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MATHEMATICS: A. EMCH 
teen minutes. . Similar studies made at the end of the exposure to environ- 
mental temperatures varying from 14° to 30°C. show a distinct tendency to- 
wards a flattening out of the curves at the higher temperatures. Thus when 
the thermal junction was passed down the front and back of the body over 
exactly the same lines and at the end of two and one-half hours' exposure, the 
difference between the highest and lowest points in the curves was 10.6°C. 
with an environmental temperature of 14.6°C.; 9.8°C. with a temperature of 
19°C.; 5.4°C. with a temperature of 25.8°C.; and4.2°C. with a temperature of 
30°C. 
This study of the temperature of the skin has two important bearings upon 
all investigations on the heat production of the human body. First, in all re- 
searches on direct calorimetry it has been necessary to corrct the heat actually 
measured by the calorimeter for the heat gained or lost from the body as the 
result of changes in temperature. Heretofore it has been assumed that as 
temperature curves measured either deep in the body trunk or in the artificial 
cavities are similar, a change of 0.1° in rectal temperature indicates a change 
of 0.1° in the temperature of the entire body. Our observations, particularly 
with cold temperature environments, show skin temperatures falling several 
degrees even when interior body-trunk temperatures may be simultaneously 
rising slightly. The correction of direct heat measurements by records of the 
rectal temperature is thus open to grave criticism. Unfortunately no sub- 
stitute correction can as yet be offered. Secondly, these pronounced differences 
in skin temperature have great significance in any consideration of the so- 
called 'law of surface area.' It is still maintained by many physiologists that, 
practically independent of species, the heat production of the quiet organism is 
determined by its surface area. Our observations show clearly that, contrary 
to popular impression, the temperature of the skin, presumably one of the 
most important factors affecting heat loss, is very far from uniform for we have 
seen that even with well-clothed individuals differences in the temperature of 
various localities of 4° to 5°C. are of regular occurrence. These observations 
bring to light and establish one more serious objection to the legality of the 
conceptions underlying the 'body-surface law.' 
ON A CERTAIN CLASS OF RATIONAL RULED SURFACES 
By Arnold Emch 
Department of Mathematics: University of Illinois 
Communicated by R. S. Woodward, May 19, 1919 
As is well known, ruled surfaces, or scrolls as Cayley calls them, may be 
generated or defined in a number of ways. There exists, for example, a one- 
to-one correspondence between ruled surfaces and a certain class of partial 
differential equations, so that the theories of the two classes are abstractly 
identical. 
