TABLE 1.-DISTANCE BETWEEN THE FIRST MOLARS. (A.)

TABLE 3.-LENGTH FROM ALVEOLAR POINT TO A LINE CONNECTING THE FIRST MOLARS. (C.)

TABLE 4.-DISTANCE BETWEEN the CanineS. (D.)

The standard deviation is significant of the amount of variability, and it can be seen from the above table that this variability is considerably higher in the abnormal palate than in the normal. This is to be expected if our contention is true-that the size of the palate (as will be brought out later) correlates with the shape and size of the head. The abnormal palate varies more than the normal because the shape and size of the head vary more in abnormal than in normal individuals.

When the averages of the abnormal and the normal palate are compared for the various measurements, it becomes evident that a true difference exists only in the case of the height of the palate. (See Table 6.)

TABLE 6.-TABLE OF DIFFERENCES.

DIFFERENCES BETWEEN THE AVERAGES OF THE ABNORMAL AND NORMAL, FOR THE FOUR MEASUREMENTS TAKEN.*

'P.D. Probable Difference. If the difference between the two averages to be compared is greater than the P. D., then the probabilities are high that the difference is a real one. It is evident from the table that the probabilities of a real difference are greatest in the case of the height of the palate (measurement B).