CH. II] LIGHTING AND FOCUSING. 51 



\ 94. Color Images. — These are images of objects which are strongly colored 

 and lighted with so wide an aperture that the refraction images are drowned in the 

 light. Such images are obtained by removing the diaphragm or by using a larger 

 opening. This method of illumination is specially applicable to the study of 

 stained microbes. (See below \ 101). 



ADJUSTABLE, WATER AND HOMOGENEOUS OBJECTIVES. 



EXPERIMENTS. 



§ 95. Adjustment for Objectives. — As stated above (§ 22), the ab- 

 erration produced by the cover-glass (Fig. 56), is compensated for by- 

 giving the combinations in the objective a different relative position 

 than they would have if the objective were to be used on uncovered 

 objects. Although this relative position cannot be changed in unad- 

 justable objectives, one can secure the best results of which the object- 

 ive is capable by selecting covers of the thickness for which the object- 

 ive was corrected. (See table in § 27). Adjustment may be made 

 also by increasing the tube-length for covers tliinner than the standard, 



the table nearest the sine whose angle is to be determined. Get the difference of 

 the sines of the angles greater and less than the sine whose angle is to be deter- 

 mined. That will give the increase of sine for that region of the arc for 15 minutes. 

 Divide this increase by 15 and it will give with approximate accuracy the increase 

 for 1 minute in the particular region. Now get the difference between the sine 

 whose angle is to be determined and the sine just below it in value. Divide this 

 difference by the amount found necessary for an increase in angle of 1 minute and 

 the quotient will give the number of minutes greater the sine is than the next 

 lower one whose angle is known. Add this number of minutes to the angle of the 

 next lower sine and the sum will represent the desired angle of the sine. Or if 

 the sine whose angle is to be found is nearer in size to the sine just greater proceed 

 exactly as before, getting the difference in the sines, but subtract the number of 

 minutes of difference and the result will give the angle sought. For example take 

 the case in the last section where the sine of the angle of 28 54' is given as 0.48327. 

 If one consults the table the nearest sines found are 0.48099, the sine of 28 45'', 

 and 0.48481, the sine of 29°. Evidently then the angle sought must lie between 

 2S 45' and 29°. If the difference between 0.48481 and 0.48099 be obtained, 0.48481 

 — o 48099 = 0.00382, and this increase for 15' be divided by 15 it will give the in- 

 crease for 1 minute; 0.00382-^-15 = 0.000254. Now the difference between the- 

 sine whose angle is to be found and the next lower sine is 0.48327 — 0.48099 = 

 0.00228. If this difference is divided by the amount found necessary for 1 minute- 

 it will give the total minutes above 28 45' ; 0.00228 -=-0.000254 = 9. That is the 

 angle sought is 9 minutes greater than 28 45' = 28° 54'. If now it is found how 

 much less the sine is than the next higher sine it will be seen that 0.48327 and 

 0.48481 differ by 0.00154. If this is divided by 0.000254 th e change in sine for 1 

 minute in this region of the arc, the result is 0.00154-7-0.000254 = 6, That is the 

 sine of 29 is too great for the sine whose angle is to be found by 6 minutes, hence 

 29 less 6' = 28 54', the angle sought. 



