it now stands, holds the shipmaster responsible for the proper use of means for preventing the shifting of cargo, and we may add the law has on one occasion been put in force. In a former number of this Magazine there is a detailed account of a case where a conviction was obtained under the Act of 1875, a cargo of linseed in bulk having shifted, the shifting boards being inefficient, and no other efficient arrangement having been made.

It has been urged as a reason for prohibiting the cargo of grain in bulk, that the cost of bags would be very trifling, perhaps no more than that of shifting boards; if such be the case, it is pretty certain that bags will come into use, whether there be fresh legislation or not; but if bags are really much more expensive than boards, and if their use is unnecessarily enforced, the extra expense of them will not fall upon the shipowner, but upon those for whose use the corn is imported. In deprecating unnecessary interference on the part of the Legislature with the shipping of this country, we do, in the first place, advocate the cause of the British shipowner, as against his unfettered foreign rivals; this, however, is a small matter compared with the interest of the millions who are dependent for their food supplies upon foreign-grown corn. Unnecessary restriction, involving expense to the shipowner, must be paid for in increased freight, and increased freight falls ultimately upon the consumer.

THE NEW NAVIGATION AND SUMNER'S METHOD. (Continued from page 30.)

Errors of Observation.—It is no purpose of ours on the present occasion to discuss the theory of errors of observation, which is known to the few, though not to the many; we are, however, more especially writing for the latter, and may therefore be permitted to make such cautionary remarks on this subject as we have reason to think will be appreciated. If we admit of no errors in the elements taken from the Nautical Almanac, a very small error

*Nautical Magazine, July, 1878, page 623.

in the Greenwich time by chronometer, and no appreciable error in the assumed latitudes, there still remain the errors in the altitudes, and these must always more or less effect the determination of the position of the ship. Errors of observation are partly accidental, and partly systematic; some cancel each other, but there must always remain a residue which, however, under ordinary circumstances, and with the exercise of a little judgment and caution, may be considered as a minimum.

There may, possibly, be a slight imperfection, at a particular part of the sextant, in the graduation of the arc; having ascertained this, keep a memorandum of the number of degrees over which it extends, and remember that at a certain spot it will be a maximum, gradually decreasing on either side. As regards the "finding of the index error," ample instructions are given in every work on Navigation; having found it by the "off and on " readings, apply it as an error to the observed altitude; however good a mechanic you may esteem yourself to be, avoid tinkering with the adjusting screws. If you have not habitually used the telescope, do so forthwith, and always be particular as to the adjustment of the line of collimation; also, remember that the more you can narrow the field of observation, the more accurate will be the altitude and the contact between two objects. The shades may always be suspected, and they sometimes give a very large error; but there is little need to use them; for the sun, a dark glass at the eye end of the telescope is preferable, as by this arrangement the rays from the object and the image are alike affected, and the angle between them remains unchanged. When using the telescope you must close the eye not required for vision; with the tube it is sometimes preferable to keep both eyes open.

For an altitude of a star or planet, it is always safe to begin by placing O on the vernier to O on the arc, then, looking at the object, gradually bring it down to the horizon by moving the index onwards; proceeding in this manner, when two or more bright stars are near together, as, for instance, Castor and Pollux, you are sure which star you have brought down.

Assuming that the instrumental errors are known, there yet remains an error which, with some persons, is as great, if not

greater, than any other. We refer to what is usually called the personal equation. Being due to a physiological cause-an imperfection in one or more of the organs of the body-the result is a constant retardation or acceleration of an event; in fact, a bad contact is made; and it even extends to an imperfect reading off of the indications of the arc; as such, it is a systematic error peculiar to the individual-essentially his own, which, however, with a little care, can be ascertained and properly applied; in health it is a constant, when ailing it slightly varies in amount, but does not change from plus to minus, or vice versa.

