132 HANDBOOK OF ACOUSTICS. 

sounded, we proceed as before. For example, let the two generators be jS. The relative rates of vibration being J J , the relative vibration rate of the differential of the first order = 5 — 4 = 1. Subtracting this from the generators 5 and 4 we obtain the relative vibration rates of the differentials of the second order viz. 5 — 1 = 4 and 4 — 1 = 3, this latter only being a new tone. Again, subtracting this 3 from the higher generator, we get another new tone 5 — 3 = 2, a differential of the third order. Thus, omitting duplicate tones we have—
generators f J ~ _{4}
Differential of 1st order, d = 1 (= 5 — 4) 2nd „ s = 3 (= 4  1) 3rd „ d =2 (=53) The 2nd, 3rd, 4th, and 5th columns of the following table show the differentials of the 1st, 2nd, 3rd, and 4th order which may be produced by the tones in the 1st column. 





•Nearly. 
