July 7, 1916] 



SCIENCE 



35 



vertical distance from line 10 to the level of 

 each integer. These ordinates are given in 

 Table II. below. 



Another element of distortion, though very 

 slight, was found in the assumption of equal 

 spacing for the horizontal intervals between 

 successive points in the plot. The spaces 

 ought to vary somewhat according to the levels 

 of pitch. It was, however, some time before 

 it became clear that the single measurement 

 determined the position of the point on both 

 coordinates — on the vertical one as pitch, and 

 on the horizontal one as time-elapsed between 

 successive wave-crests in the record. 



So amended, the scheme seems perfect. 

 Nevertheless a suggestion or two may save 

 much time and trouble to one who may have 

 occasion to use it. 



It is neither necessary nor desirable to meas- 

 ure separately every wave-length of the record. 

 It is quite as well to measure them in groups 

 of five together and take the average for plot- 

 ting, if only one measure separately the very 

 first wave and the last, so as to make sure of 

 the pitch at those points. Similarly the in- 

 tervals for the horizontal spacing need not be 

 the very ones indicated by the measured num- 

 bers, but rather some constant fraction of 

 them, such as will better bring out the fea- 

 tures of the curve. 



All the numbers concerned in the scheme are 

 merely ratios setting forth the relationships 

 between the various elements of it within the 

 compass of two octaves of pitch, which is quite 

 sufficient to cover, the range of any voice in 

 ordinary speech. The scheme may therefore 

 be used just as it stands if the measurements 

 do not exceed its limits. If they do, the whole 

 system may be raised an octave by the simple 

 device of dividing the integral numbers 

 throughout by 2, or lowered an octave by 

 multiplying them by 2. Or it may be raised a 

 fourth by multiplying them by 0.7, or lowered 

 a fourth by multiplying them by 1.5 — taking 

 pains however in these last cases to shift the 

 semitone letters correspondingly. 



Since the semitone intervals are all equal, 

 the C which represents concert pitch may be 

 placed anywhere in the field where its meas- 



ured wave-length indicates. All the other 

 semitone letters then will take their places at 

 the same constant distances as in the scheme 

 described. 



TABLE I 



Matios of the Tempered Scale 



C 10 



B 10.60 



A* 11.23 



A 11.89 



Gf 12.60 



G ...' 13.35 



FJ 14.14 



F 14.98 



E 15.87 



Djf 16.81 



D 17.81 



C£ 18.87 



C 20 



TABLE II 



Ordinates of the Number Series 



Cornelius Beach Bradley 

 University of California 



SOCIETIES AND ACADEMIES 

 THE BIOLOGICAL SOCIETY OF WASHINGTON 



The 557th regular meeting of the society was 

 held in the Assembly Hall of the Cosmos Club, 

 Saturday, May 20, 1916, called to order by Presi- 

 dent Hay at 8 p.m., with 30 persons present. 



On recommendation of the council, James L. 

 Peters was elected to active membership. 



The president announced that the council of the 

 society had voted to adopt the custom of medical 

 societies and of many other scientific societies lim- 

 iting the members to speak but once during the 



