of the Rutherfurd Photographs. 283 



the accuracy of this mode of orientation, especially as a compari- 

 son with the heliometer places indicates a further correction of 



+ 0.000098 

 to the orientations obtained by using the meridian places. T.' 

 large discrepancies are probably due to jarring of the plate durr g 

 exposure, caused b}^ stopping and starting the clock-work several 

 times ; the large difference for Plate I Y admits of no other obvious 

 explanation. 



Let us now examine the scale-values of the different plates. 

 The values of p given at the beginning of Section Y include aber- 

 ration and temperature effects. Formulas for the former cor- 

 rection are thus given by Bessel :* 



y= — (cos d Q sin a -\- tan u sin <J ) 



(5 = -f- (cos c? cos a ) 

 Then the true distance is found by adding to the observed dis- 

 tance s, 



-s(Cy-hnS), 



C and D being as before, the Besselian star numbers. 



We may also correct the values of p for the temperature at 

 which the plates were measured by adding 



+ 0.0000017 {T — 65 ), 

 T being the temperature in Fahrenheit degrees at which the plate 

 was measured, given in Table II. This expression is easily de- 

 rived from the value of v on page 223. Corrections for the tem- 

 perature at which the plate was exposed ought also to be applied, 

 but sufficient data to establish a connection between this quantity 

 and the scale-value are lacking. After a greater number of Ruther- 

 furd's photographs have been reduced we may have more definite 

 information on this point. 



The true scale-value S (so far as it can be obtained without the 

 last correction), is given thus, 



S=52 // .S7 [i+j> — C-} — ZM + 0.0000017 {T° — 65°/] 

 The following table gives the corrections and the resulting scale 

 value for each plate. The corrections for temperature are very 

 small and might well have been neglected. The last two columns 

 give the readings of the thermometer attached to the telescope 

 and of the " focus," which have been copied from Table I for con- 

 venience of reference. 



* " Astronomische Untersuchungen," Vol. I, page 208. 



