can now be drawn: and the angle h, made by the sun's meridian with the primitive circle (which is the meridian of the observer) is the hour angle to be obtained.

He now draws a line from his zenith, through the sun to the horizon, and he is in a position to solve the value of each of the three sides a, b, c, and consequently the angle at h.

It will be seen by the figure that the side a is the complement of the altitude to 90°; the side b is the Polar distance which is known, and the side c is the complement of the latitude to 90°. Therefore, having the value of the three sides, the value of the angle h is at once obtained by a known formula of spherical trigonometry. The hour angle h is apparent time, to which the equation of time must be applied to convert it into mean time. It is then compared with the time by chronometer, and the result is the longitude.

It must not, however, be assumed that every mariner who can compute the sun's hour angle understands, or is required to resort to, spherical trigonometry. A simple form is provided which can be used with complete success even by those who are completely ignorant of the principle on which it is based. This is another instance of the success of modern navigation, in bringing the results of a purely mathematical inquiry within the reach of any person who has sufficient training to work an ordinary sum with accuracy. We give, for the amusement of those readers who may be curious on the subject, the form used in navigation.* It will be seen that the only demand upon the

The nautical formula is as follows: Add together the altitude, latitude, and Polar distance; take half the sum, and from it deduct the altitude; note the remainder.

the seaman's attention is to add certain quantities together, and then to take out of tables four logarithms. The addition of these gives, in the shape of a resulting logarithm, the quantity he is in search of. He need not trouble himself about principles at all; indeed, he could work the problem equally well if he had never heard of a spherical triangle in his life. Yet the mathematical reader who examines the form will be amused to see how neatly the aid of spherics has been called in. It will be seen that to illustrate the mode of work, the case solved is that supposed in Fig. 2.

On exactly the same principle the sun's azimuth is obtained for correcting ships' compasses at sea. The same figure as that before used will illustrate the case. Here the angle z is required, which is the supplement of the angle between the meridian and the circle of altitude passing through the sun.

remainder. Add together the logarithms of the secant of the latitude, the cosecant of the Polar distance, the cosine of the half sum, and the sine of the remainder,' the resulting logarithm will give the sine of half the required arc, which multiplied by 2 is the hour angle.

Taking the observation supposed in the text for illustration, it will be seen (Fig. 2, p. 166) that by observation and correction

To find the angle h in the A ZPS having given the three sides

Hence the formula, from which it results that the hour angle is 2h. 27m. 15′′. Apparent time is therefore 21. 32m. 45".

We

We have now described the principles upon which observations both for latitude and longitude are made at sea. We have probably said enough to show that success depends, when the principle has once been mastered, on attention to exceedingly small details. But it has been impossible even to indicate the minuteness with which careful observers proceed. Chronometers, sextants, and such like instruments, are guarded with almost ludicrous jealousy. There is no greater crime than to touch a man's pet sextant, and a stranger may hardly breathe in the same room with his chronometers. The latter are slung in gimbals, and packed in carefully-stuffed boxes. The boxes are packed in sawdust, and screwed to a block of wood, which in its turn is bolted to the beams of the deck below. They are brought on board at the beginning of a voyage slung in a handkerchief and carried by hand. If they travel by rail a fresh system of screws, springs, and elastic outer casings is devised to prevent the delicate machines from experiencing the smallest jolt. An Admiralty order exists prohibiting the sending of any Government chronometer by any other than a passenger train. So closely are their performances watched, that a minute discrepancy (thirty-three seconds) in a chain of meridian distances, measured by chronometer round the globe, was accounted for by Admiral Fitzroy by the suggestion that the chronometers had been affected by magnetic action in consequence of the ship's head having been for considerable times together in the same direction.*

It is impossible to bring a paper like the present to a close without remarking on the great and rapid rise of the standard of nautical education which has taken place in the last few years. Under the provisions of the Merchant Shipping Act, 1854, no foreign-going ship can obtain a clearance from any port in the United Kingdom unless the master or mate, or both, according to the size of the vessel, possess certificates of competency from the Board of Trade.

