INVERTEBRATA, CRYPTOGAMIA, MICROSCOPY, ETC. 949 



measured in the same way from line 100 to line 1. But if we sub- 

 tract the measures from line 1 to line 100 from the corresponding 

 measures from line 100 to line 1, the dijference ivill give twice the accu- 

 mulated errors at any point for strictly periodic errors independent of 

 the comparing screw. The only exception to this rule is found when 

 the curve of errors takes a wave form. In a general way this will 

 be the case when the maximum error falls near line 25, and the mini- 

 mum near line 75. 



As an an illustration of the character of the work which may be 

 done with a comparator of this form, Professor Eogers gives a Table 

 of the measures of five standard micrometers ruled at different times. 

 As these micrometers are somewhat different in form from any with 

 which he is acquainted he gives a brief description of them. 



1. A half-inch is divided into 50 equal parts, the 1st, 25th, and 

 50th spaces being again subdivided into 10 equal parts. The length 

 of the lines is about | inch, the 5th and 10th lines being a little 

 longer. 



2, After arranging the position of the ruling carriage, so that the 

 lines of the second series of graduations should begin near the point 

 where those of the first end, coincidence is made mechanically with 

 the first line of the series already ruled. For a short distance the 

 ruling point goes over the same ground twice. A centimetre is then 

 subdivided into 10 equal parts. The 1st, 5th, and 10th spaces are 

 again subdivided into 10 equal parts, and one of the middle sub- 

 divisions is still further subdivided, giving • 01 mm. Near by is a 

 band of 21 lines, each space being equal to "001 mm. 



The table shows that the individual errors of graduation are 

 practically insensible. 



The errors obtained are, it is to be noted, entirely relative errors. 

 They give no indication whatever of the absolute value of any of the 

 spaces measured. If the entire length of the half-inch is e. g. • 001 

 inch too long, to each of the corrections given in the table must be 

 applied still further the correction • 00002 inch. 



It is therefore necessary to make a careful investigation of the 

 entire length of the half-inch and of the centimetre. 



This is done with a comparator adapted to the comparison of 

 spaces, ranging from coincidence to an entire yard or an entire metre. 

 Comparators of this class are usually constructed with two sliding 

 plates, each carrying its own Microscope. A fundamental objection 

 to this form is found in the fact that the Microscopes cannot be 

 brought much nearer together than 3 inches by any direct means. 

 For want of space and of illustrations. Professor Eogers is able to 

 give only a general description of the form which he has had con- 

 structed. 



It consists of an iron bed 60 inches long and 14 inches wide. 

 V-shaped grooves 6 inches apart run the entire length. In the centre 

 of the bed a fine-toothed rack reaches from end to end. Two sliding 

 plates are carried along the ways by means of a pinion set in the 

 centre of the plates and working so loosely in the rack that the 

 slides are free to follow the law of gravity. A Microscope is 



