lines in fi(^re 1. First in importance is the time duration of a stage 

 of development which occupies several hours, whereas a sample may be col- 

 lected during any part of the stage. Consequently, the estimate of age 

 of any given specimen would err, on the average, by a quarter of the time 

 occupied by the stage in the egg's development - a matter of three hours 

 at most. Second, there is the period of time over v;-hich spawning is spread 

 (chiefly 8:00 p.m. to midnight), which is represonted in our calculations 

 by the midpoint of this time (10 {00 p.m.). This might result in an error 

 of as much as tviro hours in a few instances. Third, not all egfjs develop 

 at the same rate even under identical conditions, although the variability 

 resulting from this cause is probably slight. Fourth, there is a possi- 

 bility of an error in the day of spavming to which a stage is referred; 

 however, an error involving tvrenty-four hours time should result in a more 

 narked discrepancy than any that have been observed. The temperature 

 data used would also contribute to the variability fn so far as it dif- 

 fxired from the actual temperature under \/hich the majority of eggs wore 

 developing at a station. This could result (1) From the concentration 

 of eggs occurring outside the 10- to 20-mcter zone in waters of different 

 temperatures than those occurring in this stratum, and (2) from the tem- 

 perature data not reflecting the mean temperature for the period of de- 

 velopment, as v^ould result if the temperature of the water changed ma- 

 terially during the period from such causes as the stirring action of 

 strong' winds^/ or upvrelling. 



However, the variability was not sufficient to destroy cither the 

 correlation^ or the consistency in slope of the regression for the four 

 stages. 



Since the Arrenhius equation Has been used by previous investigators 

 studying development of fish eggs under constant temperature conditions, 

 it is- of some interest to analyze the present data using this formula 

 for the sake of comparison. In doing this the logarithm of rate of de- 

 velopment (log l/t) is plotted agaihst the reciprocal of the absolute 

 temperature (1/T° abs.). ^ii"hon this is done for each recoird of each of 

 the foui^ stages of development previously analyzed, and a line fitted 

 to the s<:atter of points for each stage by the method of least squares, 

 as is shovm in figure 2, the four fitted lines are, of course, still 

 nearly narallcl, and are closely comparable to the lines derived in fig- 

 ure 1,1/ 



2.' The temperature would be Icn/ered if deeper, colder v/ater was mixed 

 with the upper I^^ers through wind action; contrariwise, the tempera- 

 ture could be raised somev;hat by a mixing of warmer^ surface water 

 with the waters of the 10-20 m. stratum by 'vj'ind action that left 

 depths belov/ this undisturbed. 



7/ 



Both methods are Included in the paper since, for our purposes, the 

 correlation shorm in figure 1 is more usable, v^hile the Arrenhius 

 formulation is needed for comparison of the pilchard with other fishes. 

 The Arrenhius method uses the reciprocals of the values employed in 

 the first method with the exception that the tomporaturo is expressed 

 && absolute temperature.' 



144 



