336 



H. Jacoby — Determination of the Division 



Scale A is numbered 0, 1, 2, 3, 4 ; and scale B is numbered 

 0, d, o, b, a, to avoid confusion. Operation 1 consists in plac- 

 ing scale B opposite scale A in such a way that division e 

 comes opposite 3, and d opposite 4. The microscope of the 

 comparateur is then brought over the divisions 3 and e, and 

 readings are taken on each of these divisions. The microscope 

 is then brought over the divisions 4 and d, and these are also 

 read. The operation is then repeated in the reverse order, the 

 scales remaining unmoved all the time. If we suppose the 

 microscope readings to decrease as the readings of scale A 

 increase, and if we put : 



d 4 = excess of reading on division 4 over that on division d, 

 e 3 = excess of reading on division 3 over that on division e, 



it is obvious that operation 1 furnishes the quantity : 



or the excess of the space 3, 4 of scale A over the space e, d of 

 scale B. In exactly the same way operation 2 furnishes the 

 quantities : 



d i —c i and e 2 — d^ 



or the excesses of the spaces 2, 3 and 3, 4 over e, d and d, c 

 respectively. Proceeding in this way, we may arrange the 

 results of all the operations as in the following table : 



Table I. 



0, 1 



K. 



2,3 



3,4 





K 3 



K„ 



(e-dj 



K 



Operation 1. 

 2. 

 3. 

 4. 

 5. 

 6. 

 1. 



It will be seen that each of the quantities in parenthesis is the 

 excess of one of the spaces of scale A over one of the spaces 

 of scale B. Thus the first column contains the excesses of the 

 space 0, 1 of scale A over each of the four spaces of scale B. 

 Similarly the other columns contain the excesses of the spaces 

 1, 2 ; 2, 3 ; and 3, 4. Moreover the results of each separate 

 operation will be found in the same horizontal line of the table. 

 The quantities K 15 K 2 , K 3 , K 4 , are the means of the quantities 

 above them in the columns. Thus : 



