps a little tight, and runs his boat against it, and 

 the whole affair goes to the dogs. Now, we must have something to 

 add to our formulae to take into account the skill or want of skill of 

 the engineer, and all the circumstances not included in the calcula- 

 tions. Every man's experience differs. Let any man take Dr. Bar- 

 nard's formulae, apply them universally, and they will almost univer- 

 sally fail. "We see that in bridges, in dams, and in all sorts of things. 

 The professor said he had not taken into account clearance, but 

 clearance will play the dickens with it if it is not taken into account. 

 AVhat shall we do then ? I suggested to the Institution of Engineers 

 in London the idea of using a character which should represent a 

 co-efficient in every formulas, which you may call the personal equa- 

 tion if you like, to take into account the block of wood, the careless- 

 ness of the boatman, clearance, everything, according to the notions 

 of the man that applies it. I would prefix that co-efficient in every 

 formulse, and call it the co-efficient of common sense ; and the engineer 

 must use that co-efficient of common sense all the time if he wants 

 reliable results. 



Dr. Barnard — One remark upon the relation that exists between 

 pure abstract theory and practice. It is impossible in a purely 

 abstract theory to present formula which will exactly meet practical 

 cases. But it does not follow that these mathematical formula do 

 not express the absolute truth. The formula expresses the absolute 

 truth in its simplest form. In practice tliere are conditions which 

 modify the result, but the formula shows for itself what conditions 

 are included, and all others are left for subsequent ascertainment, by 

 experiment or by a more extended formula. If we can make the 

 necessary corrections for the omitted conditions, our results will 

 agree with practice ; or if there are no modifying conditions, the 

 formula is absolutely true. 



Mr. Towle — I hope the gentleman did not understand me as 

 questioning the formula. I would look to them first, and then take 

 in other things besides. 



Dr. Barnard — I wanted to explain that mathematics are not to be 

 undervalued because they do not tell all the truth. They do tell all 

 the truth with regard to the prescribed conditions, if there are certain 