It is well known that refraction varies at times very considerably; it also produces an effect upon the dip. An unusual amount of refraction is generally recognisable by the sense of sight; but the extent to which it may alter the ordinary "correction of altitude cannot be determined with certainty. As a rule, whenever the altitude is observed at less than 10°, the mean refraction may be in error more than 1', and should be corrected by the attached barometric and thermometric tables; for precision, this is necessary in all cases.

It may be taken as generally correct that all systematic errorsthose due to the instrument and the observer-are under control, and may be checked; the accidental errors—those due to external causes-are only to be partially apprehended and appreciated. Under ordinary circumstances the errors of observation when taken together (exclusive, of course, of any personal equation) should never exceed 2' to 3′; they may, from adverse causes, and the state of the weather and sea, amount to 4' or 5'; when they are produced as the result of an abnormal refraction they may exceed 15′; but in no case can it be certain that an altitude has been observed within 1'.

It has been necessary to say this much, because there can be no doubt that the problem under discussion is destined to take a very important place in navigation; the accuracy of most of the determinations will much depend upon the accuracy of the observations, and hence chiefly, though not wholly, upon the skill and judgment of the observer. Owing to errors in the altitudes, it is certain that the position of a point cannot be ascertained at sea;

but as we may often fix the limit of the errors, we are enabled to describe a quadrilateral figure within which is the place of the ship, and which may at once be aptly described as a surface of position and certitude.

What we want to know is the position (latitude and longitude) of the ship by projection on Mercator's chart, after having made a few easy computations on the basis of the usual "chronometer problem;" the data being elements, some of which are exactly, and others nearly, correct, and among which are introduced certain assumptions derived from the estimated parallel on which the ship is found to be by the "dead reckoning." The rules, briefly stated, are as follow:

From an altitude of a celestial body taken at a given Greenwich time, to find the curve of position of the observer by projection on a Mercator's chart.-The circle of position as delineated on the sphere becomes, when transferred to Mercator's chart, a curve of position, which can only be laid down by a series of computed points. For any given altitude you can select any number of parallels of latitude crossed by the required circle. For each of these latitudes, with the true altitude deduced from the observed, and with the polar distance of the celestial body taken for the Greenwich time, compute the time at place, and thence the longitude by chronometer. Each latitude with its corresponding longitude gives a point in the circle of position. You may, by way of experiment, compute several (say ten or a dozen) such points for intervals of 30' of latitude; then, having plotted these different points on Mercator's chart you obtain, by joining them, a portion of the curve of position.

In practice, it is generally sufficient to lay down only two points; for, the approximate position of the ship being known, two latitudes are selected, such that the ship may be assumed to be between them.

To find the Latitude and Longitude of a Ship by circles of position projected on a Mercator's chart.-1. Let the altitudes of two objects be taken at the same instant. Assume two latitudes, embracing between them the ship's probable position, and find two points of each of their two circles of position as before stated, and

project these points on the chart, each pair of points being joined by a straight line, the intersection of the two lines is very nearly the ship's position. If the intersection does not happen to fall between the two assumed parallels, then, for greater accuracy, assume another latitude, such that it shall do so; compute and project again. If one person observe both altitudes, it will be necessary, as they are not exactly simultaneous sights, to take the Greenwich time for each observation; if quickly done the small change in the ship's position in the interval will not greatly effect the result.

2. The altitude of the same object-as in the case of the sunmay be taken at two different times, and the circles laid down as before. When the ship has changed her position in the interval between the two observations, either the usual reduction of the first altitude for change of place must be applied, or as is more practical-the circles of position for each observation having been projected, the first must be moved parallel to itself in the direction of the course made good, and by a quantity equal to the distance run; the intersection of its new position will give the place of the ship at the second observation.

and also somewhere on B, the intersection of the two lines at the point P at once determines the position.

But in Fig. 7 if, as in the case of the sun, where there has been an earlier and later observation, with a course and distance run in the interval, we, as before, project a line A as that on some part of which the ship is supposed to be at the time of the first observation; and B the line as derived from the second observation;