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In the second subdivision of (A) Tables 2, 3, and 4 agree in giving the highest average to equality; and Tables 2 and 4 further agree in giving the lowest average to the right side; but in Table 1 the right side holds the first place and equality comes last. Coming to the heading (B) we find, in the first subdivision, Tables 1, 3, and 4 agreeing with each other, equality having the first and the left side the last place in all three cases ; but in Table 2 the right side comes first, the left side coming last, as before. In the second subdivision of (B) Tables 1, 3, and 4 also agree, with the same order as above; Table 2 having likewise the same order that it had in the first subdivision. Lastly, under the heading (c) in the first subdivision, Tables 2 and 3 agree, equality holding the first and the left side the last place. Table 4 also gives the first place to equality, but the last to the right side ; while in Table 1 the right side comes first and the left side last. In the second subdivision of this heading the order in the several tables is the same as in the first subdivision.

In the whole twenty-four sets (eight under each heading) equality holds the first place in sixteen, or two thirds ; while in the remaining eight cases the right side comes first in

In seventeen cases the left side shows the lowest average, the right side coming last in four, and equality coming last in three cases.

It would seem, however, that the division of each table into two great parts, according as the temperature is above or below 35° C., and the consequent separate analyses of these two parts under the headings (a) and (B), are less likely to furnish accurate information on the points under consideration than the analysis of the two parts of each table taken together, as under the heading (c).

The reason of this is that, in the analysis of the separate parts, the lower values, in the case of the first part of the table, and the higher values, in the case of the second part of a table, are on debatable ground, not being near either the upper or the lower limits. The absolute values included in the comparisons are, therefore, comprised, in the one instance, between the mean level and the upper limit of temperature, and, in the other instance, between the mean level and the

seven cases.

lower limit of temperature, and not between the two extremes. As a result of this artificial division of the observations, if a given condition-equality, for instance-happen to be of frequent occurrence about the mean level, the conclusions respecting this condition may be contradictory in the two parts of a table. In the first part the condition may show relatively a low, and in the second part relatively a high, average absolute temperature. This is shown, in point of fact, in Table 1, where equality exhibits in the first part the lowest and in the second part the highest average absolute temperature. But if, in consequence of the above objections, we regard only the results of the combined two parts of each table, we still find it impossible to reconcile the contradictions obtained. Tables 2, 3, and 4 give the highest average absolute temperature to equality, but Table 1 gives the precedence to the right side, equality holding the second place. Now, if the differences between the temperature of equality and the temperatures of right superiority in Table 1 were insignificant compared with the similar differences existing in the other tables, where equality holds the first place, we might be tempted to regard it as a rule that the highest average absolute temperatures are associated with equality. Let us see what these differences are. The dif. ferences in Table 1 between the temperature of equality and that of right superiority in the two sets of values in the table are, respectively, 0.11774° C. and 0·03029° C. The dif. ferences between equality and the condition holding the second place in the other three tables are as follows:- Table 2. -0.18681° C. and 0.27266° C.; Table 3.-0.08663° C. and 015207° C.; Table 4.40:12402° C. and 0.19227° C.

The results might, indeed, lead us to ignore as unimportant one of the differences of Table 1, that of 0.03029° C.; but the other difference is too marked to be set aside. Moreover, this latter figure is the more important of the two, as it belongs to the set of values representing the absolute temperature of the side alone on which superiority of temperature exists, whereas the first difference belongs to the set of values which represent the average temperature of both sides taken together in each comparison, and which, therefore, do not fairly represent the extreme height to which the absolute temperature may rise in the case of superiority of temperature on a side.

If, on the other hand, we look to the lowest averages, we find that in three of the tables the left side holds the lowest place, the right side coming last in one table. Applying the same test in this case which was applied above, let us see if the differences of temperature between the values for the right side and those for the left side in Table 4 can be neglected, thus establishing a rule of the coincidence of the lowest average absolute temperature with superiority of temperature on the left side. The differences between the two lowest values in the several tables are as follows :—Table 1. -0.10270° C. and 0.21047° C.; Table 2.-0.09264° C. and 0.13756° C.; Table 3.-0.15926° C. and 0.13991° C.; Table 4. -0.19437° C. and 0.34687° C. Looking at these figures, it is, of course, impossible to ignore the differences shown in Table 4.

