MAGNIFYING POWER. 
11, It is contended by some that the magnifying power is more 
properly and adequately expressed by referring it to the super¬ 
ficial than to the linear dimensions of the objects. 
To illustrate this, let us suppose the object magnified to be a 
square such as a , fig. 5. Now, if its linear dimensions, that is 
its sides, be magnified 10 times, the square will be increased to 
the size represented at 
a (fig. 6); its height and 
breadth being each in- 
p creased 10 times, 
* and its superfi¬ 
cial magnitude 
being conse¬ 
quently in¬ 
creased 100 times, as 
is apparent by the 
diagram. 
Now, it is contended, 
and not without some 
reason, that when an 
object, such as a, re¬ 
ceives the increase of 
apparent size, repre¬ 
sented at A, it is much 
more properly said to be magnified 100 than 10 times. 
Nevertheless, it is not by the increase of superficial, but of linear 
dimensions that magnifying powers are usually expressed. No 
obscurity or confusion can arise from this, so long as it is well 
understood that the increase of linear, and not that of superficial 
dimension, is intended. Those who desire to ascertain the super¬ 
ficial amplification, need only take the square of the linear ; thus, 
if the linear be' 3, 4, or 5, the superficial will be 9, 16, or 25, and 
so on. 
It might even be maintained, that when an object having 
length, width, and thickness, a small cube or prism of a crystal 
for example, is magnified, the amplification being produced equally 
on all the three dimensions, ought to be expressed by the cube of 
the linear increase ; thus, for example, if the object, being a cube, 
be magnified 10 times in its linear dimensions, it will acquire 10 
times greater length, 10 times greater breadth, and 10 times 
greater height, and will consequently appear as a cube of 1000 
times greater volume. 
In this case, however, as in that of the superficial increase, the 
calculation is easily made by those who desire it, when the linear 
increase is known. 
103 
