THE SOLDIERLESS TERMITES OF AFRICA 27 



due to drying, ageing, or feeding differences of specimens. Others were eliminated 

 because they cannot be delimited by fixed points but depend upon the angle at 

 which the specimen is held ; others again are those of parts too often missing in all 

 but freshly moulted specimens. The absence of the soldier reduced the numbers 

 further. The input for the imago caste finally consisted of 25 measurements, and 

 for the worker, 13. Some of these are listed in the previous section. The remainder 

 were as follows: Imago: greatest diameter of compound eye, pronotum width, 

 pronotum length, hind tibia length, width of postclypeus, length of antennal articles 

 I, II, V and IX; Worker: pronotum width, length of hind tibia, and postclypeus 

 width. 



These measurements were recorded by means of an I.B.M. Port-a-punch on 40 

 alternate columns of special partially pre-punched 80 column-type cards, as micro- 

 scope eyepiece graticule divisions. In this form they are already acceptable to some 

 computer installations, but it was also easy to reproduce the data in the first 40 

 columns of standard cards by machine, and considerable savings of time in handling 

 and preparation of input for computer processing resulted. Conversion to milli- 

 metre values, summarization of the data and calculation of complex ratios, as well 

 as the more sophisticated techniques, were all able to proceed without the need 

 for further transcription. 



The measurements of the imago castes were subjected to two principal component 

 analyses. The first used the raw data, and the second its logarithmic transformation. 

 The purpose of the latter was partly to avoid any bias in the weighting of the charac- 

 ters arising from fairly large size differences among them (e.g. antennal articles 

 or mandible measurements were often less than one-tenth head width or tibia length). 

 In addition, it was desired to test the idea that the pattern of variation might be 

 at least as well expressed by ratios as by linear functions of the variables. The 

 weighting coefficients of the second analysis were almost identical with the first, 

 suggesting that there was little likelihood of biased weightings arising from size 

 differences. It also indicated the validity of interpreting the relationship between 

 characters by complex ratios. This was particularly useful in the derivation of a 

 set of taxonomic indices, since a positive character weighting could be interpreted 

 by a multiplication and a negative weighting by division. The larger weighting 

 coefficients of any vector tended to be rather similar in size. Because eigenvectors 

 are scaled arbitrarily, it is the relative size of the elements that is important. There- 

 fore in calculating taxonomic indices for practical use in keys, it was a sufficient 

 rough approximation to use the raw measurements without the additional com- 

 plication of weighting coefficients. 



Since the two analyses cf the imago were so nearly identical only the raw measure- 

 ments were used for a principal component analysis of the worker caste. One 

 further analysis of this type was undertaken in which the measurements of a single 

 female imago and one worker from each nest-series were combined as representing 

 a set of attributes of the colony. It was necessary to confine the choice of imago 

 to one sex because there is a slight tendency for males to be smaller than females, 

 and to mix them would have obscured the relationship between the variables. 

 The purpose of this last analysis was to see whether it gave any clearer indication 



