Mr. de Mendoza Rios on 
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direct image of the moon L is seen through the telescope, the 
angular distance to the sun, if at S, may be measured by moving 
the centre index to m , in order to produce the contact; or, if the 
sun is at S', the same operation may be performed, by using the 
contrary motion to m'. The first kind of observation, the Cheva- 
lier de Borda calls observation to the left; and the second, obser- 
vation to the right. Suppose now, that (the horizon index being 
fixed in the same position) the distance from L to S is observed 
to the left, by bringing into contact the doubly reflected image 
of S with the image of L, seen without reflection ; let us then 
turn the instrument round, keeping it in the same plane, so as to 
have the direct image of S through the telescope, and thus make 
an observation of the same distance to the right ; the position of 
the centre index being in the first observation at m, and in the 
second observation at m f , it is clear, that if o is the point where 
the parallelism of the glasses takes place, om is equal to o m! ; 
and, that the arch m m ', determined by the two positions, will 
give double the distance. 
It will be more convenient to have the centre index at o, when 
the first observation is made, in order to take the double distance 
at one reading, after the second observation. For this purpose, 
the first part of the process may be inverted, by previously 
fixing the centre index at the beginning of the divisions, and 
moving the horizon index H towards o, instead of moving the 
centre index A to m, or towards H. 
The last kind of observation, in which the incident ray, which 
produces the first image upon the centre glass, may be conceived 
to run double the angular distance, passing in its way over the 
line of collimation, has been called, by the Chevalier de Borda, 
the crossed observation. 
