474 
ME. W. H. BAELOW OX THE EESISTAXCE OF FLEXTEE 
These formulse, applied to the several forms of beams experimented upon, give the 
following equations : — 
No. 1. •67062/+1-0059 ^ =28320 
No. 2. 1-0425 /+1-1813 ^ =37020 
No. 3. 1-4473 /+1-3388 (p =46260 
No. 4. 2-3297 /+1-4698 <p =65295 
No. 5. 2-0625 /+2-2043 =77115 
No. 6. 3-0564 /+1-3512 ^ =77205 
No. 7. 3-2227 /+1-5059 9 =90000 
No. 8. -1734 /+ -2601 p = 7905 
No. 9. -13867/+ -23541?) = 7110 
No. 10. -12519/+ -25039?) = 6735 
No. 11. 1-3336 /+2-0009 p =52170 
No. 12. 1-5708 /+2-6666 p =62145 
No. 13. 1-0454 /+1-7746 p =46980 
No. 14. -9484 /+1-8968 p =44820 
No. 15. 1-281 /+1-126 p =48048 
No. 16. -711 /+1-066 p =30828 
If the metal were of precisely uniform strength, f and p would be precisely constant 
quantities, and their value might be obtained from any two of these equations ; but as 
considerable variation occurs in the strength, even in castings of the same dimensions, 
and as a reduction of strength, per unit of section, is known to arise when the thickness 
of the metal is increased, the values of y and p will necessarily vary, and can only be 
ascertained in each experiment by first establishing the ratio they bear to each other. 
For this purpose the first ten experiments may be used, all of which were made of 
metal of from three-quarters to one inch in thiclmess, the mean tensile strength of which 
was ascertained by direct experiment to be 18750 lb. per inch. 
Using this value of/ in each case, we have 
No. 1. ^^ 28.S20-67062 x 18750 ^^53.^ 
1 0059 
No, 2. .- 37020-1-0425 Xl8750 _, ^.^^« 
1-1813 
No. 3. ._ 46260-l-4473xl87.50 _]^.^«, 
1-3388 
No. 4. .- 63295-2-3297 Xl8750 _^^g^^ 
1- 4698 
No. 6, .- 77115-2-0625 X 18750 _„^^^ 
2- 2043 