At first the periodical examinations held at various ports were comparatively easy. But the crowds of applicants for examination were soon so far in excess of the demand for skilled officers (we speak of the merchant navy) that the standard of examination was gradually raised till it now represents in successful candidates a very complete knowledge of the art of navigation, as well as of practical seamanship in all its branches. We believe that the amount of knowledge of the method of nautical astro

* The distances having been measured by taking the mean of several chronometers, some of which, if they differed, must have been wrong, would account for this sufficiently without any fanciful explanation.

nomy

nomy now required is amply sufficient; and that if any increase of stringency is found practicable or expedient, owing to the greater spread of education or the increasing popularity of the merchant naval service, it had better be applied in demanding more groundwork than more superstructure. We have already observed that the ingenuity of mathematicians has been applied to devise formula, which should be easily worked without a preliminary knowledge of the mathematical considerations on which they are based. We venture to suggest, instead of requiring applicants to take up more, or higher, subjects in navigation, as it is said the Board of Trade intend to do, that the questions already asked should be more thoroughly understood; that formulæ should not be used without their mathematical proof, and that an appropriate diagram should be required to accompany every solution which admits of being solved by construction. It would be possible to pass the Board of Trade examinations simply by learning formula by rote, and applying them by means not much to be distinguished from what is called 'rule of thumb.' Nevertheless, it has been matter of considerable surprise to us to see the amount and extent of information which our merchant navy officers have proved themselves to possess. Every man holding a Board of Trade certificate has passed through an ordeal, of which we can say from observation that it is most thorough and searching. It appears to us faulty only in the particular just noted. A master must be twenty-one years of age, bring good testimonials and certificates of service, and in addition to good writing, the first five rules of arithmetic and logarithms; he must be able to work a day's work with the distance and bearing of the port he is bound to by Mercator's and the other usual methods; to perform all the corrections required by articles in the nautical almanac; to find the latitude (thus far the same rule applies to candidates for the certificate of a mate) by sun and star both on and off the meridian; to observe and calculate the amplitude of the sun, and deduce the variation of the compass therefrom; to observe and compute variation by azimuths; to find the longitude by chronometer and observation of the sun; to compare and keep the rates of chronometers; to know the law of the tides, and ascertain the state of the tide in any part of the world by the known time at the full and change of the moon; to explain the nature and mode of determining the extent of the attraction of the ship's iron on the compass. He must also pass a thorough examination in seamanship, rigging ships, shifting large spars, masts, sails, &c.; dealing with any conceivable kind of wreck; making jury rudders, rafts, and so on; the

management

management of mortar and rocket lines in case of the stranding of the vessel. He must also understand signalling, so as to know at a glance the character, and in many cases, the meaning of signals made without the signal book. It is amusing to an outsider to see the certainty with which candidates tell the subject matter, if not the exact meaning, of 'a hoist' of two, three, or four flags shown by the examiner. Not least important is the searching examination he will undergo as to the rule of the road at sea.' It were well if these rules were as well observed as they are accurately known. Lastly, he is examined as to the pilotage, lights, buoys, beacons, shoals, and mutual bearings of places of some one channel or sea with which he is most familiar; the English and Irish seas being those most generally proposed. This summary of the principal heads of the examination, which is carried out very conscientiously, will be satisfactory to those who look to see our mercantile navy keep pace with the general educational improvement of the present day.

ART. VI.-1. C. A. Sainte-Beuve. Sa Vie et ses Œuvres. Par le Vte. D'Haussonville, Député à l'Assemblée Nationale. (M. L.) Paris, 1875.

Par

2. Souvenirs et Indiscrétions. Le Dîner du Vendredi-Saint. C. A. Sainte-Beuve, de l'Académie française. Publiés par son dernier Secrétaire. Paris, 1872.

TO-M

'O-MORROW!' exclaims Mr. Phoebus to Lothair, tomorrow the critics will commence. You know who the critics are. The men who have failed in literature and art.' This is certainly not true of the literary critics of our time, who comprise an absolute majority of the most successful authors, e.g. Scott, Southey, Moore, Hallam, Sydney Smith, Gifford, Brougham, Milman, Lockhart, Lord Stanhope, Lord Houghton, Mill, Carlyle, Froude, Macaulay, Lytton. Moreover, success in criticism, like that of Jeffrey or Sainte-Beuve, is success in literature; but one of these, Sainte-Beuve, might be cited as giving the semblance of plausibility to the paradox; for, if he did not actually fail in literature, his reputation derives comparatively little lustre from his original compositions in prose or verse. The Causeries du Lundi' have thrown Joseph Delorme' and Volupté' into the shade, and it is pre-eminently as a critic that we feel bound to reconsider his claim to the high place mongst the classics of his tongue which the general voice of is countrymen has gradually and reluctantly, compulsively ather than impulsively, assigned to him.

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