We are thus finally forced to choose between concluding that no one of the three conditions of superiority of the right side, superiority of the left side, and equality of the two sides respectively, exhibits a definite and fixed preference for a higher or lower absolute level than the others, or the rejection of some of our tables and the exclusive acceptance of others. There is not, however, the slightest justification of this latter course to be found, for the observations of the several tables were made with the same care and under equally favorable conditions, and are, therefore, equally reliable. And in this connection we see the value of the accidental division into the four tables of the entire mass of observations, due, as it was, simply to the fact of there being four distinct periods of investigation. Moreover, each table contains a sufficient number of observations to preclude its rejection in favour of another on the score of numerical inferiority.

The result, then, of our two principal methods of analysis has been to furnish but a single satisfactory conclusion, the one derived from the first method and already given on page 21, namely, that the percentage of frequency of occurrence of equality of temperature is greater at temperatures at or above 35° C. than at temperatures below that point. If we

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relied solely on Table 4, we might consider it as further proved (in accordance with the theory mentioned at the outset on page 4) that superiority of temperature on the left side is relatively more frequent at the higher than at the lower levels of absolute temperature, while superiority of temperature on the right side is relatively more frequent at the lower than at the higher levels ; but, as just stated, we have no right to adopt the results of one table to the exclusion of those of another.

There are, however, certain points in our tables which have not come within the scope of our two methods, which demand attention.

If we examine the tables near the upper and lower limits, we see that the extent of range is not equal in all the tables. Taking, on the one hand, only those observations in which the higher of the two temperatures is at or above 36° C., and, on the other hand, only those observations in which the higher of the two temperatures is below 34° C., we find at the start that Table 3 is excluded from any examination based upon such limitations, and that Table 1 furnishes but fifteen observations falling within the upper limit. .

Analysing the observations in the several tables included in the limits specified, we obtain the following results :

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(E) Temperatures below 34° 0.
TABLE 1. TABLE 2.

TABLE 4.
Left side.......

15 ...

25.0000 15 25.0000 15 25.0000 Right side

45 75.0000 30 ... 50.0000 45 75.0000 Equality....... 0

0
15 25.0000

0

0
Total... 60
Total... 60

Total... 60

...

In the above sets of results we again encounter contradictions. Part of Table 1 is of doubtful value, owing to the limited number of observations made at the higher temperature. Omitting this part of the table, and regarding only the part under the heading (E), we find a total absence of equality and a decided predominance of right superiority of temperature. If we refer to the same table in the former comparison of percentages on page 21, we see how marked this excess in favour of the right side is. Table 2, however, shows a decided balance in favour of the right side at the higher temperature, the percentages for the left side and for equality being each one third of that for the right side ; while at the lower temperature the percentage for the right side diminishes, and the percentages for the left side and for equality increase. In Table 4, on the contrary, at the higher temperature right superiority shows the smallest percentage, left superiority and equality having here the same percentage, which is more than twice that for the right side; still further, at the lower temperature in this table equality is absent and right superiority is greatly in excess of left superiority.

If we take the individual observations within these last limits, we find that the highest absolute temperature noted, 36°4° C. (Table 4), accompanies equality; the second highest temperature, 36-325° C. (Table 2), accompanies right superiority; and the third highest temperature, 36-3° C. (Table 4), is found with left superiority. The lowest case of superiority of a side, 33.1° C., and which occurs twice, is in favour of the left side (Tables 1 and 2); the second lowest case, 33.25° C. (Table 2), is in favour of the right side ; and the third lowest case, 33.325° C. (Table 1), is also in favour of the right side.

We will now make another and last analysis, embracing, on the one hand, those cases in which the higher of the two temperatures compared is not below 35-5° C., and, on the other hand, those cases in which the higher of the two temperatures compared is not above 34:55° C.

The following are the results obtained by this last analysis :

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