TRACING GRAMOPHONE AND PHONOGRAPH RECORDS. 31 



For example, the amplitudes of successive waves were twice inde- 

 pendently measured with the following results: 



First measurement 4.4 5.0 5.6 6.5 7.1 7.9 7.2 7.9 8.8 7.3 Average: 6.77 



Second measurement. . 4.3 5.0 5.7 6.4 7.1 7.9 7.3 7.8 8.8 7.3 



Difference 0.1 0.0 0.1 0.1 0.0 0.0 0.1 0.1 0.0 0.0 Average: 0.05 



There was thus an average error of 0.05 ^ 6.77 or 0.0074 of the 

 average or, say, 0.7 per cent. 



To determine how precisely the apparatus is working, the same 

 piece of curve should be traced off twice independently. The corre- 

 sponding waves are measured and the differences found. For example, 

 a second tracing of the same curve as that just measured gave the ampli- 

 tudes 4.6, 5.0, 5.7, 6.4, 7.1, 7.9, 7.3, 7.9,8.9,7.5. The differences from 

 the corresponding waves in the first tracing were 0.2, 0.0, 0.1, 0.1, 0.0, 

 0.1, 0.0, 0.1, 0.2, and the average difference was 0.07, i. e., 0.07-^6.77, or 

 0.010, or 1 per cent of the average. This is the variation due to the 

 apparatus and the measuring together. If this average difference be indi- 

 cated by s, that for the measuring by p, and that for the apparatus alone 

 by q, the relation is, by a well-known law, s^ = <f + pi Consequently, 



q= Vs'—f^^ 1 0.07^-0.05' =0.049; 



this is 0.049 -f- 6.77 or, say, 0.7 per cent of the average. 



Whenever any alteration is made in the apparatus the precision 

 should be again determined. For practical purposes I have assumed 

 1 per cent as the hmit of error in the tracings. 



The various factors in the process of tracing should be tested. Thus 

 ten measurements of amphtudes for the same curve traced on certain 

 glazed and unglazed papers showed a difference of 0.016 per cent in 

 favor of the former, or practically zero. The particular kind of glazed 

 paper thus offered no advantage over the particular unglazed paper. A 

 test by comparing a record on hghtly smoked paper with one on heavily 

 smoked paper showed an average decrease in amplitude for 10 waves of 

 0.4 per cent on the heavily smoked paper. The addition of a small piece 

 of wax to the hinge so as to make the glass knob trace a whiter line 

 showed no diminution in amplitude. 



The mounting of the curves on cardboard has to be systematically 

 done. A good method is to draw a line each side of the curve and 

 cut out the narrow strip with scissors. This strip is to be divided into 

 portions as long as the mount which is to be made from it — the longer 

 the strip, the less often a curve is cut. Each portion is numbered on 

 the back before it is cut off; the angle at which the scissors cut the 



