NEW MEASUEEMENT3 OF DISTANCE OF SUN. 113 



The stars are then arranged in columns of fours; the iniages of (he 

 planet, owing to its rapid motion, are in echelon. 



Now each exposure gives very accurately the place of the planet 

 with reference to the group of stars around it, and for merely parallax 

 purposes the ideal would be to have pairs of such photographs taken 

 at the same instant at stations widely separated. By a very simple 

 use of the measures of some ten or twelve stars suitably disposed 

 about the planet, it would be possible to allow almost automatically 

 for the diiferences of refraction, orientation, scale value, etc., Avhich 

 make the plates not immediately comparable, and to find at once the 

 parallactic displacement. 



We have been speaking of the displacement as very large, and so 

 it is Avhen compared with the displacements dealt with in previous 

 determinations. But look at it this way : We saw that the earth as 

 seen from Eros subtended an angle of 53 seconds. The scale of the 

 Cambridge plates is such that if we draw a circle having a diameter 

 of a little over 1^ mm. we represent the apparent diameter on our 

 plate of the earth as seen from Eros ; and within that small circle the 

 Avhole of the parallactic displacement must necessarily lie. About 

 a millimeter was the average displacement obtained in a favorable 

 combination of observations, and when we consider that we are trying 

 to measure that with a resultant accuracy of 1 in 1,000 it does not 

 seem so very great after all. 



We have j^ut the problem heretofore in its very simplest form. In 

 actual fact the exposures at different stations were not simultaneous. 

 Early morning observations made at Cambridge might be combinable 

 with evening observations at Lick more or less simultaneous, or with 

 evening observations ten or twelve hours before at (say) Oxford; or 

 they might have to stand alone. Any general method of utilizing all 

 the results must secure the possibility of reducing each plate, so to 

 speak, on its own merits, to allow it to contribute its quota, be it 

 large parallactic displacement or none at all, to the general collection 

 of equations of condition. This requires that we shall knoAV the 

 relative places of all those stars which are to be used as comparison 

 stars for the planet, right along the whole track of the planet. And 

 this derivation of a standard star system is by far the most delicate 

 and difficult part of the whole work. One must start with a fouuda- 

 tion of stars observed with the meridian circle, and fill in the fainter 

 stars from the photographs themselves, taking care to provide at the 

 same time the places of all those faint comparison stars which have 

 been used by the visual observers. And all these places of stars must 

 be tied together, so to speak, by the overlapping of the photographs, 

 so that the system may run smoothly throughout its length. Abso- 

 lute errors of zero there no doubt will be, and must be, but it is 



