eight observations or sixteen readings is the apparent inclination with a deflector, face East.

Instead of placing the deflector at 40°, another angle, as 45° or 50°, may be taken; or a second angle may be used for the purpose of varying the observations when it may be desired to repeat them; the only essential point being, that the angle at which the deflector is placed should be the same on each side the apparent dip.

Instead of deflector N (or the North pole of a second needle used as a deflector), deflector S (or the South pole of the second needle) may be screwed into the opposite point of the back circle, and eight observations taken with it will give as before the apparent inclination with a deflector, face East.

When time permits and the circumstances are favourable, the observations prescribed in (1) and (2) may be repeated with the face of the circle to the West.

In writing down the observations the following directions must be attended to; if the needle be deflected past the vertical, the division of the limb should be read off according to the graduation and noted accordingly, but the mean of the readings must be taken from 180°, in order to give the true arc corresponding to the position of the needle: if it be deflected past the horizontal, the readings must be entered as marked on the limb, but with the negative sign prefixed, in which case the mean result will be half the difference of the means of the negative and positive readings.

The apparent inclination obtained as above directed, whether by the direct method, or with deflectors, requires two corrections to give the true inclination, viz.-1, the index-correction of the particular needle employed; and 2nd, a correction for the influence of the ship's iron dependent on the direction of her head at the time of observation. The mode of obtaining the index correction will be subsequently explained.

B.-Intensity.

3. With Weights.-The instrument being on the gimball table and levelled, the plane of the circle parallel to the magnetic meridian, with its face to the East, and the needle showing the magnetic dip, place the silk carrying the hooks on the grooved wheel; attach one of the constant weights to one of the hooks, and take four readings of the division of the limb at which the needle is in equilibrium, using the precautions already directed of altering the points of support of the axle before each observation, and rubbing with the ivory disk whilst reading off.

If the needle is deflected past the vertical or horizontal, read and enter the angles as already directed under the head of Inclination. Change the weight to the other hook, when the needle will be deflected to the opposite side of the apparent dip to what it was before,

and take four more observations. Half the difference of the mean of the arcs with the weight on either hook is the angle of deflection due to the constant weight employed; or half their sum, if one of the arcs was past the horizontal, and has therefore the negative sign prefixed.

4. With Deflectors.-The instrument being adjusted as already described (and without using the hooks, which are only designed for the observations in which the weights are used), adjust the circle at the back by means of its verniers to the apparent dip, so that the deflectors, when screwed in may coincide with the line of the dip; the needle will then be repelled to one side: make four observations of the division to which the needle is thus deflected, observing the usual precautions of moving the bracket at the back, reading both ends of the needle, and rubbing with the ivory disk.

Move the needle past the deflector to the other side of the dip by means of the bracket, and take four more observations: if the needle is deflected past the vertical or horizontal, read and enter the angles in the manner already described; half the difference of the arcs on either side of the apparent dip, or half their sum if one be past the horizontal and have the negative sign, will be the angle of deflection produced by the deflector. Instead of the deflectors, a second needle may be used as a deflector, either with the end of the needle-case marked N (containing the north pole of the needle) screwed into the arm marked N, or the end marked S screwed into the arm marked S.

The thermometer attached to the circle must be observed at the commencement and close of the observations of intensity, whether with deflectors or weights.

A convenient routine of the observations at sea may be stated as follows:

1. Take four observations of the apparent dip by the direct observation.

2. Screw in the deflectors N and S, and adjust the back circle to the dip. Make four observations of the angle of deflection produced on either side of the apparent dip; this furnishes one result for the intensity of the magnetic force.

3. Repeat No. 2 with a second needle used as deflector N, which will give a second result for the intensity of the force.

4. Repeat No. 2 with the second needle used as deflector S, which will give a third result for the intensity of the force.

5. Remove the deflector and repeat No. 1, which will give a second result for the apparent inclination.

On days when the weather permits, observe the intensity also by the constant weights.

5. Combination of Deflector and Weights.-Addition by Mr. WELSH. [The instruments most recently constructed under Mr. Fox's direction have been adapted for the method, devised by Dr. Lloyd, of

measuring the variations of the total force independent of the changes in the magnetic moment of the needles employed. The method if described in Appendix No. 2. Two of the dipping needles used for observations of the intensity with weights are employed in this process, and their poles must never be reversed or disturbed. One of the needles, A, is mounted as a dipping needle, and another, B, precisely similar in its construction, is used as a deflector. The needle B, being attached to the frame * at the back of the instrument which carries the arms of the verniers, is thus moveable in a plane parallel to that of the dipping needle. In taking the deflections, the deflector must always be moved to such a position that it is exactly at right angles to the dipping needle when the latter has come to rest in its position of equilibrium between the earth's force and that of the deflecting needle. This is accomplished by setting (first approximately and afterwards exactly) the verniers at the back to the same circle reading as shown by the dipping needle. The position of the dipping needle is then to be accurately observed, the same precautions being adopted as have already been prescribed in other observations with this instrument. The frame carrying the deflector is then to be moved until the dipping needle A is deflected to the opposite side of the line of the inclination, and the deflector again set carefully at right angles to it in its new position. The position of the dipping needle having been exactly observed as before, half the difference between the readings in the two positions is the angle of deflection u' required. In this observation it is of most essential importance that the relative positions of the two needles in the observations made at different times and places should be identical. The following rule may be useful in placing the deflector on its supports :- Set the vernier A at the back to 90 at the top of the circle (the face of the instrument being towards the east); fix the deflecting needle (in its case) upon its frame with the north pole towards the north, keeping the lettered side of the case uppermost. The utmost care should be taken that the needle is always placed in its case in precisely the same way and with the poles in the same direction, and that it is there held firmly in its proper place by the springs provided for the purpose. The observations of deflection should be repeated at two or more different distances (distinguishing the distances by numbers).

