CH. IV] MAGNIFICATION AND MICROMETRY 119 



formity of micrometers, and the difficulty of determining the exact limits of the 

 object to be measured. Hence, all microscopic measurements are only approxi- 

 mately correct, the error lessening with the increasing perfection of the apparatus 

 and the skill of the observer. 



microscope would be obtained by multiplying the number of divisions on the 

 ocular micrometer required to include its image by the value of one space, or in 

 this case, i^th mm. Suppose some object, as the fly's wing, required 15 spaces of 

 the ocular micrometer to include some part of it, then the actual size of this part 

 of the wing would be 15 X A = fths, or 0.6 mm. 



(B) By finding the number of divisions on the ocular micrometer required to 

 include the image of an entire millimeter of the stage micrometer, and using this 

 number as a divisor. This number is also sometimes called the ocular micrometer 

 ratio. Taking the same case as in (A), suppose five divisions of the ocular mi- 

 crometer are required to include the image of fjthstiim., on the stage micrometer, 

 then evidently it would require 5 h- t 2 (7 = 25 divisions on the ocular micrometer to 

 include a whole millimeter on the stage micrometer, and the number of divisions 

 of the ocular micrometer required to measure an object divided by 25 would give 

 the actual size of the object in millimeters or in a fraction of a millimeter. Thus, 

 suppose it required 15 divisions of the ocular micrometer to include the image of 

 some part of the fly's wing, the actual size of the part included would be 15-j- 25 

 = ; ; or 0.6 mm. This method is really exactly like the one in (A), for dividing by 

 25 is the same as multiplying by -}-\\x. 



( C) By having the ocular micrometer ruled in millimeters and divisions of a 

 millimeter, and then getting the size of the real image in millimeters. In employ- 

 ing this method a stage micrometer is-used as object and the size of the image of 

 one or more divisions is measured by the ocular micrometer, thus : Suppose the 

 stage micrometer is ruled in iVjth and T( Toth mm. and the ocular micrometer is ruled 

 in millimeters and y'ljth mm. Taking i 2 , T th mm. on the stage micrometer as object, 

 as in the other cases, suppose it requires 10 of the ^th mm. spaces or 1 mm. to 

 measure the real image, then the real image must be magnified |I}-^t 2 o = 5 diame- 

 ters, that is, the real image is five times as great in length as the object, and the 

 size of an object may be determined by putting it under the microscope and getting 

 the size of the real image in millimeters with the ocular micrometer and dividing 

 it by the magnification of the real image, which in this case is 5 diameters. 



Use the fly's wing as object, as in the other cases, and measure the image of 

 the same part. Suppose that it required 30 of the j 1 ^ mm. divisions = \% mm. or 3 

 mm. to include the image of the part measured, then evidently the actual size of 

 the part measured is 3 mm, -h— 5 = ■§ mm., the same result as in the other cases. 



In comparing these methods it will be seen that in the first two (A and B) the 

 ocular micrometer may be simply ruled with equidistant lines without regard to 

 the absolute size in millimeters or inches of the spaces. In the last method the 

 ocular micrometer must have its spaces some known division of a millimeter or 

 inch. In the first two methods only one standard of measure is required, viz, the 

 stage micrometer ; in the last method two standards must be used, — a stage mi- 

 crometer and an ocular micrometer. Of course, the ocular micrometer in the first 

 two cases must have the lines equidistant as well as in the last case, but ruling 

 lines equidistant is quite a different matter from getting them an exact division of 

 a millimeter or of an inch apart. 



