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by Raper to be but an approximation; for strict accuracy he recommends a solution invented by a French astronomer, the Chevalier de Borda, to whom seamen are indebted for many improvements in their art. It was he who, in 1787, published an account of what he called a cercle de réflexion,' which led to the modification of Hadley's quadrant into the sextant now in use. Borda's method differs from that of Mendoza Rios, in that we find by calculation the true distance directly from the apparent distance and the apparent altitudes, while in the former we find only the corrections which are to be applied to our own observation of those quantities.

No one likes extra trouble, and perhaps the following extract from Raper's directions for the lunar observation will suggest to some minds an additional reason for distaste to it.

'The observer fixes himself firmly in a corner, or lies on his back on the deck, in order to remove as much as possible the sense of bodily effort and inconvenience which disturbs the eye and the attention.'

We have heard of graceless young officers with a taste for caricature making merry with their friends at the expense of a stout captain lying on his back, and struggling with his sextant in the pursuit of science under difficulties. But we trust that this is not a common practice.

We cannot resist giving one more extract from Lieut. Raper's navigation. As it is the only occasion, so far as we know—and we speak of his, book as of a well-thumbed friend—in which that intrepid calculator has ever admitted the existence of a difficulty, the objection may reasonably be supposed to be a real one. 'A single observation is not capable of affording a decisive result: great practice is necessary for measuring the distance successfully; and the application of so many small corrections as are necessary when accuracy is required is, even with extraordinary care and some skill scarcely compatible with extreme precision.'

Yet lunar observations are indispensable under certain circumstances; for instance, our Arctic Expedition will depend for longitude almost entirely upon lunars, for chronometers, owing to reasons given further on, will not be very reliable. In Captain Parry's North-Westerly Expedition the longitude of the farthest point was determined by 1500 lunar distances.

It is, perhaps, a pity, at least many skilful officers regret it, that the method by chronometer has in practice greatly superseded the lunar observation. The theory of this is certainly simple enough. It is to set a watch to Greenwich time at the beginning of a voyage, and refer to it whenever Greenwich time is Vol. 141.-No. 281.

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wanted. The difficulty here is purely mechanical. No chronometer can be absolutely depended on, and if it stops, the navigator must resort to lunars, or give up the hope of finding his longitude at all. Most well-found ships carry three or even more chronometers, and it is considered unlikely that all should stop; indeed, it is supposed that the error of one is likely to compensate in some degree the error of another, as it is against the doctrine of chances that all the errors should be in the same direction. No chronometer as yet made can be trusted to go with the same accuracy as an observatory clock; but their performance is a wonderful triumph of human skill and ingenuity. We will try and explain the degree of dependence which can be placed on them. It is said that Gemma Frisius, about the year 1530, first proposed to tell the longitude by carrying a time-piece accurately giving the time under a known meridian. The state in which horological machines were at that time prevented his accomplishing the design. The idea, however, once suggested, was valuable. Harrison, an English watchmaker, was at last able to produce a time-piece which was sufficiently accurate to gain the whole reward of 20,000l. offered by the Act of Queen Anne. It is historically though not otherwise interesting to note, that though the reward was paid only, we think, in 1774-some time, at any rate, after Captain Cook's voyages in 1772-3, when the prize instrument was triedHarrison had made a very excellent chronometer as far back as 1726. This machine, placed on board a ship under the direction of the Board of Longitude, procured for him a gratuity from Government, and a desire to continue his labours. From 1726 to the date of Captain Cook's voyage, Mr. Harrison seems to have been without a rival. He reported himself ready for the official trial in 1764, and set sail for Barbadoes. On arrival, the error of the chronometer, allowing for its given rate, was found to be 43 seconds; and on the return of the vessel to England the instrument was but 54 seconds in error, allowing for its declared rate. A committee was then appointed by the Board of Longitude to take the machine to pieces and report on its construction. They declared themselves satisfied both as to theory and performance; and it was decided that the reward should be paid so soon as a maker could be found to execute Harrison's plan with equal success. This task was undertaken by Mr. Larkom Kendal, and the chronometer made by him on Harrison's lines was handed over to Mr. Wales, and sent, under charge of that astronomer, round the world with Captain Cook. It is now exhibited at the United Service Institution.

Dr. Hutton says that this machine performed even better than Harrison's.

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Harrison's. In 1774 a new Act was passed, offering a fresh reward to still further stimulate makers to increased accuracy, and to reward them for expensive and tedious investigations necessarily undertaken. From this time constant improvements took place, but the history of them is mixed up with a very pretty quarrel, in which the Board of Longitude, the watchmakers, Dr. Maskelyne (the Astronomer Royal), Sir Joseph Banks (President of the Royal Society), and a free lance, named Dalrymple, apparently a hasty friend of Sir Joseph's, all took part. The engagement was begun by Mr. Mudge, a chronometer maker, who published a Narrative; Dr. Maskelyne, an Answer to the Narrative;' Mr. Mudge, a 'Reply to the Answer.' Then came the Report of the Commissioners of Longitude, followed by An Appeal,' by Sir Joseph Banks; then Dalrymple, and so on. It seems to have been thought that Dr. Maskelyne was so much attached to the lunar method, which he had so great a hand in perfecting, that he was unable to appreciate the merit of other inventions. Dr. Rees, of the 'Encyclopædia,' appears to have taken sides rather warmly against the Astronomer Royal, for we constantly find little digs at that official, which appear oddly in a learned book-e.g. apropos of some unimportant question: "We applied to Dr. Maskelyne for authentic information, but, with his usual reserve, the doctor declined giving us any information on the subject."

