than on May 28, and still lower June 2, the total difference being almost exactly one ohm for each coil. This corresponds to about 2.5° C., and is due to the lower temperature of the laboratory on the later days. We were surprised to find evidence of a positive temperature coefficient in one coil and a negative coefficient in the other, and therefore made some direct comparisons of the two coils with each other with a view to testing this point. Le, being maintained at a constant temperature of about 21.5° C., Lp was cooled about 3° by leaving it in a cooler room over night. The two coils being balanced against each other, with a variable inductance included with the smaller, Lp was warmed in an inclosed space and its inductance was observed to decrease about 3 parts in 10,000. On another day L was kept constant and Le heated in a similar manner. The result was an increase in the value of L. L being again heated while Le remained constant, its value decreased with respect to L. An exact measure of the change of temperature was not obtained, and hence no definite value of the temperature coefficient was found.

A possible explanation of the opposite sign of the temperature coefficients suggested itself when we removed the covering of L. This coil is wound on a spool of serpentine, and the wire is embedded in paraffin. The formula for the induction of such a coil is

8a
L= 4πn'α (log 2
R

where a is the mean radius of the coil and R is the geometric mean distance of the wires in the cross section of the coil. When the paraffin (which has a temperature coefficient many times larger than copper) expands, it tends to increase the geometric mean distance of the wires and so decrease L, and this effect may be greater than the increase due to the expansion of the copper, which increases a. The other coil, however, is wound on a spool of mahogany with dry, silkcovered wire, and there is no such tendency to increase R. Whether part of the observed increase of Le with increase of temperature is due to the spool itself we do not know.

It is evident that we must either keep these coils continuously at a constant temperature when measuring their inductances, or else get some new ones not subject to so large temperature coefficients. Whether this is possible we do not know, but hope soon to make some trials in this direction and also to study more carefully the magnitude of the temperature coefficients of these coils and their causes.

This method of measuring inductance is capable of yielding somewhat better results than those given above, when all possible refinements are introduced. It seems to us desirable to measure in this way some carefully constructed inductance standards whose values can be computed from their dimensions. The determination of such pairs of values of I would amount to an absolute determination of the international ohm.

We are indebted to Mr. C. E. Reid for assistance in making some of the observations recorded in this paper and to Dr. N. E. Dorsey for assistance in analyzing the curves.

THE ABSOLUTE MEASUREMENT OF CAPACITY.

By EDWARD B. ROSA and FREDERICK W. Grover.

1. THE METHOD EMPLOYED.

The usual method of determining the capacity of a condenser in electromagnetic measure is Maxwell's bridge method, using a tuning fork or a rotating commutator to charge and discharge the condenser,

which is placed in the fourth arm of a Wheatstone bridge. This is a null method, is adapted to measuring large and small capacities equally well, and requires an accurate knowledge only of a resistance and the rate of the fork or commutator.

The formula for the capacity of the condenser as given by J. J. Thomson," is as follows:

in which a, c, and d are the resistances of three arms of a Wheatstone bridge, b and g are battery and galvanometer resistances, respectively, and n is the number of times the condenser is charged and discharged per second. When the vibrating arm Ptouches the condenser is

charged, and when it touches R it is short circuited and discharged. When Pis not touching Q the arm BD of the bridge is interrupted and a current flows from D to C through the galvanometer; when P touches the condenser is charged by a current coming partly through e and partly through g from Cto D. Thus the current through the galvanometer is alternately in opposite directions, and when these opposing currents balance each other there is no deflection of the galvanometer. This is accomplished by varying one of the resistances, a, c, or d. The capacity may then be computed from the formula (1).

a Phil. Trans., 1883.

Under ordinary circumstances the capacity of the condenser is very

nearly given by the first part of the formula

a ned'

the remainder

constituting a correction factor which we may represent by F. Then

If after the experiment we replace the condenser and commutator by an accurately calibrated resistance box, and vary its resistance until the bridge is balanced while a, c, and d remain unchanged, then and hence

a 1 cd R

This is not practicable for very small capacities, as R would then be inconveniently large at ordinary values of n. But for capacities of 0.01 microfarad and larger this can usually be done. Of course, if a, c, and d are all known with sufficient accuracy this operation may be omitted.

2. THE CORRECTION FACTOR F.

The correction factor F, as we have called it, shown in equation (1), may be written as follows:

It is, of course, desirable to have this factor as nearly equal to unity

b d

as possible, and therefore the quantities (1++)

a a

should be as large as possible. To this end a should be small, c and d relatively large. Under these circumstances the values of b and g are not very important, although it is generally better to have them small. If b is nearly zero, the first parenthesis of the denominator disappears, as well as one term in the first parenthesis of the numerator, and the expression for F is somewhat simplified. Since c and d are opposite branches of the bridge, their product is constant, and therefore increasing e decreases d; both should be as large as possible, in order to make Fas near unity as possible, but there are other reasons to be given later which make it desirable to have a much larger than c.

5834-No. 2—05—3