12 THE CALIFORNIA SPECIES OF MEALY BUGS 



segments, differences which are somewhat difficult to express. Attempts 

 to present these differences in a tangible way have led to the introduction 

 of the familiar "antennal formulae" and the more recent "antennal 

 graphs." The weakness of the antennal formulae is now fully realized 

 and they are at present but little used, yet their pernicious effects remain, 

 for few, if any, of the species established largely upon them have ever 

 been redescribed and many of these must stand in our literature as doubt- 

 fully recognizable, or even not recognizable at all, until their types have 

 been re-examined. I cannot but consider the original introduction of 

 these antennal formulae as the most unfortunate mistake that has been 

 made in the study of the Coccidae. 



The antennal graphs have been but recently introduced and have 

 not received any extensive trial. It will therefore be desirable to consider 

 them at some length. It may be said in their favor that if the antennae 

 are at all to be used as specific criteria no better method than this can 

 be devised by which to present the facts. The weakness of the method 

 will be in large part due to the unsatisfactory character of the material 

 with which it must deal. It can at the best do nothing more than transfer 

 difficulties from the slide to the paper before us where they may perhaps 

 be analyzed. 



The method of constructing these graphs is quite simple. The actual 

 measurements of the individual segments are obtained by the use of an 

 ocular micrometer. Then upon a sheet of co-ordinate paper certain units 

 are laid out along one axis to represent the individual segments and upon 

 the other axis are plotted the lengths. Connecting up the points thus 

 obtained we have a graph which will give a very clear indication of the 

 relative and actual lengths of the segments. Plotting the graphs of sev- 

 eral antennae will indicate the range of variation. The method of con- 

 structing these graphs has been discussed at length by Brain (2) and 

 Hollinger (6) and for the purpose of this paper a combination of the 

 methods used by both of these authors has been employed. 



In order that these graphs may be of value for taxonomic purposes 

 it must be shown that the graphs of different species are sufficiently dif- 

 ferent and sufficiently constant to permit of differentiation between the 

 species. Brain and Hollinger have considered that this condition is met, 

 the former having relied very heavily upon these graphs and the latter 

 having stated that with him the graphs "formed the working basis" for 

 specific indentification. 



I may say without reserve that I consider these graphs to be fully 

 as illusory and fully as dangerous as were the now wholly discredited 

 antennal formulae. 



The objections to these graphs are both general and specific. 



