VOLUMETRIC CHANGES IN EGG OF BROOK LAMPREY, 97 



fertilized and after about ten minutes they were outlined again 

 in a similar manner through the planes of their diameters. 

 The drawings thus obtained were then measured by means of a 

 planimeter which recorded the area in square centimeters. 

 From these areas and the long diameters in the case of the 

 unfertilized eggs, and the areas and the diameters in case of 

 the fertilized eggs, the volumes were calculated according to 

 formulas as follows: The volume of an ellipsoid of revolution is 

 equal to the constant .8488 times the square of the area of the 

 plane of its major axis divided by the major axis; and the volume 

 of a sphere is equal to the constant .8488 times the square of 

 the area of its great circle divided by the diameter. 1 Formulas 

 involving the use of planimeter areas and diameters were used 

 because they seemed to introduce the least number of factors 

 and thus eliminate chances of error. Since the same factors 

 were used in each case the errors ought to average up about the 

 same for both sets of drawings. 



The volumes of 48 eggs at 'a magnification of 80 diameters 

 were thus ascertained before and after fertilization. The volumes 

 thus obtained were divided by the cube of 80 in order to get the 

 actual volumes of the eggs. This gave as a result an average 

 volume of .6017 cubic millimeter for the unfertilized eggs and an 

 average volume of .5205 cubic millimeter for the fertilized eggs. 

 This shows that the average decrease in size is .0812 cubic milli- 

 meter or 13.48 per cent, of the original volume. 2 



The above results are so striking that they have seemed worth 

 recording at this time. Analogous conditions have been found 

 by O. C. Glaser 3 in the egg of Asterias forbesii. Here the egg 



1 1 am indebted to Professor Theodore R. Running for suggesting the use of 

 these formulas. 



2 Professor Reighard has called my attention to the fact that since the unfer- 

 tilized eggs are heavier than the water in which they are kept and rest on a plane 

 surface, they may be slightly flattened by gravity. The fertilized eggs, on the other 

 hand, which are immersed in a perivitelline fluid of greater density than water 

 and rest on the curved vitelline membrane, are less likely to be flattened by gravity. 

 For these reasons my measurements for the unfertilized eggs might be larger than 

 those for the fertilized. I have examined unfertilized eggs that have been fixed in 

 various fixing solutions but have found no evidence of flattening in these. There 

 is no fresh material available at present. Since the eggs are small and were kept 

 in water when they were outlined it does not seem probable that they would 

 flatten to any appreciable extent. 



3 Glaser, O. C., Science, N.S., Vol. 38, 1913. 



