90 THE STUDY OF SPEECH CURVES. 



to insure their correctness. The patterns themselves may be prepared 

 from these schedules by having a Uthographer engrave a stone with rec- 

 tangles 12mm. by 5mm. For a set of 12, 24, 3G, and 72 patterns a total 

 of 72 prints on cardboard is made; a supply of prints on paper is also 

 required, one print for each analysis to be done.* 



To prepare a pattern the rectangles marked + and — are cut out ; the 

 holes for those with + are surrounded by a black Une, those with — by a 

 red line. 



On the paper ruled in columns and Unes the values of y are written 

 in the first column. If 72 ordinates are used, each of these values of y is 

 to be multipUed by 1.00000, 0.99619, 0.98481, 0.96593, 0.93969, 0.90631, 

 0.86603, 0.81915, 0.76604, 0.70711, 0.64279, 0.57358, 0.50000, 0.42262, 

 0.34202, 0.25882, 0.17365, 0.08715, 0. For 38 ordinates the multipliers 

 are 1.00000, 0.98481, 0.93969, etc., namely, every second one of the 

 above set for 72. For 24 ordinates they are 1.00000, 0.96593, 0.86603, 

 0.70711, 0.50000, 0.25882, 0. For 12 they are 1.0000, 0.86603, 0.500000, 0. 

 Positive products are written with black ink, negative with red. These 

 products may be taken from Crelle's Rechentaf eln ; this suffices for two 

 or three places, but requires an extravagance of time for four or five places. 

 When large numbers of waves are to be analyzed, it is well to prepare a 

 table of products with a multiplying machine, using seven places and 

 then condensing to five. The table should be made for 72 ordinates; 

 for 72 ordinates each Une is copied completely; for 36 ordinates every 

 second column is used; for 24 ordinates every third column, and for 12 

 ordinates every sixth column. For much of the work it is not necessary 

 to use more than two or three decimal places; a condensed table can be 

 readily prepared. 



To calculate a coefficient the requisite pattern is laid over the sheet 

 with the products. All the figures seen through the holes are added; 

 those whose color corresponds with that of the lines around the holes are 

 positive, the others are negative. As this work— particularly with 72 

 ordinates — requires an enormous amount of time, and as it must be done 

 over at least twice in order to insure against mistakes of addition, the use 

 of adding machines is to be strongly recommended. f The result of each 

 addition is divided by half the number of schedules. The values a and 

 6 thus obtained are used to calculate c = Va'+h'- 



When the analysis has been made, the serial numbers of the suc- 

 cessive harmonics are laid off on the X-axis and ordinates proportional 

 to the amplitudes c are erected as straight lines. The tops of the ordi- 



* Prints can be had by mail from G. Heinicke, Dorotheenstr. 39, Berlin, Germany, at 10 marks 

 per hundred for cardboard and 6i marks per hundred for paper, 

 t Burroughs, Felt and Tarrant, etc. 



