536 Royal Society :— 



2. The strength as affected by the diameter. 



A precisely similar law is found to hold in reLation to the diameter. 

 Tubes similai' in other respects vary in their resistance to collaj)se 

 inversely as their diameters ; and with a view of testing this law, we 

 may place the calculated pressure beside that derived from experi- 

 ment, as under : — 



Resistance of tubes to collapse 5 feet long. 



Diameter. By Experiment. By Calculation. Variation. 



Inches. lbs. per square inch. lbs. per square inch. lbs. 



4 43-0 



6 32-0 28-6 -3-4 



8 20-8 21-3 .... +0-7 



10 16-0 17-2 +1-2 



12 12-5 14-3 +1-8 



The above variations are slight when compared with the resisting 

 powers of the tubes ; they are doubtless caused by the varying rigid- 

 ity of the iron, or by defects in the cylindrical form. Similar results 

 follow in the experiments on tubes 2 feet G inches long ; and although 

 some slight variations occur, they are nevertheless not more than 

 might have been anticipated within the ordinary limits of error. 



3. The strength of tubes as affected by thickness. 



In these experiments it is found that the tubes vary in strength 

 according to a certain power in the thickness ; the index of which, 

 taken from the mean of the experiments, is 2*19, or rather higher 

 than the square. 



Combining the above laws into a general expression, we have, as 

 the formula for the strength of tubes subjected to a uniform external 

 force, 



LxD 



where P is the collapsing pressure, k the thickness of the plates, 

 L the length of the tube, which should not be less than 1'5, or 

 greater than 10 feet ; D the diameter, and C a constant to be deter- 

 mined by the experiments. For tubes of greater length than those 

 above specified, a variable quantity, dependent upon the length, must 

 be introduced ; and the value of this has yet to be determined. For 

 ordinary practical calculations the following formula will probably, 

 however, afford the needful accuracy : — 



P=806,300Xt-^. 

 LxD 



Thus, for example, take a tube or boiler-flue 10 feet long, 2 feet 

 diameter, and composed of plates \ inch thick ; and the collapsing 

 pressure will be 



P=806,300x — £l_ = 2I01k. 

 10x24 

 per square inch or nearly so. 



Some experiments have also been made upon elliptical tubes ; and 

 the results have been most conclusive as to the weakness of such 



