to the Longitudinal Expansion in Rods of Spring Steel. 43 



If this was the case, it showed itself in a difference of the differ- 

 ences X'— X" and Y'— Y", on the observations in which the 

 weights did not act. There was such a difference, but in all sets 

 of observations it seldom exceeded 0*2 of a division of the scale, 

 and can therefore be readily accounted for from errors of obser- 

 vation and accidental disturbances. 



From the directly observed values of X', Y', X", Y", I have 

 formed the following values by taking the mean between those 

 which held for the same conditions : — 



X'. 



Y'. 



X". 



Y". 



. . . 137-10 



88-20 



25-64 



92-52 



100 .. . 101-20 



122-85 



62-95 



56-40 



100 .. . 101-60 



52-90 



61-60 



127-20 



From these are obtained 









(X). 



(Y'). 



(X"). 



(Y"). 



. . . 136-00 



86-96 



26-91 



91-08 



100 .. . 100-20 



121-07 



63-45 



55-81 



100 .. . 101-20 



52-43 



62-67 



125-42 



From the first and second of these 



horizontal serit 



follows that, 









it 



8(x-')- 8( x') =36 , 17) 8 (Y»)-a(Y' ) = _ 34 , 69; 



from the first and third, 



«(g)-8(g) 2EMJQ =34 -43. 



Half the sum of the two values of 



S(X")-S(X') 



I will designate 



by B, half the difference of the two values of — — ' - — - by T ; 



we have then 



B = 35-72, T=34-56. 



Using weights of 200 gr. there were obtained, — 





X'. 



Y'. 



X". 



Y". 



. . , 



131-5 



93-1 



20-1 



97-5 



200 . . 



65-8 



157-2 



100-3 



20-0 



. . 



136-8 



87-7 



25-5 



91*9 



200 . . 



64-2 



16-7 



95-4 



161-0 



. . 



137-0 



89-2 



25-7 



93-6 



200 . . 



66-1 



156-8 



100-5 



19-6 



. . 



. 136-7 



873 



25-3 



91-5 



200 . . 



, 67-0 



177 



98-0 



1620 



. . 



. 137-2 



88-2 



25-8 



925 



