PHYSICS: A. G. V/EBSTER 
173 
the line joining the loci is perpendicular to the average direction of crossover 
planes. The crossover value for lines in any other directions would seem to 
be proportional to their projections on such a perpendicular. In short, both 
of Castle's alternative subsidiary hypotheses to account for the rarity of 
double crossovers are inconsistent with his primary assumption that distances 
are proportional to crossover values. 
1 These Proceedings, 5, 1919, (25). 
2 Abnormal is a character that is separable from wild-type only under certain environ- 
mental conditions; and is also simulated by accidental abnormalities. It is, therefore, not a 
reliable character to use in linkage experiments. 
^ Carnegie Inst., Washington, Pub., No. 237, 1916. 
^ Sturtevant, these Proceedings, 3, 1917, (555), and Muller, Amer. Naturalist, .0, 1916, 
(193, 284, 350, 421). 
B Bridges, /. Exp. ZooL, 19, 1915, (1), and Plough, Ibid., 24, 1917, (147). 
® Bridges and Sturtevant, Bio'. Bull., 26, 1914, (205), and Morgan and Bridges, loc. cit., 
note 3. 
That Castle tacitly recognized this is shown by the fact that he omitted lethal 2 from 
his model, without even mentioning the fact. It is obvious from an examination of the 
data in this case that the crossover values are inconsistent with those obtained in other 
experiments not involving lethal 2. 
^ Provided the relations of the loci are to be represented by straight lines joining them 
and proportional in length to the corresponding crossover values. 
' It does not follow that 4.7 is to be taken as the locus of bifid, for the mean value indi- 
cated by all bifid experiments is the one most likely to coincide with future experiments; 
i.e., to give the best predictions. 
Castle concluded that the white forked value of 45.7, used by him, is somewhat too high, 
which is true; but there were available to him more than 40,000 flies (Bridges, Genetics, 1, 
1916, (1), and Weinstein, Ibid., 3, 1918, (135) ) giving the lower value, in contrast to the 
less than 4000 flies on which the high value was based. 
A COMPLETE APPARATUS FOR ABSOLUTE ACOUSTICAL 
MEASUREMENTS 
By Arthur Gordon Webster 
Clark University, Worcester, Mass. 
Read before the Academy, November 17, 1915 
The apparatus here briefly described is the result of researches begun many 
years ago in the attempt to solve the problem of measuring the intensity of 
sound at any given point of space in terms of absolute units, by means of in- 
struments that may be reproduced from specifications, and that shall be con- 
venient and portable. For this purpose three things are requisite; first, a 
source of sound that shall continuously produce a simple tone of known in- 
tensity — this will be denoted by the term 'phone;' second, an instrument for 
measuring in absolute units a constantly maintained simple tone, here called 
