314 PROCEEDINGS OP THE AMERICAN ACADEMY 



If we compare the ultimate deflections of all the pieces with 

 their moduli of rupture, we shall find as a rule that those beams 

 which were the strongest bent the most before breaking. 



The values of £J in Tables I., II., and III. were computed from the 



expression £J = . „ .^ , A denoting the deflection in inches. The 

 values of H were computed from the formula ^ = | j^,- 



From further observations of the tables we shall see that the 

 deflections of Pieces Nos. 6 and 7 of Series No. 3 increased 100 per 

 cent ; or the deflection when the load was applied was only about 

 ^ what it was when the beam broke. 



Also that the deflection of Piece No. 9, Series No. 2, and of Piece 

 No. 8, Series No. 3, is much less than one half of what the ultimate 

 deflection would probably be. 



Hence I think it perfectly safe to conclude that for spruce-beams 

 of small section a load which will produce a deflection of one half 

 the maximum deflection of the beam before breaking will ultimately 

 break the beam. 



From a study of Tables VII. and X. it appears that a load of 

 one half the so-called breaking load of a beam does not injure the 

 beam when applied only for a short time; for it will be noticed that 

 for both Pieces No. 9, Series No. 2, and Piece No. 8, Series No. 3, 

 the deflection of the beam upon the second application of the load 

 was almost the same as upon the first application, the difference being 

 very slight indeed. 



Effect of the " Annual Rings " on the Strength of a Beam. 



After computing the moduli of rupture for the first five pieces of 

 Series No. 2, the writer was surprised to see that three pieces had 

 nearly the same modulus, and that the remaining two pieces also 

 agreed almost exactly, but that there was a great difference between 

 the moduli of the three and of the two pieces. 



The writer could think of no reason for this phenomenon until he 

 examined the fractured section of the beams, when it was discovered 

 that in the three beams which had the high moduli the " annual 

 rings " were parallel, or nearly so, with the top and bottom surfaces 

 of the beam, while in the other two the " annual rings " made an 

 angle of about 45° with these surfaces. 



