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off diametrically, and svibseqnently run into their positions with a good 

 parallel ruler. The inconvenience of this method is not much felt in plotting 

 compact surveys, although even in such cases the use of the Semicircular 

 Protractor confers great advantages ; but in the case of long and narrow- 

 surveys, such as railway work almost always presents, the inconvenience and 

 liability to error attending the use of the circular instrument is such that the 

 other method seems, in comparison, perfect. 



For about eight years the writer used, as occasion required, the old method, 

 and then determined to adapt to more extended use than its inventor seemed 

 to have intended the instrument described by Mr. Howlett, as quoted in 

 Heather's Treatise on Mathematical Instruments, in Weale's well known series. 

 Several alterations, however, from Mr. Howlett's design suggested themselves, 

 and the improved protractor was made by Messrs. Elliott Brothers, of London, 

 from drawings supplied by the writer, and its use by him for the last eleven 

 years, in eveiy variety of woi'k, has demonstrated its great superiority over the 

 old method — in points of accuracy, comfort in using, rapidity with which work 

 can be laid down, and the great facility which it offers in tracing the 

 occurrence of any error in plotting. 



Mr. Howlett fastened the drawing paper to a board, and used a T square, 

 whose edge represented the meridian, hence any angle to which the arm of the 

 proti-actor was set could at once be transferred to any position on the paper, 

 by keeping its meridional edge in contact with the square, and moving both on 

 the paper until one edge of the arm coincided with the point reqiiired. But 

 long rolls of paper cannot be used with a T square or drawing board, and the 

 writer uses in such cases the same parallel ruler which is required in using the 

 circular protractor. If the work lies mainly north and south, one meridian 

 line is drawn in lightly in blue ; if it lies otherwise, several meridian lines 

 may be required at varioiis intervals, laid down with g'reat care. The edgfe of 

 the heavy brass parallel ruler, then, represents the meridian, and its truth can 

 be compared with the nearest line at any moment. The protractor is moved 

 along the edge of the ruler nntil in position, just as with the use of the 

 T square. Of course, when the size of the map or plan is such as to admit of 

 the paper being fastened on a board, the T square forms the most perfect 

 parallel ruler, and should be used in preference. 



The operations which must be gone through when using the circular 

 protractor — ^consisting of laying down the bearings, reading off the particular 

 one required (sometimes among a crowd of others of nearly the same angle), 

 setting the rulei", and running it into place — may, by the method here 

 advocated, be said to be comprised in one movement, such is the comparative 

 and absolute ease attending its use. 



While setting the vernier arm, the instrument is held in the hand, and in 

 the most suitable light. This, besides being a source of much comfort, is 



