TWO DEGREES OF THE NORTH POLE. 49 
the saine stars when found on an adjacent piate. ‘They are obtained 
by a least squares solution of equations (2) in which the quantities 
(a — a’) sin x and (x — z’) are the differences in right ascension and 
polar distance of all the stars, standard and unknown, common to the 
two plates in question. Their numerical values are taken from the 
original «’s and z’s of which Table VI contains the means. Hence the 
X axis points to the equinox of 1888.0 and the a’s and z’s are the mean 
places for the same epoch. Fach pair of adjacent plates will furnish 
such a set of corrections to their plate constants, and there will be 
eight combinations of the 89° plates one with another. There will 
also be eight combinations of the go° plate with each of the 89° plates, 
making sixteen combinations inall. Theresultsof these least squares 
determinations are found in Table VII which follows. The numbers 
in the first column designate the plates which are included in each 
comparison. The number of equations involved in the least squares 
solution stands in the second column. It is equal to twice the num- 
ber of stars common to the two plates. The remaining columns give 
the corrections d>, dy, dA’ and dw to the plate constants. For exam- 
ple, in the first comparison the values inserted in equations (2) are 
in the sense plate 16-2 minus 16-7. Hence if the corrections in the 
first line of Table VII are substituted in equations (2) they will give 
the corrections to be added to the results of plate 16-2 in order to 
secure closer agreement with 16-7. 
TABLE VII.—INTER-COMPARISON OF PLATES. 


Plates. 


— Ke qqqjqqqqqe_ OOOO 






16 no. 7 and 16 no. 7 go | — .0025 | — .0065 | — .0036 | — .0055 
16 no. 7 and 21 no. 15| 122 | — .0033 | + .0036 | + .0066 | — .0034 
21 no. 15 and 18 no. 3 S2 | iv 10024 ja- 0100s) ts 0018 |. +  .0027 
18 no. 3 and 16 no. 4 74 |} — .0033 | — .o010 | — .0046 | + .0070 
16 no. 4 and 16 no. 5 96 | — .0093 | — .0075 | — .0005 | + .0058 
16 no. 5 and 21 no. 13| 128 | + .0033 | — .oo19 | — .0029 | + .oo10 
21 no. 13 and 18 no. 1 120 | + .0028 | - -:or18 | + .oo13 | — .0058 
18 no. 1 and 16 no. 2 o0/)- + .OO1Gh. + §.0029. | -F .0023°} — .0039 
go° and 16 no. 2 86 | — .0005 | + .0059 | — .o001 | — .0033 
90° and 16 no. 7 76 | — .oo11 | — .0044 | — .0055 | — .0055 
90° and 21 no. 15 78 | — .0021 | — .oo1r1 | + .0017 | — .0050 
go° and 18 no. 3 58 | — .0004 | + .0096 | + .0006 | + 
go° and 16 no. 4 64 | — .0029 | + .0045 | — + 
go° and 16 no. 5 78 | — .or10 | — .0032 | — 2 F 
go° and 21 no. 13 98 | — .0067 | — .0065 | — ss 
go° and 18 no. 1 84 | — .0015 | + .0056 | — > 

