beats number in health about 70 or 75 per minute, so that we should allow about 305 yards for each pulsation.

We may also hum the time of a quick march, beating the feet in time and counting the number of paces; then multiply the number of paces by 210, and we obtain the number of yards. This latter method we have found a very rapid one and very accurate.

Should the reader be desirous of entering more fully into the subject of surveying, sketching, &c., he should procure some work which treats entirely of this subject, supply himself with a pocket-sextant and a compass, and practise in the manner recommended in the works he may possess. It is also a very

good plan to practise drawing a plan of the roads between any two places we know by memory alone, and then comparing our plan with a correct map. We may thus acquire a knack of representing ground from memory alone, which in itself is a very useful accomplishment, and one that aids us considerably when we undertake any regular survey or sketch.

PERSPECTIVE AND SKETCHING.

Perspective is the art of representing on a flat surface objects as they appear in nature, not as they are.

The first step towards comprehending the effects of perspective is to hold up a piece of glass, and look through at two parallel lines which are directed

nearly towards us. A wall, the side of a house, or a straight road, the sides of which are well defined, will serve for this purpose. It will then be found that as these lines approach nearer to each other, if they are traced on the glass, the farther they are from us.

Unless we understand the most simple rules of perspective, all the drawings or sketches we make are painful to the eye of any real observer of nature. The first proceeding in perspective is to fix on the point or points of sight, the point of sight being the point towards which the parallel lines in nature will each point.

The point of sight, as a general rule, is on the same level with the eye, and directly opposite where we happen to be standing.

We will first take the simple cube, that is, a block of wood or square box, to represent in perspective, as an example of one point of sight.

Suppose A B C D, Fig. 1, to represent a side of a box, this side being placed opposite to us, but slightly to the left. Having drawn the face A B C D, we will draw the horizontal line R S on a level with the eye, and mark s, the point on this directly opposite to us: the sides of the cube, viz., D Q, B Y, A X, will all be directed to the point s, and if produced would meet there. Supposing the cube to be transparent, the sides C P, P Q, P X, would be visible, as shown in the diagram.

We will next take for example the interior of a room, the floor of which is boarded, to show the effect in perspective of parallel lines. Suppose we are standing at F, Fig. 2, then the height of the eye marked at s would be the

point of sight. A B being the breadth of the room, and A G the height, the lines A C, B D, GE, H F, are all directed towards s, and if produced would meet at s. Each of the boards also has its sides directed towards s, and thus appears to decrease in breadth the farther it gets off. As an example of the painful effect of bad perspective, two pictures are shown on the walls, one, P, drawn so that the sides, if produced, would meet at s; the other, Q, so that the sides are parallel to each other: the picture Q at once appears unnatural.

When we have to represent any objects of uniform size on a plane or horizontal surface, such as the sea, for example, our horizontal line will be the distant sea horizon; then this horizontal line will cut the masts of the vessel, or the shoulders of men, or any objects we may represent, at exactly the same

height. Thus in Fig. 4 there are four ships of equal size, each farther off than the other, but the horizontal line must cut the masts of each at the same height, as shown at A and B.

Again, if the vessels are the same length, and are anchored or sailing parallel to each other, we must draw these between two lines which converge and meet at the point of sight.

These are a few of the simple rules of perspective, which must be attended to in all sketching or representations of nature. Unless we do this all other portions of a sketch are mere failures as representations of nature, and are unpleasant objects for a skilled eye to look at. We will next consider

THE APPLICATION OF PERSPECTIVE TO SKETCHING.

