Secondly the relay magnets require some time to lose their magnetism sufficently for the armature spring to break the contact. There is first the chronometer relay, then the signal relay, and last the magnet of the register, so that the absolute time of the record on the tape is later than the chronometer break by the sum of these three armature times. The armature times of the signal relay and the register, however, equally affect the break of the other chronometer, and therefore vanish from the difference of the chronometer times, leaving in the result only the difference of the armature times of the chronometer relays.

The remaining errors are, therefore, the difference of these armature times, irregularities of the break circuit mechanism of the chronometers, and irregularities in the rate of running of the tapes off the reels of the registers. All these are very minute, and the irregularities of chronometer and register mechanism are reduced to a minimum by taking a large number of comparison breaks, while the difference of armature times may be considered as a constant, and affects the personal equation determinations as much as it does the comparison of local times, and so disappears from the final difference of longitude.

The time of passage of the electric current over the length of wire separating the two stations, is quite appreciable, but it affects the two tapes in opposite directions, and therefore disappears from the mean of the two results.

The length of a break on the tape is usually about one-twentieth of the two seconds length, corresponding to a time of about one-tenth of a second. If, then, the difference of time between the signals of the two chronometers be less than onetenth of a second, it will be impossible to distinguish the beginning of the break of the following chronometer, and the above method fails. In this case a different arrangement of the relays is made. Each chronometer relay works directly on the register circuit instead of on the line, serving merely to graduate the tape into twosecond spaces. One of the observers then taps on his break circuit key at irregular intervals. These taps are recorded on both tapes, and the several taps having been identified, serve to compare together the chronometer beats. This operation must be repeated, the other observer giving the taps, so that from the two results the time of passage of current may be eliminated by taking the mean.

Another arrangement of the switch board is made by cutting off the line circuit from any communication whatever with either the chronometer or the register local circuit. The chronometer relay then serving to graduate the tape into time spaces, transits of stars may be recorded by pressing a key in the register circuit.

Three local batteries are necessary at each station; one for the chronometer, one for the register and one for the sounder. I ordinarily used a gravity cell for the chronometer, which requires a comparatively weak, but constant circuit, and ought to be kept in circuit night and day during the whole time of observation at a station, to avoid change of rate. For the register and sounder, after trying the gravity battery, I ultimately concluded that the Léclanché cell was the best. Since this battery rapidly polarizes, it must not be kept in circuit more than a few minutes at a time, or no longer than the time necessary to record a star transit or run off a comparison tape.

We now come to the consideration of another source of error, which cannot be eliminated by any reversal of instruments or change in the method of observationthe "personal equation."

It is found that observers differ in their estimation of the instant of the passage of a star over a thread. When the " eye and ear" method is used, i.e., when the observer, listening to the beat of the chronometer and watching the star crossing the field of view, notes with the eye the position of the star with reference to the thread at the beats before and after its crossing, and estimates thereby the fraction of a beat at which it crosses, it is a question of the accordance of the senses of sight and hearing. When the electric key is used to tap the instant at which the star appears bisected by the thread, and to automatically record the instant without reference to the audible beat of the chronometer, the accordance of eye and hand is involved.

In either case large differences are often found between different observers, frequently amounting to half a second of time or more. This difference is called the relative personal equation of the observers and is a nearly constant quantity with practised observers. The effect of personal equation is to give a value of the chronometer correction too great or too small, and therefore the deduced difference of longitude will be in error by the amount of the relative personal equations of the two observers. It is therefore necessary to determine its amount.

The best method is for the two observers after a few nights exchange of time to exchange stations and take an equal number of nights observations. The two results for longitude will differ by twice the personal equation, and their mean will be free from it.

Another method is for the observers to meet and take the transit of the same star with the same instrument on the same night, one taking the transit over two or three of the threads and the other observer the transit over the remaining threads. This method is not to be recommended, as the necessarily somewhat hurried exchange of observers at the instrument is unfavorable to each observing in his usual deliberate

manner.

The method employed by Mr. Klotz and myself was that of setting up our instruments near one another and observing each with his own instrument a full set of stars in exactly the same manner as if a difference of longitude between two remote stations was being determined, stellar observations being taken to determine the chronometer corrections and a comparison of chronometers being made with the electric apparatus. Working out the results and correcting them for the measured difference of longitude between the two instruments, the difference of longitude obtained is the personal equation, which must be applied to all other differences of longitude. It is requisite in this method (as in any other) that at least as many nights observations be taken for the personal equation as are taken at any station.

Peculiarities of the chronometer break circuit apparatus, armature times of the chronometer relays, &c., are involved in this result along with the strictly personal difference, but disappear with it from the final longitudes.

