584 



SCIENCE 



[N. S. Vol. XXXIX. No. 1007 



population should show the character of length 

 4. The column of volumes, however, shows 

 that there is only one out of the 64 with a 

 volume 4^. All others with factors for length 

 four have larger volumes, because their factors 

 for breadth and thickness are greater than 

 four. ■ Here again the law of the golden mean 

 is followed as all combinations bearing unequal 

 size factors are forced to build cubes by the 

 modifying factor shape. Evidently all mat- 

 ings resulting in equal volumes will make 

 equal cubes and therefore show equal char- 

 acters of length, breadth and thickness, though 

 not necessarily possessing equal size factors 

 nor even the factor for the size which they 

 exhibit. If we group the results by volume 

 and length of side, we have: 



Volume Instances 



64 

 96 



144 

 216 

 324 



486 

 729 



Side_of Cube 

 1^64 =4. 

 lf96 =4.57—. 

 #'144 = 5.25+. 

 #'216 = 6. 

 #'324 = 6.87+. 

 #'486 = 7.86—. 

 #'729 = 9. 



That means that the chance for a parental 

 size (whether line or surface or volume) to 

 reappear is only 1 : 64 instead of 1:4. More- 

 over it is clear that each of the 8 possible 

 combinations given on page 7, when mating 

 with its like, will breed true to all three size 

 characters, and continue to breed true there- 

 after if self ed. That means that these matings 

 will form constant races, viz. : 



Mating 

 1X1 

 2X2 

 3X3 

 4X4 

 5X5 

 6X6 

 7X7 

 8X8 



Resultant 

 4X4X4 

 4X4X9 

 4X9X4 

 9X4X4 

 9X9X4 

 9X4X9 

 4X9X9 

 9X9X9 



Volume Size 



64 

 144 



144 

 144 

 324 

 324 

 324 

 729 



4 



5.25 



5.25 



5.25 



6.87") 



6.87 [ 



6.87 3 



Besides the parent-like strains then, we shall 

 seemingly have two other races, one of volume 

 144, size 5.25, the other of volume 324, size 

 6.87, which will continue to breed true if 



selfed. Each of these strains consists of three 

 gametically difEerent, though visibly indis- 

 tinguishable lines, which when crossed will 

 give an F^ equal to both parents, but segre- 

 gating to some extent in the F„. The finding 

 in the F, or later generations of lines which 

 breed true to size characters is thus not proof 

 of the presence of multiple size factors in the 

 original parents, etc. 



In the bulletin in preparation I intend to 

 discuss the bearing of the law of the golden 

 mean upon the interpretation of inheritance 

 of shape and number, mutants, latent factors, 

 inhibitory factors, coupling and repulsion, 

 factors other than those of size, shape, and 

 number, and other points as they may come 

 up, but for the sake of science I invite inves- 

 tigation into these relationships on the basis 

 I here offer, even before I am able to publish 

 the bulletin, which may not appear for several 

 months. 



B. H. A. Groth 



" THE LOWEST TEMPERATURE OBTAINABLE WITH 

 ICE AND SALT " 



Fahrenheit placed the 0° mark on his arbi- 

 trary thermometer scale at " the lowest tem- 

 perature obtainable with ice and salt " or 32° 

 below the freezing point of water, believing 

 that water did not have a constant freezing 

 point because of the undercooling which pre- 

 cedes solidification.^ 



While discussing freezing mixtures with a 

 friend recently I stated that a temperature of 

 — 19° C. could be easily obtained and main- 

 tained for some hours with an ice and salt 

 mixture. My friend questioned the accuracy 

 of the thermometer inasmuch as — 19° 0. is 

 below 0° F. (0° F. = — 17.78° C). I have, 

 therefore made a careful test to ascertain 

 whether an ice and salt mixture may not show 

 a lower temperature than 0° F. 



AbcMt a gallon of finely chopped, hard, ice 

 was mixed with a quart or more of coarse salt 

 in a water-tight wooden box, the wooden box 

 being used because of the insulation which it 



1 See Encyclopedia Britaniiica, 11 ed., "Heat," 

 article 2. 



