280 Prdesepe Group; Measurement and Reduction 



Trail Measurements. 



^\^ Star. 

















15. 



22. 



23. 



27. 



31. 



37. 



PlateT\^ 















I 



—•0443 





—.OI93 





— .0084 



+ .0183 



III 



— .0676 





— .0404 



—.0398 



— .0292 





IV 



—•0535 





—.0312 





— .0169 



+ .0070 



VII 



— .0772 



— .0422 



—.0499 





— .0294 





VIII 



—.1054 



— .0766 



—.0718 





—.0510 





II 



—.0850 





—.0568 





—•0356 



— .0070 



The distance from each trail to the middle point between the 

 corresponding images was measured approximately as follows, 

 being practically the same for all the stars upon a plate : 



Plate, I III IV VII VIII IX 



s, 35- o, 35-i, 35-o. 39-3. 48.1, 39-4 millimetres. 



We shall now consider what corrections must be applied to the 

 above offsets in order that the true orientations of the plates may 

 be computed from them. * 



Instrumental Corrections. The only correction of this kind 

 is that for rotation, the data for which have already been given in 

 Table II. Using the same notation as before the correction to the 

 offset is 



— s. i. sin 1" 



which is the same for all four stars. Having applied this connec- 

 tion, the offset ma}' - now be converted into seconds of arc by mul- 

 tiplying by the approximate scale value, 52.87. 



Transformation Corrections. For the present purpose it will 

 be convenient to use Ball and Rambaut's formulas quoted on page 

 238, in which X sec ^ and Y appear in the second members instead 

 of Aa and A3. We need only the second of these formulas : 



Ad — y = — % (Xsectf ) 2 sin2<5 — J F 3 — (Xsecrf ) 2 Z 

 For the trail, X sec 8 is diminished by 



2 = 52.87 -S- sec<5 , 

 while Y remains practically unchanged. Hence the correction to' 

 the offset is, 



+ X s i n 2 ^o -z ' ( z — 2Xsecrf ) -j- z- (z — 2Xsecrf ) Y 



Refraction Corrections. The trails were taken somewhat later 

 than the principal images of the group, and as the zenith distance 



