54 TROWBRIDGE: THE THERMOMETRIC MOVEMENTS 
being so small as to prevent solidification. Consequently it i 
possible that under certain conditions sap does not freeze (even 
fractionally) until at least at a very low temperature, but the 
evidence of the thermometric movements of branches and the 
thermometric opening and closing of frost cracks indicate a cha 
which begins at 32° F. and continues below that point, which 
as the temperature falls without the fractional freezing proce 
but parallel to such a change of state of the sap. 
A considerable number of experiments were performed i in 
order to ascertain, if possible, the coefficient of expansion of t 
tree trunk just below the bark. It was found that below freezing 
with the reduction of temperature a very large contraction occurred 
in the horizontal direction, transverse to the grain; on the ot 
hand, that there was only a very small contraction in the lon 
tudinal direction; also, that this contraction in the transvet 
direction was far greater than for a corresponding range abo 
32° F. Owing to a number of uncertainties in the experimen 
they have not been published, and have been discarded for a me 
accurate method, which has been devised. The results indicat 
correspond with some measurements of Dr. J. G. Grossenbacher, 
who measured the circumferences of a number of trees and det 
mined that for a fall of temperature the decrease in circumferen 
per degree was greater below freezing than above that point. 
The fact, mentioned above, of greater coefficient of expansi 
below 32° in the transverse direction also corresponds with t 
published observation of Caspary who found that the circu: 
ference of the bark changed more rapidly than that of the w 
cylinder in certain trees.+ 
GENERAL CONCLUSIONS 
In this investigation the mechanics of the thermometiil 
movements of branches has not yet been determined, but 
* Crown rot of fruit trees; field studies. New York State Agric. Exp. Sta. T : 
Bull. 23. 1912. 
Caspary, Neue Untersuchungen iiber Frostspalten. Bot. Zeit. 15: 329 
345-50; 361-71. 1857. 