This supposes that it is constant. Any variation in the personal equation is to be considered as an accidental error to be diminished in effect as much as possible by repetition of observations. Care is to be taken that the conditions under which personal equation is determined are as similar as possible to those prevailing during the observations at distant stations. For instance, if the latter be taken in the middle of summer, and the personal equation observations during cold weather, the different bodily condition of the observers is very likely to introduce an unknown and constant variation in the personal equation.

The chronometers used were compensated for temperature between 45° and 95° Fah. These are about the usual limits for compensation of chronometers, and makers state that it is difficult to compensate satisfactorily beyond, especially below, these limits.

In our work the chronometers are exposed to great extremes of temperature. Placed in a temporary wooden building, during the hot summer day of the North West they become heated to near the upper limit of compensation, while at night the temperature falls below the lower limit, and in the autumn nights frequently to near the freezing point. Consequently, the chronometer rates are large and variable. This cause of error I consider the most serious one with which we have to contend, and it is only to be fully avoided by the use of the greatest care in guarding the chronometer from changes of temperature.

Probably the most effectual plan would be to place the chonometer in a cellar or other place of tolerably uniform temperature, and in connecting it by wire with the electric apparatus in the observatory, so that transits might be recorded with the register. A pocket chronometer or a clock in the observatory electrically controlled by the chronometer could be used for the purpose of setting for stars.

Mr. Klotz observed with the zenith telescope the latitudes of the stations which he successively occupied. The latitude of a place being an absolute quantity depend

ing only on the position of the vertical line with reference to the axis of the earth, but one observer is necessary, and no corresponding observations at other places are required as in the case of the longitude. Mr. Klotz gives in his report an interesting description of his methods and results.

This longitude work has now been carried from the Pacific Coast to Port Arthur. Several important points have been located, but the determination of some intermediate stations would give valuable results. Winnipeg is probably the best centre from which to determine points in Manitoba and the North-West Territories. I beg to point out to you however that its absolute longitude, upon which the longitudes of these other points will depend, has not yet been obtained with the precision its importance merits.

The present determination of its longitude depends upon the longitude of Seattle, Washington Territory, through the observed differences of longitude between Seattle and Kamloops, and between Kamloops and Winnipeg. The longitude of Seattle itself has been brought across the continent by the United States Coast Survey. In such a long circuit there is plenty of room for accumulation of error. Further, the longitudes Seattle Kamloops and Kamloops Winnipeg were determined without an automatic signal exchange apparatus, and the results are therefore probably inferior in accuracy to those which we now have in our power to obtain.

On these grounds I beg leave to recommend that a re-determination of the longitude of Winnipeg be made from some well-determined station nearer at hand.

On the 16th October I arrived at Kamloops and proceeded to set up my instruments for observation, according to the programme arranged with Mr. Ogilvie.

Mr. Ogilvie had, in the early summer, started from the Pacific coast at the Chilkoot Inlet, and, crossing the mountains there, travelled down the Lewis and Yukon Rivers, making a micrometer survey as he went along. He intended to winter near the international boundary line, which, there, is the one hundred and forty-first meridian of longitude west from Greenwich.

It was important for him to get his longitude there as accurately as possible, both as a check on his survey and also to give an approximation to the point where the boundary line, as defined by the treaty, crosses the Yukon River.

There being no telegraph line, and the journey being too long and too rough to permit him to carry his time by means of a chronometer with any certainty of it keeping its regular rate, the alternative was lunar observations.

The principle of lunar observations is this: the place of the moon among the fixed stars being determined at any known local time and the place of the moon being predicted and tabulated in the Nautical Almanac for each hour of Greenwich time, the Greenwich time is found at which the moon has the place given by the observation; that is, the Greenwich time corresponding to the local time of the observation is found, and thence by the difference of these times the longitude from Greenwich is obtained. The Greenwich predictions, in fact, supply the place of the corresponding observations as well as of the signals in method by the electric telegraph. The local time of course must be accurately determined in this as in the other method.

The methods commonly used for determining the Greenwich time are moon culminations and occultations of stars by the moon.

In the former of these methods, the transit of the moon is observed, as well as the transits of a sufficient number of stars to determine the adjustment errors of the instrument used, and the chronometer correction. The deduced time of transit of the moon's centre over the meridian is the right ascension of the moon. This by comparison with the right ascensions tabulated for each hour in the Almanac, gives the Greenwich time of the moon's transit, and the local time is given by the chronometer with its correction applied.

