The probable errors of rates at Wellington, Melbourne and Christchurch, 1913. 

 may be taken as : 



Wellington* (about) 0-01 sec. daily correction to time of s\ving0-6x 10~ 7 sec. 



Melbourne* (about) 0-01 0-GxlO- 7 sec. 



Christchurch, 1913 (about) 0-04 ,, 2-4xl()- 7 sec. 



At Cape Evans, the error of the clock rate cannot be calculated from the time 

 observations alone, since, in working these out, a constant azimuth has been taken 

 which is not calculated simply from the sights. The assumption that the direction 

 of the azimuth mark remains unchanged during the course of the observations is quite 

 justifiable, but the method of obtaining the value of the azimuth of the fixed mark 

 is not at all free from objection. On the other hand, if the same stars are observed 



each night or stars with the same mean value of K = - -&-, ' ' \, the error introduced 



L cos ,5 I 



by an error in the assumed azimuth is inappreciable. For this reason, the probable 

 error of the clock rate can be calculated directly from the observations in the case of 

 series D. 



Thus, probable error of observation on Ai:g. 12th, +0-08 sec. ; on Aug. 18th, 

 0-25 sec. 



Probable error of G-day rate == v/(0-08) 2 +(0-25) 2 = 0-26 sec., or, 



Probable error of daily rate = 0-04 sec., which means a probable error of 

 2-4xlO~ 7 sec. in time of swing. 



The case of series " C " is more complicated. Here, the probable error of the 

 azimuth constant may be taken at +2-0 sec. The azimuth corrections calculated for 

 an azimuth constant of 7-05 sec. are : 



These become, when the azimuth 

 constant is reduced by 2-0 sec. 



July 12th .. -8-12 sec. July 12th .. -5-83 sec. 



14th .. -7-98 14th .. -5-73 



15th .. -7-98 15th .. -5-72 



IGth .. -7-70 Kith .. -5-51 ,, 



The changes in daily rate due to such an error in the azimuth constant therefore 



amount to 



0-02, -| 0-01 and 0-07 sec. for the three intervals. 



We may take the probable error of the observations for rate as 



v/(0-25) 2 -h(0-08) 2 = 0-2(i sec. 

 in an interval of 3| days. This gives a probable error for daily rate of 0-07 sec. 



* A calculation of tin- actual probable errors gives somewhat lower values ( 0-006 sec.). The 

 above figures may be taken as the upper limits. 



87 F 4 