Nearly every person either sketches or would like to be able to do so. To carry in the pocket a sketch-book, and to be able to represent the country in which he travels is a very general wish. Too many persons are, however, deterred from this amusement because their sketches are very unsatisfactory, or take too much time and trouble. The common error of young would-be artists is to take too much trouble about their drawing, to put too much on the paper, and to think too little about the meaning of their lines. A sketch may be made in pencil, and need not take more than five minutes, nor require more than a dozen lines. Here is an example:

A line of cliffs is here shown, with a portion of beach and the distant horizon. The cliff-line where it approaches us is drawn towards the point of sight of our sketch, and by this means we obtain the appearance of distance. Again, on the beach we have two or three lines, which as they approach us separate farther from each other, just as in the example of the boards in a room in Fig. 2. If we count the lines in this sketch, we find there are two for the cliffs, three for the beach, and one for the horizon, making six in all. Two or three strokes on the cliff, showing jutting-out portions, merely add to the form of the cliffs; without these we have a sketch of a coast.

Another point to which we may call attention is that all circular lines on the ground appear ovals when seen from a distance; thus a circular bay in our coast sketch becomes a portion of an oval when put on paper.

A

When any additional life is required in a sketch, we can give this by many means a man or a tree, a boat or an animal, may all serve our purpose. flock of birds are represented in our coast sketch, but these are put in in perspective; they get smaller and smaller as they are farther off, just on the same principle that the small vessels did in Fig. 4; and these few items make up a coast sketch which is, at least, not offensive to the eye-for that which truthfully represents nature is never unpleasant to look at, whilst that which falsifies her is ever hurtful to the eye.

A sketch of an undulating country is usually very attractive, but is considered by the young amateur very difficult. The fault here is usually attempting too much. There is an endeavour made to put in all that is seen, instead of only the most prominent items.

We should first draw some six or seven lines across the paper, and meeting each other, as shown in the annexed figure, the lines nearest to us being dark

FIG. 6.

and bold, whilst those more distant are finer, these lines representing the undulations of the country.

On these lines we may build up our various objects, taking care that they

FIG. 7.

graduate in size according to their distance. The annexed sketch represents some filling in added to the lines, and would occupy about four minutes in execution.

The lines of a sketch may be divided into three classes: those for the foreground should be bold, those for the middle distance medium thickness, those for the distance very fine and delicate.

Sketching obliges us to be great observers of nature and of natural objects, and we can then represent even from memory such things as vessels or animals, vehicles or trees; but we should, whenever possible, make accurate sketches of any objects which indicate distinctly any locality. Thus the fishing-boats of seaports, the lobster-pots of the coast, any peculiarly-shaped building, &c.,

are all valuable reserves, for a fishing-boat may be found wonderfully useful to give life to an otherwise dull sketch, but this boat must be accurately drawn from any point of view to be of real service. If we have by practice acquired considerable skill in representing any particular objects, such as horses, cows, men, or boats, we need not hesitate about placing these in the foreground of our picture; if, however, we are not skilful in these details, we should place these farther off, or not draw them at all.

Cows and horses add greatly to the life-like appearance of a rough sketch

and both these can be very readily obtained in the following manner. For cows draw rectangles, as shown in the annexed Fig. 8, with two detached lines as there shown. These serve as frameworks on which the cows may be built, as shown in Diagram 2. Groups of cows may thus be roughly sketched, and with good proportions, especially if attention be given to details. Again, for a horse draw three ovals, as shown in the annexed Fig. 9; then on these build an outline as shown in Diagram 2, all the detail being a mere matter of care and observation.

There are few amusements which call forth more observation than sketching, and few which repay us better. A sketch-book is always interesting: it recalls past scenes and country; explains often better than pages of writing the style of country in which we have travelled, and, in fact, is a pictorial history in itself. In a long experience we never yet heard any person capable of sketching say that he found his skill of no amusement or use, whilst hundreds have stated that they were never at a loss for occupation as long as they could sketch. Again, regrets often repeated have come to our ears from those who, not capable of sketching, have lamented their want of early attention to this art, and who have frequently remarked that, had they only been able to sketch, they could have delighted scores of their friends by a representation of the strange scenes they had witnessed.

Young would-be artists are usually fond of obtaining prints, and on these daubing brilliant colours, thus defacing what was before worth looking_at. Let such fancies be put on one side, and in their place let a taste be acquired for real art, when a few weeks or months will enable these daubers to produce something worth looking at, though it be only half a dozen simple lines,