The needle A must now be removed, and B substituted in its place, and a series of deflections with weights made with B. Needle A may then be used as a deflector, and a series of deflections of B made in the manner already described: needle A is then to be again mounted as

By removing one of the supports for the deflecting needle which have been added to the instrument, and substituting for it a tube which is provided, the second needle may be mounted and used as a deflector in the manner formerly practised and described above. The grooved wheels of the needles are now, by Mr. Fox's directions, made of aluminium, which advantageously reduces their weight."

at first, and observations with weights taken with it. This will give two complete sets of observations, one with each of the needles. The thermometer must be recorded for each operation.

When the ship is on her voyage it may not be convenient or possible to perform all those operations at each observation. It may therefore be proper to arrange the order of observing as follows:-In the ordinary daily determinations of the inclination and force, observe-1st, the inclination in the usual manner with needle A (which we will suppose to be the needle in ordinary use); 2nd, deflections of needle A with weights; 3rd, deflections of needle A by needle B by the method now described; 4th, repeat the observation of inclination with needle A. It will be desirable, once in a month or six weeks, when weather and circumstances are favourable (and always on shore when opportunity offers), to go through the whole of the processes above described in the following order :-1, observation of inclination with A; 2nd, deflections of A with weights; 3rd, deflections of A by B; 4th, deflections of B by A; 5th, deflections of B with weights; 6th, observation of inclination with B; 7th, observation of inclination with A. In exchanging the needles care should be taken to mount them always in one way, viz. with the pulley on the side next the observer. The third needle supplied with the instrument is a plain dipping needle, whose poles may be reversed, and which is intended to be used on shore as directed in Appendix No. 2.

6. Calculation of the Observations; 1st, with Weights.-Let R be the intensity, expressed either in absolute or relative measure, and u the angle of deflection produced by a constant weight at the base station; R. and u, being the intensity and deflection at any other station; then

where CR sin u, a constant; to the temperature of the needle at the second station; t that at the base station; and q the correction for the decrease of the magnetic moment of the needle produced by an increase of temperature of 1° Fahr., a quantity which must be experimentally determined at a fixed observatory for each needle.

2ndly. With Deflector by Dr. Lloyd's Method.-Let u' and u'o be the angles of deflection at the base station and at any other station; then

where DR sin u', a constant; the other quantities having the same meaning as before.

3rdly, By Combination of the two methods.-When the observations with the deflector are combined with those with weights, e.g. when

observations of deflection of A with weights and of B by A are taken at one time, the formula becomes

the effect of temperature being thus eliminated. The value of Ro will always be intermediate between the values derived separately from the two methods of deflection, and the difference (if any) will be a measure of the loss of magnetism of the needle between the observations at the two stations.

4thly. With Deflectors by the Original Method.-Where deflectors are used in the manner hitherto adopted, that is, with the deflector placed at right angles to the plane of the instrument, the intensity is obtained by the formula

where R, v, and w are the intensity, angle of deflection, and equivalent weight at the base station; and Ro, vo, and wo those at any other station.

:

A table of "equivalent weights" may be formed in the following manner :- The plane of the instrument being placed perpendicular to the magnetic meridian, and the needle in its natural position of rest (which in such case is a vertical position), the deflector is placed successively at angles from the vertical, each differing one degree from the preceding the needle is thereby deflected to an angle on the side of the vertical opposite to the deflector, and is brought back to its natural position of rest by weights applied to the grooved wheel on the axle. These weights are called the equivalent weights, corresponding to the angles from the vertical at which the deflector was successively placed, and which ought to include all the angles likely to occur in the course of the observations.]

III. OBSERVATIONS ON SHORE.

1. The instrument being adjusted with the plane of the circle coinciding with the magnetic meridian, and the face East, make a complete series of observations of the Inclination with and without deflectors, and of the Intensity with the deflectors and weights, similar in all respects to the observations which have been or which are intended to be made at sea; the needle, deflectors, and weights to be those employed, or to be employed, in the sea-observations.

2. Repeat the same with the face West.

3. If unfurnished with a separate apparatus for determining the true inclination, substitute in Mr. Fox's apparatus the needle which admits of its poles being reversed (viz. that needle which is not intended to be