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: 
E 
_V (7 X 10 c) 600 
wv 
in which # equals expansion and V the range of variation. £ there- 
fore is equivalent to 25 < 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 5em. 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. 
