OF ARTS AND SCIENCES. 389 



EQUATIONS OF CONDITION BETWEEN W AND 7?/^ 



At 62° 



jr-i?2'2 (T-62°) n- -/.'/* 



+ 1G.3 div. = a — 0.3 6 +18.6 div, 



+ 9.-4div. = a —1.8 6 +23.1 div. 



—129.5 div. = a —19.7 6 +20.0 div. 



+ 59.4 div. = a + 5.2 6 +19-9 div. 



Mean +20.4 div. 



Normal Equations. 



—44.4= 4 a —10.06 6 = +7.59 



+2838.2 = —16.6 a + 418.4 6 a = +20.4 



We have, therefore, for 62° Fahr., 



W— Rf = +.000402 in. 



But Rf—T= —.000008 m. 



Hence, W — .000394 in. = T 



Another investigation, the details of which are not given here, gave 

 the equation JF — .000364 in. = F. 



Probable Errors of Observation. 



The errors of observation to which the comparisons are subject 

 may be classified as follows : — 



(a.) Accidental errors of observations for coincidence of micrometer 

 line with defining lines of standard. 



(b.) Errors due to an imperfect focus of the defining lines under 

 the objective, and which are not included under (a) . 



(c.) Errors due to the failure of the thermometer to indicate the 

 real temperature of the standards compared. 



The comparisons of T"' with T\ R^' with R^\ and R^' with Rf\ 

 furnish the data for the computation of probable errors of the first 

 and second classes. 



Using the formula of Peters we have for the probable error of a 

 single comparison, — 



.8453 



'^n (n — 1) 



