To illustrate this point by a hypothetical example, two species might seem equidistant, serologically, from a third species. Additional testing should indicate if the first two species are equidistant in the same direction (therefore, by implication, close relatives) or in opposite directions (therefore, distant relatives). A single test supplies only two dimensions of a three dimensional arrangement.
It is impossible to interpret and to picture the serological data satisfactorily in two dimensions; therefore, a three-dimensional model (Figs.[ 22],[ 23]) was constructed to summarize the serological relationships of the birds involved. Each of the eleven kinds used consistently throughout the investigation is represented in the model. By use of the percentage values (Table[ 2]), each bird was located in relation to the other birds. Where possible, averages of reciprocal tests (Table[ 3]) were used in determining distances between the elements of the model. In this way seven of the birds were accurately located in relation to each other. Lacking reciprocal tests, the positions of the other birds were determined by the values of single tests (Table[ 4]). Although these birds were placed with less certainty, at least four points of reference were used in locating each species. At least one serological test is represented by each connecting bar in the model. The lengths of the bars connecting any two elements were determined as follows: a percentage value (Table[ 3] and Table[ 4]) representing the degree of serological correspondence between two birds was subtracted from 100 per cent; the remainder was multiplied by a factor of five to increase the size of the model and the product was expressed in millimeters; a bar of proper length connects the two elements involved.
From the model it is observed that, Molothrus and Passer excluded, the birds fall into two distinct groups: one includes Piranga, Richmondena, Spiza, Junco, and Zonotrichia; the other includes Estrilda, Poephila, Carpodacus, and Spinus.
Table 3.—Reciprocal Values Used to Determine Distances Between Elements of the Model; Each Value Represents the Average of Serological Tests Between the Species Involved
 | ||||||||
 |  |  |  |  |  |  | ||
| Estrilda amandava | .. | 92 | .. | 72 | 72 | 59 | .. | |
| Poephila guttata | 92 | .. | 74 | 78 | 78 | .. | .. | |
| Richmondena cardinalis | .. | 74 | .. | 85 | 63 | 77 | 79 | |
| Spiza americana | 72 | 78 | 85 | .. | 77 | 77 | 85 | |
| Spinus tristis | 72 | 78 | 63 | 77 | .. | .. | .. | |
| Junco hyemalis | .. | .. | 77 | 77 | .. | .. | .. | |
| Zonotrichia querula | .. | .. | 79 | 85 | .. | .. | .. | |
Table 4.—Single Values Used to Determine Distances Between Elements of the Model; Each Value Represents a Single Test Between the Species Involved
| ||||||||
| |  | | | | | ||
| Passer domesticus | .. | 74 | 73 | .. | 72 | .. | .. | |
| Molothrus ater | .. | 54 | .. | 65 | .. | 69 | 75 | |
| Piranga rubra | .. | 77 | .. | 91 | 73 | 74 | .. | |
| Carpodacus purpureus | 70 | 71 | .. | 61 | 93 | .. | .. | |