Astronomical and Nautical Collections. 189 
catalogues varies gradually with the polar distance from 0’ 
to 5"! This is a good example of the inutility of the modern 
theory of probabilities, as it has been frequently employed on 
the continent. 
ull. Elements of a Table ef Refraction, deduced from Observa- 
tion only. 
Refraction B. 30 Correction 
Star Observations Altitude Fa. 489 Fa. 469 for—1° F, 
y Cygni 13 Groombr. i 3i 20 56.1 91 32 3°54 
a Lyre 44Brinkl 217: 16 53.9 16 59.5 2:81 
« Cygni 9 Groombr. 6 15 8 9.4 8 11.5 1.07 
The method of reduction employed has been this: First, To 
correct the height of the barometer for the small difference of 
temperatures, so as to make it a barometer without. Secondly, 
To reduce all the refractions to their mean value, with the 
barometer at 30 inches, by applying corrections simply pro- 
portional to the differences, as usual. Thirdly, To find the 
mean temperature by the exterior thermometer. Fourthly, To 
find the differences of the several temperatures from the mean, 
and add them all together, without regard to the signs. Fifthly, 
To find the mean refraction and the differences from the mean, 
and to add together such of them as are regular, that is, such 
as agree with the differences of the thermometer in their cha- 
racter, and to subtract the sum of such as are irregular. 
Sixthly, To divide this result by the sum of the differences of 
the thermometer, in order to obtain the experimental correction 
for temperature. Seventhly, To apply this correction to the 
reduction of the mean temperature of the thermometer to 48° 
or 46°: and Lastly, To reduce the mean apparent altitude to 
the nearest minute, according to the differences of any existing 
table, for the more ready comparison of the results of this 
method of reduction with those of any theory to be examined. 
A ninth step will be required, with respect to the correc- 
tion for temperature, if we wish to determine it with great 
accuracy ; that is, to correct the mean altitude for any supposed 
temperature, and to add to the correction found the difference 
