AND MEASURING PLANE ANGLES. 31 



The diagonal scale of '20 parts to an inch will he of a very- 

 convenient size for the above purpose — On this the half inch 

 is divided into 100 equal parts, each of which will correspond 

 to 6 minutes. 



But this method of subdividing lines of equal parts, though 

 no doubt susceptible of great accuracy, is yet attended with in- 

 convenicncies which it would be desirable to obviate — such 

 lines occupy so much room on the scale, that but few of them 

 can be inserted, and among such a multiplicity of crossing 

 lines, the eye is liable to mistake one for another. 



The following method which is only an application of the 

 nonius division, is susceptible of even greater accuracy and 

 minuteness than the diagonal method, and yet free from all its 

 ineonveniencies. — Let each of the larger divisions of the line 

 be subdivided into 10 equal parts, as the line of inches on the 

 common scale; then if you would farther subdivide these, say 

 each into 10 equal parts, you must set off before the beginning 

 of the line, a space equal to 1 1 of the smaller divisions, which 

 divide into 10 equal parts, numbering them backwards 1, 2, 

 3, &c. and then each of these divisions on the nonius will 

 exceed one of the smaller divisions on the scale just ^ part of 

 the latter. 



The manner of using this nonius in laying down or mea- 

 suring lines is sufficiently obvious — Thus if you would take off 

 with a pair of compasses 21 -% you "must extend from 6 on the 

 nonius to 21 (27-6) on the scale, if you would take off 51 -l- s 

 extend from 7 on the nonius to 50 on the scale &c. But a still 

 more minute subdivision may be easily made by combining 

 the nonius and diagonal methods together — thus if each of the 

 lesser divisions, both on the scale and nonius were, by diagonals, 

 subdivided into 10 equal parts, then each of the larger divisions 

 would in fact be subdivided into 1000 equal parts, and yet 

 none of the lines, even on the scale of 20 to an inch, would 

 be less than -J^ of an inch assunder. Such a degree of minute- 

 ness can however seldom if ever be necessary, and therefore 

 the use of the diagonal scale may be entirely dispensed with. 



In Plate in. Fig. 7. the nonius occupies a space equal to 13 

 of the smaller divisions on the scale, and is divided into 12 



