## Abstract

It will be seen at once that the mean values obtained for calcium are higher than most of those recorded in the literature, and that the values for inorganic phosphorus are perhaps lower. It is well to bear in mind, however, that the significance that may be attached to any series of determinations of calcium and inorganic phosphorus in the blood of animals depends largely upon the conditions under which the determinations are made. As is well known, there are many factors that may affect the values obtained, including inherent differences in the animal material and the method of analysis used as well as the particular procedure employed in carrying out a given method. When all other conditions are uniform, irregularities in the handling of the blood after it is drawn will give rise to surprisingly large differences in the results for both calcium and inorganic phosphorus, as permitting blood to stand tends to decrease calcium values and to increase those for inorganic phosphorus.

It seems desirable, therefore, to emphasize the fact that the results recorded above are to be viewed as results obtained under certain definitely prescribed conditions which differ in several important respects from those governing determinations made by other workers in this field. Moreover, it is to be noted that the conditions varied to some extent with each of the 4 groups of animals comprising this series. For example, there was a small but definite age difference. The animals of Groups I and II were older and more mature than those of Groups III and IV at the beginning of the experiments, and this initial difference was increased by the extension of the experiments on Groups I and II over a longer period of time, so that the observations made on these animals not only included data for a more advanced age, but represented a mean age considerably above that of the observations made on the animals of Groups III and IV. There was a similar difference of experimental conditions between Groups III and IV, while the observations on Group II differed from those on Group I in that no blood analyses were made on the animals of Group II for 2 months after they were placed under observation.

These particular features of the experiments are mentioned because an examination of the text-figures will show that a line of cleavage between Groups I and II on the one hand, and III and IV on the other, is traceable through all of the distribution curves and to some extent in the tabulated results. With the combined values as the axis of distribution, Groups I and II invariably hang together, or swing to one side, while Groups III and IV swing to the other. Moreover, the extreme positions are usually represented by Groups II and IV.

Whether these peculiarities of the results are in reality attributable to the conditions mentioned or to some other cause, such as the length of cage life (2), or the particular period covered by the observations, the suggested relation is sufficient to indicate the extent to which even slight differences in experimental conditions may affect the results obtained for blood calcium and inorganic phosphorus.

The values obtained for calcium may be regarded as showing a fairly close agreement (Tables I and II and Text-fig. 1). The extreme difference between the means for the 4 groups of animals is only 0.5 mg. or approximately 3.00 per cent of the mean for the combined groups. Still, the small absolute difference between the means for Groups I and IV is nearly 6 times its probable error and, hence, cannot be disregarded.

The most important feature of these results is, however, the range of normal variation. The distribution curves (Text-fig. 1) show a remarkably close agreement in the frequency with which values of a given magnitude occurred and an unusually symmetrical distribution of all values. The coefficients of variation are comparatively small (7.09 to 8.9 per cent), but values anywhere between 14.0 and 16.0 mg. of calcium per 100 cc. of serum occurred with great frequency, while figures as low as 13.5 or as high as 17.5 mg. (Table II) were by no means rare; and the extreme limits of observation indicate a potential difference in the calcium content of the blood of normal rabbits of as much as 100 per cent.

Inorganic phosphorus was found to be subject to much wider variation than calcium (Tables III and IV and Text-fig. 2). The coefficient of variation is approximately twice that for calcium (17.29 and 8.01 respectively), while the group means for phosphorus show a difference of 0.85 mg. per 100 cc. of serum. This difference is small in absolute value, but is nearly 20.0 per cent of the mean for all groups and is 15 times its probable error. It is safe to assume, therefore, that the values obtained indicate an actual difference in the inorganic phosphorus in the blood of the several groups of animals.

This conclusion is borne out by the distribution frequencies (Table IV and Text-fig. 2) which show that the values obtained for Groups I and II lie at a distinctly lower level than those for Groups III and IV; the difference between modal classes is, in fact, of the same order as that shown by the means.

The limits of probable variation as determined by the standard deviation of the combined results are 3.73 and 5.29 mg. per 100 cc. of serum, but one-third of all values lie outside of these limits, while the extreme limits of normal are sufficiently wide to include values that may differ by as much as 200.0 or even 300.0 per cent.

From the values obtained for calcium and inorganic phosphorus, the relation existing between the two substances may be measured in a number of ways. The ratio of the calcium to the phosphorus and the product of the amounts of the two substances have received the greatest attention. In addition to these values, we have computed values for the sum and for the ratio of the product to the sum, and also for the sum of the calcium-phophorus ratio and the product-sum ratio.

The value for the sum of the calcium and inorganic phosphorus in the serum is determined largely by the calcium, but as it is also affected by the phosphorus, one might expect that the constancy of the value as compared with that of calcium would be diminished unless the variations in the two substances were so related as to neutralize each other. As is well known, there is an apparent tendency in this direction and in these experiments it was found that on the whole the values for the sum showed less variation (coefficients 6.42 and 8.01 per cent) and were more uniformly distributed than those for calcium (Tables V and VI and Text-fig. 3). It is true that differences between groups were distinctly greater than in the case of calcium, but the agreement is sufficiently close to give evidence of a tendency to the maintenance of an inverse relation between serum calcium and inorganic phosphorus.

Values for the product of calcium and inorganic phosphorus emphasize the phosphorus factor rather than the calcium, reversing the conditions that obtain in the case of the sum. A consideration of the product values given in Tables VII and VIII and Text-fig. 4 show that, while the order of variation is essentially the same as that of inorganic phosphorus (coefficients 17.09 and 17.29 per cent respectively), the distribution of values is more uniform. This may be attributable to the occurrence of coordinate variations in calcium and inorganic phosphorus.

The situation presented by the values obtained for the ratio of calcium to inorganic phosphorus is somewhat surprising in that the ratio between the two substances proves to be less constant than the absolute amounts of either substance (Tables IX and X and Text-fig. 5). There are considerable differences between the standard values for individual groups of animals, and the distribution frequencies are inclined to be irregular. Moreover, all groups show a large standard deviation and correspondingly high coefficients of variation, but combining the results for the 4 groups of animals gives a fairly uniform and symmetrical distribution, a striking feature of which is the high frequency with which values occur over the entire range of standard variation, that is, from ratios of 2.85 to 4.29.

It thus appears that, despite the evidence of a tendency to the observance of an inverse relation between the calcium and inorganic phosphorus in the blood, the ratio of one substance to the other is by no means constant.

By using the product and the sum as a basis of expressing the relation between calcium and inorganic phosphorus, the form of the relation is ???

## Footnotes

- Submitted: 25 January 1928