108 Reduction of Stellar Photogra^^hs. 



where it will be noticed that Table II A gives the values of 

 either of two quantities, because A^ and J/ differ only in sign. 



Similarly for Table III we have : 



Table III A gives value of — D^ {x seedy with argument xsec^ 



or " 





Z>/ Aa^ " " 



Aa 



III B " 





Z),' Aa2 / io3 " " 



Aa 



III C " 





— Z), (a;secrf)2X lo^with" 



a; sec (5 



IIIZ» " 





Z>3' Af53 with " 



A6 



or " 





-A y' 



y 



The transformation formulae then become 



Aa = xsecrf±(Tab.II4) ^ + (Tab. II (7)^-^'°-'^ (Tab. II D)\lZlHTT. 

 ^ '^1000 ' ^ ■* 100 ^ ' [ a; sec 5 negative 



AcJ = 2/-(TableIII.4)-(TableIIIC)^^^^(Tablemi)){^P^^^;[4 



.sec.^ = Aa^(TableII4)^:„±(TableII5) {"Z^^, 



2, = AJ_+(TableIII^) + (TableIIIB)^^±(TableIII D) {"^.l^^^^ 



In the above formulae the upper signs belong to positive values 

 of the arguments and the lower to negative values, as indicated 

 at the end of each formula. The numbers given in the tables are 

 invariably positive. All the multiplications can be effected with 

 Crelle's tables. 



I have not thought it worth while to prepare special scale-value 

 tables for the 24° belt, because it would not be possible to make 

 them definitive, in the absence of any data with regard to the 

 errors of the Paris reseau and screw. These errors have been 

 neglected in the present example. The preparation of such tables 

 would, of course, be extremely simple, as they are little more than 

 mere multiplication tables. I have accordingly altered the units 

 in which M. Henry gives his measured co-ordinates ; and at the 

 same time applied the factor 0.995, which is the approximate 

 ratio of the millimetre to the minute of arc for the Paris instru- 

 ment. All of this would be done with the special scale-value 

 tables in actual reductions. I thus get for the data of the prob- 

 lem : 



