IV. Results. 



Constants. — Making the least square solution for each plate 

 as explained Sect. Ill, we get the constants set down in Table 

 IX. They all depend on eleven standards, except in the case 

 of Plate I, where two of these are missing, owing to inaccurate 

 pointing of the telescope. The probable errors computed for 

 / and r in no case differed by more than a unit in the last place ; 

 I have therefore given only one value, which applies to both 

 these quantities. 



Table IX. — Constants. 













Probable 



jEr- 





Piob. Er- 





Prob. Er- 



Plate. 



I 





P 





r 



ror of/ < 



3r r. 



k 



ror of k. 



c 



ror of c. 



-)-0.000240 



40.000117 



±0.000030 



II 

 + 0.135 



II 

 ±0.056 



— 0.II9 



±o'.o53 



II 



+ 



238 



+ 



205 



i 



28 



+ 0.131 



±0.058 



— 0.083 



±0.054 



in 



+ 



308 



+ 



192 



-i^ 



26 



+ 0.148 



±0.052 



—0.174 



±0.048 



IV 



+ 



233 



+ 



194 



± 



26 



— 0.073 



±0.050 



—0.178 



±0.047 



V 



+ 



265 



+ 



540 



4= 



28 



+0.003 



±0.056 



— O.IOO 



±0.052 



VI 



+ 



260 



+ 



187 



zb 



26 



+ 0.166 



±0.052 



— 0.I6I 



±0.049 



VII 



+ 



210 



+ 



92 



zh 



24 



+ 0.139 



±0.046 



— 0.084 



±0.044 



VIII 



+ 



215 



4- 



118 



± 



27 



— 0.018 



±0.053 



— 0.176 



±0.050 



IX 



+ 



290 



— 



140 



■±L 



24 



-f 0.160 



±0.048 



—0.095 



±0.045 



X 



+ 



283 



+ 



II 



± 



24 



+0.069 



±0.048 



■ — 0.060 



±0.045 



XI 



+ 



307 



+ 



60 



± 



25 ' 



+ 0.089 



±0.049 



— 0.089 



±0.046 



xir 



+ 



266 



+ 



199 



■±^ 



29 



+ 0.093 



±0.057 



— 0.108 



±0.053 



xin 



+ 



307 



— 



132 



zb 



24 : 



+0.161 



±0.048 



— 0.107 



±0.045 



XIV 



+ 



304 



— 



25 



-±^ 



24 



+0.093 



±0.048 



— 0.017 



±0.045 



It will be seen that the probable errors agree very well, so 



that the final positions from all the plates are entitled to an 



equal amount of confidence. A probable error in p ox r oi 



=t 0.000025 corresponds to an uncertainty of about o".o8 of 



arc of a great circle in the position of the most outlying star. 



The great diversity in the values of r is due for the most part 



to the accidental position in which the plate was set in the 



measuring machine. 



(116) 



