152 Analyses of Books. [Aue. 
distance thus formed was made the ground-work of a microme- 
‘trical telescope. Of this original instrument, not described in 
any English work, an account is given; and the improvements 
consequent upon the discoveries of Malus, Arago, and Lenoir, 
are successively noticed. 
But before the doubly-refracting prism can be rendered useful 
in measuring small angles, Dr. Pearson states that the constant 
angle which it measures, as viewed by the unassisted eye, must 
be accurately known; and also the magnifying power of the 
telescope as used with it; foron these data, the accuracy of the 
measure taken by this method entirely depends. The remainder 
of the memoir is accordingly devoted to a consideration of these 
two necessary objects. As « specimen of the manner of con- 
ducting these investigations, the second method of determining 
the constant angles of the prisms may be transcribed. ‘“ The 
prisms were now applied in succession to the small cap at the 
eye end of the telescope of 45°75 inches, with the view of mea- 
suring the distance between the centres of the same disc that 
had been used with the prisms in the cap of the object end. In 
the first position, all the three spider’s lines were doubled; viz. 
the horizontal one and the two vertical ones. But turning the 
cap which held the prism round a little, brought the two images 
of the horizontal line into one, while it opened the other images 
or lines wider apart: a little motion given to the screw, however, 
soon brought the second and third lines into one strong black 
line, and left the first and fourth more faint, at equal distances 
to the right and left. In this situation I found I had obtained 
the measure of the angle wanted ; for the second line of the first 
image was become coincident -vith the first line of the second 
image ; and the distance of either of the extreme lines from the 
strong black one in the middle was the quantity of the measured 
angle, as indicated by the micrometer. The same thing was 
done at the other side of the micrometer’s zero, and a mean of 
the two measures gave the true one without any index error. 
This process is as simple as accurate. When any prism is 
screwed into its place, the two images of the horizontal line must 
first be brought into one strong line, and then the two or four 
images of the coincident or separated lines (as the case may be) 
must be brought nicely into three, of which the middle cne will 
be always much darker than either of the others by reason of 
there being then two images occupying the place of one. It is 
indeed astonishing with what degree of precision the small angle 
of any prism may be taken in this way; and what at first was 
not suspected, the micrometer indicated the same quantity, to 
whichever telescope it was thus applied with any prism, or 
even when it was detached from the telescopes altogether.” 
Respecting the determination of the magnifying power of the 
telescope, the second of the objects before alluded to, the follow- 
ing quotation may suffice: “ Ithas already been said, that if the 