The occultation of a star is the passage of the moon between the observer and the star, eclipsing the latter. The observation consists in noting the exact time at which the star disappears under the moon's limb and again when it reappears. Transit observations of stars must also be taken to determine the correction of the chronometer. The Greenwich time of the occultation is found from the tabulated

right ascensions and declinations of the star and the moon and the moon's parallax by a somewhat lengthy calculation.

Both these methods are capable of considerable accuracy, but in comparing them with the telegraphic method it is to be noted that in the latter an error in the observations amounting to one-tenth of a second causes an error in the longitude of just the same amount, but in any lunar method, on account of the comparatively slow motion of the moon with reference to the stars, its right ascension changing only about one second in twenty-seven seconds of time, an error of one-tenth of a second in the observed right ascension produces an error in the longitude twenty-seven times as great.

In the moon culmination observations moreover there is difficulty in accurately observing the transit of the moon's limb. The accuracy of this observation is not to be compared with that of a star transit. In this respect the occultations are preferable, since the disappearance and reappearance are perfectly instantaneous.

All lunar methods however are subject to great uncertainty, from the fact that in the present state of the lunar theory, the place of the moon cannot be predicted with the accuracy required in this work. To cut out the effect of these imperfectly known discrepancies in the moon's motions, corresponding observations had to be taken at some place of known longitude as near as possible to Mr. Ogilvie's station, so that corrections might be obtained from the observations at the known station to be applied to the tabulated moon's place in the subsequent working out of the corresponding observations taken by Mr. Ogilvie.

For this purpose I went to Kamloops, the longitude of which had been determined by telegraph, and which was the nearest point so determined to the locality in which Mr. Ogilvie intended to winter.

Some idea of the size of Canada is obtained by considering the distance from Kamloops in the heart of British Columbia to this remote station, which is not far short of 1,300 miles in a straight line, the direction being about due north-west.

I remained at Kamloops during two lunations from the new moon in October to the new moon in December, observing the transit of the moon whenever possible, as well as all the star occultations which occured above the horizon at Kamloops and at the northern station. Mr. Ogilvie was to observe the same phenomena. Unfortunately my list of occultations observed as well as of moon transits is very fragmentary. Unusually cloudy weather prevailed during the whole time of my stay, very few nights being clear.

A further programme was arranged to be carried out in April and May next. The partial failure of the October and November programme renders the carrying out of this one more important, and I hope that greater success will be obtained.

I have collected the magnetic observations taken by different surveyors employed by our Department in tabular form, but the list is not yet quite complete, and I think it inadvisable to publish it at present. I have hopes of including in it some declinations observed at widely different dates which may give information as to the secular change of the declination.

The Surveyor General,

I have the honor be, Sir,

Department of the Interior,
Ottawa.

Your obedient servant,

W. F. KING,

Chief Inspector of Surveys,

In charge of Longitude Determinations.

No. 3.

REPORT OF OTTO J. KLOTZ, D.T.S.

DETERMINATION OF LATITUDES AND LONGITUDES.

PRESTON, ONT., 10th December, 1887.

SIR,-I have the honor to report on the continuation of the astronomic work during the past season.

The results of this work since its inception in 1885, under the Technical Branch of the Department of the Interior, have amply demonstrated its extreme utility and ultimate economy.

Beginning work on the Pacific Coast, using Seattle, W. T., as base for longitude (there being at that time only two places, Seattle and San Francisco, which were accurately established in longitude and referred to Greenwich, the former being the more convenient for our work in British Columbia) the latitude and longitude determinations have now been carried through British Columbia, and eastward two thousand miles from the Pacific Coast along the line of the Canadian Pacific Railway.

The method of observing (both for latitude and longitude) has remained the same, with but slight modifications, as suggested by you.

TRANSIT.

During 1885 and 1886 for longitude work two transits F. O. 1 and F. O. 2 by Troughton and Simms, each of 28 inches focal length and 2 inches aperture, were used. These transits were used by the British Commission on the International Boundary Survey of the 49th parallel.

The diaphragm carries five vertical spider's threads and two horizontal ones; a micrometer with movable threads is also attached but was not used.

The equatorial intervals of F. O. 1 as determined from transits of Polaris, & Ursae Minoris and ε Ursae Minoris are

19.080
9.582

⚫016

9.584 + 19.062

When reversing, the instrument is always grasped symmetrically, that is one hand on each side of the axis, thus practically eliminating any effect from tempera

ture.

A reversing apparatus would however be a great convenience.

STRIDING LEVEL.

The striding levels are of the old type, being imbedded in plaster of Paris, and hence subject to greater variation in the value of a division from change of temperature. Neither one is provided with an air chamber for adjusting the length of bubble. The following values for one division were obtained for striding level of transit F. O. 1.