MAGNIFYING POWER. 



Fig. 6. 



Fig. 5. 



11. It is contended by some that the magnifying power is more 

 properly and adequately expressed by referring it to the super- 

 licial 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- 

 creased 10 times, 

 and its superfi- 

 cial magnitude 

 being conse- 



a 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 