Mr. Mudge the younger, after his father's death, published a book in 1779, at which time eleven chronometers had been sold and more were nearly complete. The fact will give a tolerable measure of the degree to which they were in use at that date. Mudge's chronometers were sold at 150 guineas each, and the Admiralty declined, partly on account of their high price, to give any other than occasional orders for the use of the Navy. There is a letter, as we are informed by the courtesy of Sir George Airy, written by Captain Hurd, R.N., then hydrographer to John Pond, Esq., then Astronomer Royal, dated September 1821, in which he says, 'These instruments when first placed in my care did not exceed thirty;' but the date of the first trust is not given. Captain Hurd proceeds to give a list of the chronometers, the property of the Government on the 3rd of September, 1821; their number was 131.

At the present time the number of Government chronometers is about 1090. Most of these are on actual service; some are at the depots of Portsmouth and Devonport; some in the hands of makers for repair, and 141 at the Observatory. The number in private hands must be enormous. Few well-appointed ships sail without carrying at least three of them, but there is no

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means of making even an approximate estimate of their number. They may be said to be in general use.

As regards the degree of dependence which may be placed on them, those most competent to judge estimate that, supposing the rate of a chronometer to have been determined from six weeks' rating, and the ship then goes on a voyage of six weeks, it would be possible and fair to suppose that the mean rate may have changed 10 seconds of time per week, and this change of rate would produce at the end of six weeks an error of 1 minute of time, or at the equator, 15 miles of longitude, about 9 miles in the English Channel. But it must not be supposed that in practice such an error would occur; there are many methods of ascertaining the rate of a chronometer, and in careful hands such an error would be noted and allowed for, at any rate, with approximate accuracy, and that in result would be the same as if no variation of rate had taken place at all. Besides, observation shows that where more than one chronometer is used, the variation of one may be partly depended upon to correct the variation of another, and the mean of two or three instruments, though not absolutely true, will be much nearer the truth than any one taken singly. In short voyages, such as an expedition to pick up a cable, if a sufficient number of chronometers is taken, and the rates at starting are known, error is almost eliminated.

The difficulty of trusting implicitly to chronometers for longitude in our Arctic Expedition arises from this circumstance: that in all probability the Expedition may arrive at its most distant point (where it will be locked fast for a time) some months after leaving the last point of well-defined longitude, and that it is impossible to say how wild the rates of the chronometers may have been during those months. And this arises not only from the length of time, but also from a chronometrical fact which has not yet been brought under control; namely, that when the temperature is at or about the freezing-point of water, the rates of chronometers become unmanageable. No form of compensation yet tried has succeeded perfectly in correcting this. It may possibly depend on the quality of the oil: in that case it is likely to be different for every chronometer, or for every different maker's chronometers. Increase of temperature usually retards the rate of a chronometer, and vice versa. The object of what is called by makers' compensation' is to correct this defect, and produce uniformity of rate in spite of change of temperature. This is effected by the adjustments of weight to the balance; but it is a delicate, slow, and, consequently, costly process, and, moreover, can only, in the present state of

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science as applied to chronometer making, be partially successful; and for this reason: the diminution of force in the spring proceeds uniformly in proportion to the increase of heat, and may be represented graphically by a straight line inclined at some angle to another straight line, which is divided into degrees of temperature. But the inertia of a compound balance cannot be made to decrease quite as fast as the heat increases; and therefore its rate of variation can only be represented by a curve; and, consequently, only coincide with the straight line representing the variation of force in the spring in two points. In other words, the compensation can only be exact for some two temperatures for which you may choose to adjust it.

But supposing the Greenwich time to be known by reference to the chronometer, or in any other way, it is necessary to find the time at ship wherewith to compare it. When the sun is rising or falling rapidly, generally about three hours before or after noon, the observer takes a series of altitudes with a sextant, and notes the corresponding times. He then takes the mean of the altitudes and the mean of the times, and applies to the mean altitude all the necessary corrections. He will then, by reference to his journal and to the Nautical Almanac,' become possessed of the information necessary for his calculation.

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It may assume, we will suppose, something like the following form January 11th, 1876, at about nine o'clock in the forenoon, observed the sun's altitude, which (when corrected) was 23° 39'. The declination (corrected for time and longitude) was 21° 44' S.' Whence the sun's polar distance was known to be 111° 44' (because from the Pole to the equator is 90°, and from the equator to the sun ex hyp. 21° 44'-111° 44'). The latitude, by account, 35° 55' N. Required the local time of the observation. The mean of the times of the observation, corresponding to the corrected altitude, is the Greenwich time by chronometer, which has been obtained by applying the accumulated daily rate of the instrument to the error on Greenwich mean time, shown by it when last ascertained at a standard observatory. The local time is to be compared with the time thus determined. The observer will now have the means of constructing the diagram (Fig. 2, p. 166). For, as the elevation of the Pole is equal to the latitude, he can mark the position of the Pole, and also of the equator, which is 90° from the Pole. The sun's declination being known, the position of the dotted line is determined. The sun's altitude is 22° 39', and as he must be on the dotted declination circle, and his distance above the horizon is known, the sun's place can be pricked off at S. The meridian passing from north to south through the sun

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