382 PROCEEDINGS OF THE AMERICAN ACADEMY 



Normal Equations. 



—3007.1= 9a + G9.93 6 

 +3180.1 = 69.93 a +1209.66 b 

 Whence 



6 = 36.57 = 18.39 /z 



Combining this value with the values 18.09 y* derived from R^, and 

 18.10 /x derived from li.^, we have : 



Coefficient of expansion of bar TFin one meter = 18.19/i for each 



degree Centigrade. 



For the relation between IT and A^ at 1G°.67 C. = 62°.0 Fahr., we 

 have : 



IT— 2G3.0^ = i?2 = A + l-6/* TF— 263.6 /i = i?3 = ^0+1.2 /i 

 TT— 264.6 ,i = ^o TF— 264.8 /x = ^ 



And finally, JF— 564.7 ^ = A 



Reducing to 0° C, with the coefficient 18.19 /i, we have at 0° 



Tr+38.5/x = A 



A slightly different but probably more accurate value of this relation 

 will be obtained by selecting only those comparisons which were made 

 near 0°. From these data we have : 



No. 8612 n„—W No. 8612 ^a— ll' 



Obs. o 7?,— tV atO'C. Obs. o ^s— '^ at 0° C. 



3 _2.74 — 490.6 div. — 2J9.6// 3 —2.74 — 220.4div. — 132 6/i 



8 +1.88 —496.9 —247.9 4 +1.88 —301.4 —136.9 



3 +3.43 —499.2 —247.6 3 +3.00 —313.7 —1.32.4 



6 +5.73 —501.0 -216.2 6 +5.73 —351.2 —132.2 



Mean —247.8 —133.5 



Whence F+36.1,i = Jo Tr+3G.0^=J^ 



COMPARISON OF STANDARD Qi WITH STANDARDS R^ AND TJg. 



Eqoatioxs of Coxdition between 7?o and Qy 



7?,-(?, 

 No. Obs. 7?5— (?, atl6°.67 Residuals. 



6 —580.2 div. = a +10.02?) —604.9 div. +1.0div. = +0.5,u 



4 —586.9 = a +12.54 6 — (iOG.2 —0.3 = —0.2 



2 —597.1 =a + 6596 —607.2 —1.3 =—0.6 



4 —627.1 = a —14.066 —605.4 +0.5 = +0.3 



Mean -005.9 



