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POPULAR SCIENCE REVIEW. 
Eeal libration in longitude = + 178 sin { 0-480 T } 
+ 150 sin [i - 24" sin a, according to Wich- 
mann. 
+ 61 sin { 0-396 T + 90°} 
+ 124 sin fi - 21" sin a, according to Hart- 
wig.* 
It will be seen that these results are very far from being as accordant as 
they ought to be, and show that there have been grave systematic errors in 
one, or both, of the two series of observations or reductions. It is much to 
be desired that a reduction should be made of a great number of observa- 
tions made by Herr Schliiter in 1841-44, and it would be desirable to have 
Herr Hartwig’s results reduced with values for the arguments derived from 
his own observations, and not from those of Wichmann. 
Prof. Pritchard, of the Oxford Observatory, is also reducing a number of j 
measures of photographs of the Moon, with the view of determining the 
real libration. His results are not yet published, but he has stated that j 
they are in accord with those found by Wichmann. In a recent communi- 
cation to the Koyal Astronomical Society, Prof. Pritchard speaks rather 
despondently of the prospects of determining the actual amount of this 
real libration. Quoting from an account of his remarks at the Society 
( Observatory , February 1881), he says : ‘We must accept this — that these 
measures and these calculations, though beyond all doubt they show that j 
there really is a lunar physical libration, and that it is somewhere between 
these numbers, yet you will never get it within 20 or 30 or 40 
seconds.’ But there are far superior methods for determining this real 
libration than have ever been employed as yet ; and so far from accepting 
the gloomy view taken by Prof. Pritchard, it is probable that astronomers 
will look to one of these improved methods to reduce the uncertainty to far 
smaller limit than supposed by Prof. Pritchard. It may be here mentioned 
that 20 to 40 seconds of selenographical longitude corresponds at the mean j 
distance of the Moon to only one to two tenths of a second of arc ; a small 
enough quantity. 
The Diameter of Mars. — Lately {Monthly Notices R.A.S. Nov. 1880) 
Mr. Downing has determined, from some five hundred measures with the 
Greenwich Transit Circle, the mean diameter of the planet Mars, which he 
finds to be — 
= 9"-697 ± 0"-107 
He also finds that there is a constant correction required for irradiation, j 
which is equal to — 
= + 2"-369 ± 0"-175 
As Mr. Downing points out, the correction is unusually large, that for the 
Washington 4-inch Mural Circle being only 1"T92. 
Mr. Stone, F.R.S., has also lately made a communication to the Astro- 
nomical Society on the same subject. He finds that different observers have 
a considerable personality in observing the diameter of the planets, some ] 
* In these formulae, T = the number of mean solar days for January 1, 
1845; y denotes the mean anomaly of the Sun; and a, the mean anomaly 
of the Moon. 
