Vol. 6, 1920 
MATHEMATICS: S. D. ZELDIN 
541 
(6) There was no material difference in temperature between a depth 
of 6 inches and one of 7 inches, while there was a distinct difference of 
temperature between a depth of 4 inches and one of 6 inches, thus showing 
the unreliability of measurements of temperature at a depth of less than 
6 inches. 
(7) The standing as compared with the lying position of the animal 
had hardly any effect on the body temperature, but there was some indica- 
tion that the temperature was slightly affected when measured shortly 
after the change in position had been made. 
(8) There was no difference in body temperature when measured before 
or after defecation. 
(9) Daily fluctuations in body temperature depend to a great extent on 
the individuality of the cow. 
Q(10) A variation of 0.8° F. in the rectal temperature of the same animal 
was observed, when measured at the same hour of the day under identical 
conditions and outside the influence of water or feed, while under the 
influence of water a difference of 1.3° F. was observed at the same hour 
on two consecutive days. 
A detailed report of the results will appear in the Journal of Agricultural 
Research. 
ON THE STRUCTURE OF FINITE CONTINUOUS GROUPS WITH 
EXCEPTIONAL TRANSFORMATIONS 
By S. D. ZeIvDin 
Department of Mathematics, Massachusetts Institute oe Technoeogy 
Communicated by Edwin B. Wilson, August 2, 1920 
r + q 
LetXk = fikM^. ^^^^ ^ ^ ^' ^' , f, r + 1, . . . f + g, be 
'c>Xi, 
1 
the differential symbols of a finite continuous group G of order r + and 
r + q r + q 
let Ek E ^jQki ^ be the symbols of the operators of the 
1 1 
adjoint of G. We then have 
r + q 
1 
r + q 
{i, y = 1, 2, . . . f + 
and (Ei, Ej) = ^iJkEk, 
1 
where the c's are the so-called structural constants. We assume that 
