706 Transactions of the Society. 
table, such as E, F, we get an amplification due to a distance greater 
than ten inches. 
A little consideration will in fact show, that if we desire to inves- 
tigate the true dimensions of an object by examining its virtual image 
projected upon an area of uniform magnification, we must employ 
for this purpose, not the plane surface upon which such measurements 
are usually made, but a concave spherical surface, having the eye at 
A for its centre, and for its radius a length of ten inches, or whatever 
other distance may be convenient to the observer, or may be conven- 
tionally agreed upon, as affording a standard by which different 
observations may be compared with one another. 
Fig. 78. 
Reverting to the figure, if E F be a measurement taken across the 
image of an object projected upon the plane of the table, the amount 
of magnification deduced from such measurement will be in excess of 
the magnification due to a distance of ten inches, by as much as the 
length of the straight line E B F exceeds that of the circular arc 
C B D ; and any conclusions drawn therefrom, either as to the magni- 
fying power of the glasses employed, or as to the dimensions of the 
object under examination, will be affected with a corresponding error. 
The error here involved may be corrected by a simple calculation, 
provided care be taken that the line to be measured is so placed (like 
the line E B F in the figure) as to be bisected by the central point of 
