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TABLE 4.

peratures of

Temperatures of

Number

Number

of ex. periments.

of ex

Air.

Air.

Head.

periments.

6:1111°C.

14.1666°C. 13:3333°C.

10 5

5.5555°C.

10

5

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12.4444°C.

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5:0000°C.

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12.2222°C. 11:1111°C.

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4:5000°C.

10:0000°C.

10 5

94444°C.

4.0000°C.

33.90°C. 33:30°C. 34:30°C. 33:90°C. 33.80°C. 33.70°C. 34:00°C. 33.90°C. 32:80°C. 32:55°C. 34.20°C. 34:10°C. 33.95°C, 33.85°C. 33.75°C. 32.60°C. 34:30°C. 34:00°C. 33.95°C. 32-55°C. 33.95°C. 33.80°C. 33 55°C. 32:55°C. 32 50°C. 34.00°C. 33.85°C. 33.70°C. 33:50°C. 32:90°C. 32:50°C. 33.95°C. 33.80°C. 32:50°C. 32.45°C.

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8.8888°C.

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10 5

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2 5555°C.

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7.7727°C.

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2.00'00°C.

Head.

35-55°C. 35.90°C. 35.75°C. 35.60°C. 35:15°C. 36:10°C. 35.80°C. 35.90°C. 35.75°C. 35.45°C. 35.40°C. 35.40°C. 35.20°C. 35.00°C. 34.65°C. 35.50°C. 34:70°C. 34:40°C. 34:30°C. 35.80°C. 35-20°C. 35.05°C. 34.90°C. 33.95°C. 33:53°C. 33.10°C. 34.90°C. 34:60°C. 34:30°C. 34:10°C. 34:55°C. 34:40°C. 34:20°C. 34:05°C. 34:40°C. 34:00°C.

10 5

10 5

6111°c.

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ANALYSIS OF TABLES 1, 2, 3, AND 4.

A.

Highest temperatures

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of air.

TABLE 1

.21•1111°C.

.17.2222°C.

לל

14.1666°C.

14.1666°C.

22

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Commencing with the division "a" of the analysis, we find that, in each table, the highest temperature of the air is associated with a higher temperature of the head-average, maximum, and minimum temperatures all included—than the lowest temperature of the air. Thus in Table 1, the temperature of the head for the highest temperature of the air is, on

an average, 0.3667° C. above the sponding value, associated with the lowest temperature of the air. The degrees of superiority of the temperature of the head at the higher of the two temperatures of the air, in each table, are as follows :

corre.

Degrees of superiority of temperature of the head at the higher of the two temperatures of the air given in the analysis.

Table 1. Table 2. Table 3. Table 4. Maximum-0.5000°C...1.1000°C...1.0000°C...1.6000°C.

Average-0.3667°C... ... 1.2643°C...2:2500°C. Minimum-0•3000°C...

...1:5000°C...3:1000°C.

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Moreover, if the tables are compared with each other, there appears, at first sight, to be a certain rough relation between the degree of difference of the two atmospheric temperatures and the degree of difference of the corresponding two temperatures of the head; thus in Table 1, for a difference of 4:4445° C. in the air, we have an average difference in the head of 0.3667° C. ; while in Table 2, for a difference in the air of 6.6667° C., there is an average difference in the head of 1.1° C.; and in Table 4, the difference in the air being now 12.1666° C., we have a difference in the head of 2•25° C.

In proof, however, that the above relation is by no means a close one, if we take the difference between the two temperatures of the air, and the difference between the two average temperatures of the head, in Table 1, each as equal to 1, we have the following proportional values for the corresponding differences in the other tables.

Table 1. Table 2. Table 3. Table 4. Proportional differences in tempe

ratures of air................ 1.000°C......1:50°C. ......1.437°C......2:737°C. Proportional differences in temperatures of head

1.000°C......3.000°C.... ...3.447°C......6•108°C,

Thus in Table 2, for a difference between the two atmospheric temperatures 1.5 times greater than the similar difference in Table 1, we have a difference between the two average temperatures of the head three times greater than the corresponding difference in Table 1; while in Table 4, for an atmospheric difference 2:737 times greater than that of Table 1, we find a difference of average temperature in the head 6·108 times greater than the corresponding difference in Table 1. The rate of change of average temperature in the head for each degree Centigrade of difference of temperature in the air, between the highest and lowest thermal levels of the latter, in each table, is as follows:

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Comparing, still further, with each other, the results of the analysis of the different tables in division “a," we see that although the highest and lowest temperatures of the head there given (average, maximum, and minimum all included) are associated respectively with the highest and lowest atmospheric temperatures, yet beyond this accordance discrepancies exist. Thus Table 2 with a temperature of the air of 17.2222° C. shows a temperature of the head of 35-40° C.; while in Table 1, with a temperature of the air of 16.6666° C, we have an average temperature of the head of 35.6333° C., with a maximum of 35.8° C., and a minimum of 35.5° C. Again, Tables 3 and 4, with a temperature of the air of 14:1666° C. give a temperature of the head of 35.55° C., Table 2-as we have just seen-giving a temperature of the head of 35.40 for an atmospheric temperature of 17.2222° C. The question with which we are dealing is still further elucidated by the results of division “b” of the analysis. We find here that the lowest individual temperature of the head is associated with the lowest individual temperature of the air, but that the highest individual temperature of the head occurs not with the highest, but with the second highest individual temperature of the air, namely, 20.8333° C. In like manner, in Tables 2 and 3, in which the highest temperature of the head noted is 35.90° C., this value coexists, in the first instance, with a temperature of the air of 13.8888° C., and in the second instance with a temperature of the air averaging 12.7777° C.-the maximum and minimum being, respectively, 13.3333° C., and 12.2222° C.-while the highest temperatures of the air noted in these two tables are, as we have seen, 17.2222° C., and 14:1666° C., respectively. Also Table 4, in which the highest temperature of the air is 14:1666° C., shows the highest temperature of the head coexisting with a temperature of the air of 12:4444° C. In Table 1, the lowest temperature of the head is found with an atmospheric temperature of 17.5° C., the lowest temperature of the air being 16.6666° C. Again, in Tables 2 and 3, the lowest temperatures of the head are associated with temperatures of the air of 11:1111° C., and 8.8888° C., respectively, while the lowest temperatures of the air in these tables are, respectively, 10-5555° C., and 7.7777° C.

Table 5 gives the average, maximum, and minimum temperatures of the head, associated with each of the thirty-nine temperatures of the air, at which observations have been made-- all four of the preceding tables being included in the estimates. The fifth column of the table gives the proportional values of the averages of the temperatures of the head, taking the lowest average, 33:3° C. as equal to 1000.

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