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THE AMERICAN NATURALIST [Vol. XL 



method by assuming that after the first abrupt expansion the sap 

 flowed off through the tissues to the wood fibers, or to more distant 

 parts of the tree faster than expansion took place. 



Let us take the same case cited under the water-expansion 

 theory of a maple tree 20 meters high and 5 dm. in diameter at the 

 , base, and a volume approximately 3.926,98 cu. m. as determined 

 above. The radial coefficient of expansion for dry maple wood 

 is 0.000,048,4; if wet it would be greater, suppose 0.000,088,4. In 

 tangential direction it would probably be greater still owing to the 

 absence of pith-rays, say 0.000,15 or an average coefficient of 

 0.000,119,2. The radius is 0.25 m., and for one degree of rise 

 it would become 0.250,029,8 m.; the area would be 0.196,396 

 sq. m., and assuming that the length remains the same, the 

 volume would be 3.927,92 cu. m., an increase of 940 cc. for 

 one degree, or 3660 cc. for four degrees. This is only about 3.6 

 liters to be compared with the actual flow often of 10 or more 

 liters. Under the most favorable conditions, presupposing the 

 transmission of pressure from the most distant parts of the tree, 

 and the equal penetration of heat, the flow would be only a fraction 

 of the total flow on many days. If the pressure is transmitted 

 only eight feet each way the flow would be slight indeed, and if 

 produced only in the outer layers, as it would be necessary to 

 suppose if we consider the pressure due to contrast between inner 

 and outer temperatures, the flow would be insignificant. 



In order that the pressure should become evident at all from 

 such a source an almost absolute impermeability of the fiber walls 

 must be assumed, otherwise the very insignificant amount of 

 expanded water would in a very short time pass through and 

 pressure would soon cease. This theory, therefore, fails to account 

 for the volume of sap flow; and pressure can be accounted for 

 only by assuming the almost absolute impermeability of the walls 

 and saturation of the vessels, the former of which at least, is very 

 improbable. 



the resistance within the tree is reduced to a point considerably 



