ON DIVIDING ASTRONOMICAL INSTRUMENTS. 101 



sured by sixteen times its angular value upon the sectorial 

 arc, or 22° 30' ; but this does not represent any nnmber of 

 equal parts upon the instruntient, the subdivisions of which 



\° 24' 22"3 



are to be 5' each ; for -^ — is exactly lC|, therefore 



so many divisions are exactly equal to a mean space between 

 the dots, the errours of which have been tabulated. Let, 

 therefore, the arc of the sector be divided into l6 spaces 

 of 1° 20' each, and let a similar space at each end be sub- 

 divided into eight parts of 10' each, as in Fig. 4; we shall 

 then have a scale which furnishes the means for making the 

 true divisions, and an immediate examination at every bi- 

 sectlonal point. 



I have always divided the sector from the engine, be- Di\iclinsj bj 

 cause that is the readiest method, and inferior to none in the engine, 

 point of accuracy, where the radius is very short ; but, as 

 it is more liable than any other to centrical errour, the ad- 

 justment of the arc by the screw E becomes necessary : by 

 that adjustment, also, any undue run in the action of the 

 roller may be reduced to an insensible quantity*. 



When the utmost degree of accuracy is required, l give Division by 

 the preference to dividing by lines, because they are made ''"^'' prefer- 

 with a less forcible effort than dots are ; and also because, if' 

 any small defect in the contexture of the metal causes the 

 cutter to deviate, it will, after passing the defective part, 

 proceed again in its j)roper course, and a partial crooked- 

 ness in the line will be the only consequence ; whereas a dot, 

 under similar circumstances, would be altogether displaced. 

 But, on the other hand, where accuracy has been out of the 

 question, and only neatness required, I have used dots; 

 and I have done so, because I know that when a dot and 

 the wire which is to bisect it are in due proportion to each 

 other, (the wire covering about two thi.ds of the dot) the 

 nicest comparison possible may be obtained. It may be 

 farther observed, that division by lines is com{)lete in it- 

 self; whereus that by dots requires lines to distinguish their 

 value. 



On the upper side of Fig. 1 is represented the apparatus Apparatus for 

 for cutting the divisions. It consists of three pieces J K L, dWisioL?'^ 



* See note page 130. 



jointed 



