14 GROWTH IN TREES. 



measured, and if the variations were to be recorded during the entire 

 year the range would be even greater. The change in dimensions of a 

 floating frame of invar arranged in the form of a polygon with a total 

 perimeter of 60 cm. may be estimated from the following data. The 

 temperature coefficient of this metal is 0.00000015 per degree, and the 

 daily range of air temperature does not vary beyond 25 C., usually 

 much less. The daily rise in temperature of this yoke, which would 

 tend to increase its radius and to make the daily shrinkage of the tree 

 appear to be greater than it really is, would therefore be found by 

 the following formula: 



V (0.7 X 10 c) 600 



E= 



7T 



in which E equals expansion and V the range of variation. E there- 

 fore is equivalent to 25 X 0.0000007 X 600 divided by 3.1416. The 

 possible enlargement of the diameter of the yoke, if the temperature 

 rose from 10 to 35 C., which would be a maximum, would be no more 

 than 0.0036 mm. Part of this is practically compensated by the 

 radially arranged contact screw of invar which projects inwardly 

 30 mm. It is to be seen that when this error is amplified 12 times it 

 could amount to no more than about 0.04 mm., which would not be a 

 discernible interval on the record. The use of invar or bario may be 

 taken to furnish a floating frame, the variation of which would be 

 negligible in measurements of variations in the trunks of trees. 



One additional feature of the instrument yet remains to be described, 

 this being the devices by which the floating frame is kept in its hori- 

 zontal position around the trunk. This is accomplished by a series 

 of clamps and upright flexible wire supports. Sections of bronze wire 

 or bronze-coated steel wire, about 10 cm. in length, are fastened to a 

 foot or base of brass 3 by 5 cm. Such supports are placed in suitable 

 positions on the upper surfaces of the wooden blocks of the encircling 

 belt and fastened in place by clamps of proper size. Each upright 

 wire carries a small brass clamp which may be moved up and down and 

 fastened at any point. The free end of this clamp is slotted to receive 

 the flat members of the floating frame which are fixed firmly in place 

 by set screws. Adjustments of positions of the wire supports and of 

 the clamps on the members of the floating frame are made until the 

 last named is held in such position that the contact screw exerts a 

 small amount of pressure on the trunk, so that any variation will be 

 expressed by movements of the quartz rod of the lever set on the oppo- 

 site side of the tree. 



The adjustment of the contacts is a matter of some nicety. A 

 broad chisel may be used to slice away the bark until a thickness of 

 not more than a millimeter remains outside of the living tissue, over an 

 area about equal to that which might be pressed lightly by a finger tip. 



