mirror of the instrument and reflected from that to a scale. The relative position of the various parts of the apparatus is shown in fig. 2.

At first readings were taken with the edge of the sun and centre alternately on the instrument. On account of the very rapid fall in heat near the edge, this plan was not found to give satisfactory results; and at present the best results are got by allowing the image of the sun to transit across the instrument, and by recording the motion of the spot of limelight by means of a falling photographic plate.1

It became evident, from the first photographic curve obtained, that to translate its meaning, corrections would have to be applied for some disturbing causes, such as the damping effect of the air, and the variation in intensity of the source of heat to which the instrument was exposed. Dr. Rambaut has investigated these matters, and below will be found an exposition of the methods he has adopted to surmount the difficulties. What we now propose to do is to take frequent curves of absorption from time to time throughout a sun-spot cycle of 11 years, and thus try to solve the problem-Whether the sun's atmosphere varies in depth in that time. From a comparison of the photographs taken of it in maximum and minimum years, it would appear that the sun's corona varies in form, and also that the spots alter their characters in the same period. Is it not probable that changes are also taking place in the solar atmosphere? If we find that such changes are taking place, as will be shown by the alteration in the ratio of the heat from the limb

1 See British Assoc. Report, Cardiff, 1891; Trans. of Section A.

202

and centre of the disc, we think it will be quite possible, by an investigation of the co-ordinates of these curves, to determine the change in the value of the solar constant.

EXAMINATION OF THE CURVES.

From the nature of the instrument it is clear that the only forces acting on the system are the directive force of the magnet, the force of torsion, and the resistance of the surrounding medium. If we denote the angle of torsion by p, and the difference in temperature between the two ends of the couple by, we obtain the following differential equation representing the motion :

do
dt

in which 2a is the resistance of the medium, bp the torsion, and

CO the directive force of the magnet.

Also, if K denotes the intensity of the heat falling on the heated end of the couple, we have the equation

For the following method of obtaining this euqation we are indebted to Professor G. F. Fitzgerald:

If we suppose, and 0, to be the elevation of temperature of the two ends of the couple above that of the surrounding medium, and if we suppose the couple divided into a number of segments ds, taking into account the resistance of the couple, a Peltier absorption of heat at the hotter, and emission of heat at the colder end, and a Thomson effect at other parts of the wire, we have, for any segment after the first, an equation of the form

do
ds

in which TC is the Thomson effect, c the conduction, p✪ the radia

tion, and rC2 the heating by resistance. At the ends themselves we have a Peltier, instead of a Thomson, effect; and for the heated end

in which PC and PC represent the Peltier effects at the two ends of

We may also assume that the terms and are each to a first

ds

ds

approximation proportional to the difference of temperature, so that we obtain

The last term here is so small that in an investigation like the present we may neglect it so that we reach the result given in equation (2). If now we eliminate between equations (1) and (2) we obtain the following linear differential equation of the third order

In the method of observation described above the intensity K is a function of the time, so that we obtain the equation

Denoting the roots of the equation x2 + 2ax + b2 = 0 by and remarking that

+ (b2 + 2al) + b2l$ = f(t).

(4)

we obtain the solution of equation (4) in the form

The general term of this series may be written in the form

f(t) is given, the motion of the couple is determined, and by means of this equation any assumption with regard to the law of variation of the sun's heat from point to point of its disc might be tested.

The question before us at present is, however, the inverse of this, namely, from the curve which represents this equation to determine the corresponding values of f(t).

Now, it is obvious from equation (4) that if we can obtain the values of the constants a, b, and 7, and the quantities

at any point along the curve, we can compute the corresponding value of f(t).

In order to determine the constants, we have proceeded in the following manner:-If the couple be mechanically displaced from a position of equilibrium, its motion is represented by the equation

The solution of this equation gives us as the equation of the curve traced by the spot of light

The first of these gives a continuously increasing value of -this ordinate only reaching its maximum value after an infinite time. The second equation gives a curve proceeding by a series of continually diminishing waves to the final position of equilibrium. From the form of the curve in fig. 5, which is a reduced copy of a photograph taken on 12th October, 1890, it is easily seen that it is an equation of the

second form with which we have to deal in the case before us. In this case the period in which the oscillation takes place will give the value

2π

of while the logarithmic decrement of the ordinates will give the

value of

ап

We shall thus be in a position to determine both a and d from which we can immediately deduce the value of b.

FIG. 3.