TRANSACTIONS OF SECTION A. 543 



The Table sliows that, at least in the cases discussed, there is a real drift in 

 longitude with reduction of latitude. This is especially noticeable in the cases 

 bet-\veen — 26° and —8°. The diagrams in which the faculje are set down in position 

 at successive periods show the drift in a most strikiug and convincing manner. 

 An apparent lagging of faculje behind the leading spot of a group is accounted 

 for by the disappearance of the following members of the spot groups, and not by 

 a retrograde drift of the faculaj. 



5. On an Exceptional Case in the determination of the Constants of a 

 Photograjyhic Plate from hnoivn Stars. Bij Professor H. H. Turner, 

 F.R.S. 



At the University Observatory, Oxford, the places of stars on about 800 

 photographic plates, each 2" x 2°, have already been measured ; the whole number 

 of plates to be measured as the share of this observatory in the International 

 Astrographic Survey being 1,180. Each plate contains on an average about 350 

 stars, but the number varies considerably (from 100 to 2,000). Of these a certain 

 number (from 10 to 30 per cent.) have already been observed on the meridian, so 

 that their places are known ; and from these known places the * plate constants ' 

 are determined (scale value, orientation, &c.), so that the places of the remaining 

 stars in the sky can be inferred from the measures of the plate. The constants 

 are found by two sets of linear equations, one set from measures of the ,r 

 coordinates, another from y : and the correctness of the solution is checked (a) by 

 the agreement of the results from the two sets, which are solved independently ; 

 (6) by the accordance of the residuals for the knovsm stars with those found from 

 other plates. 



The equations are solved, not by the method of least squares, but by a 

 process in many ways equivalent to it. To avoid the heavy work of squaring and 

 multiplying numerous coefficients, the stars are grouped so that by mere addition 

 we can form three equations presenting the chief features of the normal equations 

 which arise in the work by least squares, viz., that the coefficient of each 

 unknown quantity should be relatively large in one equation. In almost all cases 

 hitherto this process, which is comparatively simple and expeditious has been 

 found quite satisfactory. 



A plate with centre 13'' 0'", + 27°, taken on 1899 May 5, presents a curious 

 exception. There are only fifteen ' known ' stars on it, and these are so arranged 

 (all near the line x = j/) that the usual method of grouping failed to give a solution 

 at all. A deliberate regrouping was then made with special attention to the 

 characteristics of the plate, but the solution obtained was unsatisfactory when 

 judged by either of the criterions («) and (6) above mentioned. 



The machinery of ' least squares ' was then set in motion, with the result that a 

 satisfactory solution was obtained. It seems worthy of note that this machinery 

 does practically give satisfactory results in cases where simpler methods fail. 

 This instance is of some importance as representing an extreme case out of 800 

 tried. 



6. On the Position of a Planet beyond Neptune. By G. FoRBKs, F.R.S. 



SATUBDAY, SEPTEMBER 14. 



The Section was divided into two Departments. 



Department I. — Mathematics. 



A joint Discussion u-ith Section L on the Teaching of Mathematics, opened 

 by Professor John Perry, F.R.S. 



