310 W. M. BALE ON THE 



objective, in combination with an eye-piece giving a power of 

 about 370 diameters, there was a difference of about 22 diameters 

 between the results obtained when the collar was set at the two 

 extremities of its range. It should be set at a position suitable 

 for average slides, and always brought to that position when 

 measurements are to be taken. The fine adjustment should be 

 at about the centre of its range, if it is one of those which act on 

 the nose-piece only. I suppose it will rarely happen that the 

 field-diameter will vary in different directions, yet I have in one 

 instance found a slight variation, owing to the diaphragm not 

 being truly circular. In such a case the eye-piece may be marked 

 so as to show which diameter is taken. If a pair of eye-pieces 

 is in use they should be tested to see if the fields are equal ; if 

 not, one only should be used for measurements. 



Having done the sums it remains to prove them, which we can 

 easily do by proportion. As the power of, say, a 1-inch with a 

 certain eye-piece is to the power of a one-fourth with the same 

 eye-piece, so will be the power of the 1-inch to that of the one- 

 fourth with any other eye-piece. If on making a series of com- 

 parisons like this the results correspond fairly with the figures 

 obtained by measurement, we may be satisfied ; if not, we must 

 conclude that there is an error somewhere. In a few instances 

 it may probably be found that the field measures an exact number 

 of micrometer-divisions without fractions ; the results in such 

 cases should reach a high degree of accuracy, and should be relied 

 upon rather than those in which there have been fractions to 

 estimate. For example, a 2-inch objective with a J-inch eye- 

 piece gave a field which measured 26 thousandths with the inch 

 micrometer, and 66 hundredths with the millimetre micrometer. 



The effective magnified field-diameter was 6fV inches, or 157 milli- 

 metres ; the respective results therefore were 237 '98 and 237 '87 

 diameters. 



Of course if we are certain that we have ascertained correctly 

 the powers of our whole series of objectives with any one ocular, 

 it will suffice to measure the powers of each of the other oculars 

 with one objective only, and then the powers with the other 

 objectives can be found by proportion. 



We will now revert to the subject of the deduction to be made 

 from the apparent field-diameter to compensate for the unequal 

 magnification of the different zones of the field. When we speak 



