CHAPTER IV. 

 QUANTITATIVE ANALYSIS: APPARATUS, METHODS. 



The term "quantitative analysis" is used here to include such analy- 

 sis of sound curves as may be obtained immediately by measurements. 

 It is distinguished from more complicated methods— such as harmonic 

 analysis — which are leased on measurements, but which aim at both qual- 

 itative and quantitative distinctions. 



For measurements the following pieces of apparatus have been found 

 useful: For long pieces of curve a millimeter scale is advantageous; when 

 tenths of a millimeter are required, they can be estimated by the eye. 

 For the finer measurements either a metal scale in tenths of a miUimeter 

 read by a watchmaker's eyeglass or a low-power microscope with ocular 

 micrometer, or a low-power microscope traveling on a milhmeter thread 

 with barrel reading in hundredths, may be used. Each of these methods 

 has its special advantages and difficulties. The only convenient scale in 

 tenths of a millimeter which the writer has been able to find is the " petite 

 echelle en argentan cUvise d'un cote en dixiemes de miHimetres" for 20 

 francs from the Societe genevoise, Geneva. It is 110mm. long. The 

 measurements can be made quickly, but the work is fatiguing. Except 

 in a very few cases the ordinary low-power microscope with micrometer 

 ocular is not available, because the field is not large enough. To meet the 

 needs of the work I have arranged a microscope as described in the follow- 

 ing paragraphs. 



The "coordinate measurer" shown in figure 45 comprises a micro- 

 scope mounted on a car movable in two directions by micrometer screws. 

 The microscope is held on a projecting arm, which can be replaced by other 

 arms adapted to hold other microscopes or magnifying glasses; the sights 

 in the posts are for adjusting the carrying arm in the plane of the horizontal 

 screw. The screws must be accurately made and must not show any wobble 

 or back-lash. The whole apparatus should be stoutly built; the rails shown 

 in the figures should, in the future cases, be replaced by V-bearings. It 

 is made rather small so that it can be readily placed anywhere on a plate 

 of curves and clamped to the table or drawing-board. The ocular may 

 have cross lines or a scale. 



The apparatus is placed over the curve to be measured, with the hori- 

 zontal screw parallel to the axis of the curve. This is accomplished by 

 scratching beforehand on the celluloid covering of the plate a line that is 



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