308 Lieutenant Bartlett on the Expansion 



We have neglected the sixteenth experiment, because we can- 

 not* employ it without using some other experiment twice, thus 

 giving the latter an undue influence, and because the middle 

 term should have the least weight in determining the common 

 difference. 



By the above table, we find, as the combined result of all 

 the experiments, that .3708 should be 817 times the common 

 difference ; and hence the common difference for one degree of 

 Fahrenheit is .0004538 inch. Now, assuming 94.05 inches as 

 the mean length of the granite, which is sufficiently near, we find 

 the linear expansion for one inch of stone for each degree of 

 Fahrenheit to be '^^^ = .000004825 inch, and for one foot this 



94.05 ' 



expansion would be .0000579 of an inch. By proceeding in 

 the same way with the experiments on the other stones, we ob- 



To apply these results to the case in question, let us suppose 

 two coping-stones, of five running feet each, to be laid in mid- 

 summer, when they have a temperature of 96° Fahrenheit; in 

 winter their temperature may safely be assumed at zero, so that 

 the total variation of temperature will be 96° ; and if we suppose 

 these stones to contract toward their centres, which would be the 

 most favourable supposition as regards the tightness of the 

 joints where a number of these stones are used, the whole length 

 of stone put in motion by a change of temperature would be 

 five feet. If the coping be of granite, the distance by which 

 the ends of the stones would be separated, in consequence of 

 one degree'^s variation, would be sixty inches, multiplied into 

 .000004825 = .0002895; and for a variation of 96 degrees, this 

 distance becomes .0002895 X 96 = .027792 inch, giving a crack 

 a little wider than the thickness of common pasteboard. For 



