80 ROYAL SOCIETY OF CANADA 
The systematic errors due to instrumental peculiarities can only be 
obtained from the discussion of plates of the same star in sufficiently 
large numbers to ensure that the systematic displacements for this 
particular spectrograph become accidental in character. It is possible 
however that there may be slight constant systematic differences in the 
values given by different spectrographs. We have in the three disper- 
sions plates to the number of 24, 11, and 38, and, by treating the resi- 
duals from the mean velocities, we can obtain the probable error of a 
single plate in which, although as before stated we have the accidental 
errors of measurement included, we get a good relative idea of the sys- 
tematic errors, and which certainly gives us an accurate idea as to the 
total error involved which in the ultimate analysis is what we wish to know. 
The following tables contain a summary of the measures in the three 
dispersions. 
SPECTROGRAPH III L. 10.1 T.M. PER MM. 















x Probable Errors of Single Regions. 
0. 
Plate of Velocity. | Errors of Setting Total Residual. 
No. Regions. — Accidental 
Baw ore Errors Km. 
1426 11 —5.74 j=: 0.0015 | + 0.59 == 0882 0.23 
. 1455 11 4.97 | .0008 .32 .59 . 24 
1456 16 5.64 |  .0009 5) .52 .13 
1514 12 5.91 .0017 .66 .93 .40 
1515 13 5.78 .0008 sol) | -57 .27 
1529 10 6.14 .0010 .41 .65 .63 
1585 13 5.59 .0020 .78 TA .08 
1586 10 5:94 | 5) 0012 .49 .61 .43 
1588 11 6.93 .0013 .53 .62 1.42 
1595 12 4.14 | .0009 .37 .93 1.37 
1596 13 5.43 .0010 .39 .69 0.08 
1597 13 6:12 .0011 .43 .66 STE 
1606 12 5.42 .0009 a .61 .09 
1615 12 6.24 .0011 .42 .14 .173 
1616 12 6.86 .0009 -37 .76 1.35 
1619 16 5.14 .0011 .40 .82 0.37 
1620 14 5.80 .0011 .43 .64 .29 
1622 15 4.58 .0015 .57 .61 .93 
1635 | 14 3.97 .0014 .53 .48 1.54 
1645 16 5.00 .0015 .54 .64 0.51 
1662 12 4.98 .0011 .45 .72 .53 
1671 | 16 6.10 .0009 . 32 61 .59 
1672 14 5.18 .0013 .5l .45 .33 
1709 | 15 4.62 .0009 .35 .74 .89 
Means.. | 13 -§.57 | 0.00117' + 0.453 | + 0.628 
Average Probable Error of Setting Single Region = +0.45 km. 
2 re Total Accidental Error Single Region = :1-0.63 “ 
- 6 < “ Single Plate =+0.17 “ 
Total Probable Error (Accid’]. + System, c) “ I =+0.50 “ 
