18 E OC. Pickering—Light of Comparison Stars for Vesta. 
ets. If the presumed error of 30° is left without correction, 
this residual would become —0°9 instead of —0°2. 
separate reduction of the four comparisons gives the greys 
—2°4, 0°0, —0°5, +0°1. Correcting the first reading by 80°, i 
residual is reduced to —0°3 
No. of Date, Obs. Residuals 
Series. 1884, 2168 2164 
249 March 16 P: —0°1 0-0 
251 March 18 W. 0-0 0-0 
252 March 22 Rees 00 —0°1 
254 March 25 W. +01 O1 
255 March 31 P. [-—0:2] —0-2 
261 April 14 PB; +071 +0°2 
The corrections to be applied to the DM. magnitudes of the 
stars appear from these observations to be +°28 for DM.+ 22° 
2163 and+ ‘18 for DM. + 22° 2164. From these corrections 
may be derived the formula /@—m='023m+'058, in which M 
denotes the photometric magnitude of Vesta corresponding to. 
the magnitude m given by Professor Harrington. 
In the following table the first column is repeated from Pro- 
fessor Harrington’s table in the article above mentioned. The 
second column contains the corresponding magnitudes of Vesta 
computed for mean opposition, after correction by the formula 
just obtained. By mean opposition is understood, as usual, the 
situation in which a planet is in exact opposition to the Sun, 
while both the planet eps the Earth are at their mean distances 
rom the Sun. e third column contains the residuals from 
the mean, 6°64, of the meric magnitudes thus found. The 
last column contains the residuals showing the ees of 
ee Harrington’s observations of the two comparison stars. 
e differences between the two columns of his table 
headed 2164 and 2163, we have a series of quantities expressed 
in seconds of time, the mean of which is 20: 6 ; it corresponds to 
the photometric difference in magnitude resulting from the 
observations made here with the meridian photometer. This 
photometric difference is 9°06—5-48 = 358. These data show 
that in Professor Harrington’s observations one second of time 
may be expressed in terms of magnitude by ‘174. The final 
column of the table here given accordingly contains the products 
by ‘174 of the differences between Professor Harrington’s 
columns 2164 and 2163, diminished by the photometric differ- 
ence 3°58 If reduced to the equator, the quantity ‘174 
becomes ‘16, which furnishes a determination of the constant 
of reduction required by the particular wedge employed. The 
last line of the table contains the numerical means of the 
quantities in the tot three columns. It may be observed that 
in the first and third lines of the table the large residuals in the 
third ee are accompanied by large residuals in the final 
Oo EE ae 
