THE UNIVERSITIES.-III. CAMBRIDGE.-I. We purpose in this, and another article which will follow, to give our readers some slight sketch of the University of Cambridge, and of its mode of proceeding to degrees, coupled with a few hints on the general course, and the method of passing through its curriculum with the least possible expense. Our remarks will form, so far as our space will allow, a brief practical guide to the student who desires to obtain from this University the degree of B.A., as well as to candidates for the "non-gremial" examinations, as they are called, for boys and young men, and the examinations for women, which this University has been the first to institute. Let us first of all distinguish between the colleges and the University. Of the former there are seventeen, and these together form the University, which has its own proper officers selected from the resident members of the colleges. It is necessary, therefore, for a student, first of all, to become a member of a college, and then on going into residence he will matriculate as a member of the University. To become a member of a college, it is necessary to produce a certificate, signed by some Cambridge M.A., to the effect that he believes the candidate to be a person qualified, "both as to learning and moral character," to be a member of the college. At St. John's and Trinity there is also an entrance examination. This, of course, is only intended to exclude such as are not up to the standard of the lectures delivered in the college. At some colleges also the baptismal certificate is required. statics, optics, Newton, and astronomy. An interval of about ten days then elapses to allow of the examination of the papers in these subjects, and a list is then issued of the candidates who have satisfied the examiners. Those only whose names appear in this list are admitted to the five days' examination, which embraces all the higher branches of mathematics. The marks obtained in both examinations are added together to determine the order of those who pass in mathematical honours, and obtain the degree of B.A. either as wranglers (first class), senior optimes (second class), or junior optimes (third class). A student who goes up to Cambridge with a fair knowledge of mathematics can scarcely fail to pass this examination by merely following and using the lectures of his college. But to obtain a good place it is almost absolutely necessary to have the assistance of a private tutor, in undergraduate language called "a coach." To any one considering the question of expense this will be a serious drawback, and more will therefore be said on the subject under the head of "tuition." Suffice it here to say that, starting with a fair knowledge of Euclid, algebra, trigonometry, and perhaps a little conic sections, a man of ordinary ability may reasonably expect to place himself, by the aid of the college lectures alone, amongst the senior optimes. At St. John's and Trinity the college lectures are said to be sufficient to place a man, by hard work on his own part, amongst the wranglers. Some years ago it was believed that the degree obtained by just passing into the junior optimes was the easiest of all. Happily, the tendency lately has been to make this much more difficult. The examination for the classical tripos is held in the latter half of February, and consists of papers in It is advisable that the student should decide, either before Greek and Latin, prose and verse, composition, translation from or immediately after commencing residence, as to the course of the standard Greek and Latin authors, and ancient history. reading which he intends to pursue. He may take his degree The list of those who pass is arranged in three classes, accordeither in honours or in the ordinary examination. If he decide ing to the number of marks obtained by each student. This for the former, he will pass the previous examination after one tripos is of much more recent date than the mathematical, and year, and there will lie open to him the mathematical, classical, until lately did not entitle to a degree. To take a good place moral science, natural science, and law triposes. The examina- in it, it is absolutely necessary to have undergone a thoroughly tion for each of these is held once in the year; and the whole of good classical training and grounding while at school. For the the student's readings should be specially arranged with a view mathematical tripos a man may prepare himself by diligent to the final examination. On this part of the subject we shall 'coaching" after going into residence, but this cannot be done make a few mere remarks further on. If he decide for the in the case of the classical. It will be useless for any to attempt ordinary degree, he will-according to the new scheme issued it who have not a sound groundwork of Greek and Latin knowby the Council in May, 1865, and recently put into operation-ledge before entering the University. The examination ranges have to pass three examinations over the whole field of classical literature, and its object is to i. The previous examination, or "little-go," about the end of test the knowledge rather than the memory of the candidate. the first year of residence. ii. The general examination at the end of the second year. iii. The special examination at the end of the third year. The student's choice will, in some cases, be guided by the question of expense. For the ordinary or poll degree it is only necessary to reside from October in one year to the following May two years. This is the shortest possible time, inasmuch as the University requires a residence of nine terms (of which there are three in each year) before granting the degree of B.A. For honours, on the other hand, although the number of terms required by the University is the same, yet the residence cannot be less than three years, on account of the times at which the examinations are held; and the time can only be made thus short by going into residence in January, whereas the generality of students go into residence in October, and the course of college lectures is framed, reckoning that as the commencement of the academic year. The student, therefore, who goes into residence at any other time does so under considerable disadvantage. On the subject of terms, it may be sufficient to say that there are three in the course of the year: the Michaelmas or October term, from October 1 to December 16; the Lent term, from January 13 to the Friday before Palm Sunday; the Easter or May term, from the Friday after Easter Monday to the last Tuesday but one in June. To keep any term the student must reside in college or in a lodging-house licensed by the University, and must dine in hall and attend chapel during two-thirds of the above specified periods. It is with a view to this that the pieces are selected, and it fre- We have now to make a few general remarks upon the honour VOL. III. 71 We have thus passed in review all the honour triposes. We have now to consider the ordinary or poll examination, which confers, probably, as many degrees as all the triposes put together. The scheme which we have to describe is a new one, only recently come into operation, and the change has been made with a view to rendering the course of education more comprehensive, and enabling the student to prepare himself during his last year of residence for that occupation or profession to which he is destined. To take this, which is called the Poll degree, the student will have to pass, as we have mentioned above, three examinations. The first, or "Previous Examination," occurs about the end of the first year of residence. This is required of all, whether candidates for honours or for the ordinary degree. But the former are required to pass in what are called "Additional Subjects," as well as in the ordinary in the practical application of mechanics and hydro-mechanics, heat, electricity, and magnetism. It will be necessary for the student to have previously attended a course of lectures by the professor of that subject in which he purposes to take his degree. These are the various methods by which a student may attain the object of his residence at Cambridge. In our next we shall consider the general subject of expense, under which tuition will be included, and give some account of the various emoluments and rewards which the University and colleges hold out for the encourage ment of successful competitors. LESSONS IN ARITHMETIC.-XLIV. CROSS MULTIPLICATION. subjects, which are common to all, and consist of the following, 9. A METHOD much used in practice by workmen in finding viz. :- (3.) The same of some Greek classic. (4.) One of the four Gospels in the original Greek. (5.) Paley's "Evidences of Christianity." (6.) Euclid I., II., III., VI. 1—-6. (7.) Arithmetic. It is obviously necessary that the student should have some knowledge of these before going into residence. The additional subjects for those who intend to graduate in honours are— (8.) Elementary Algebra. (9.) Elementary Trigonometry. (10.) Elementary Mechanics. Of this examination it may be enough to say that, as it is intended for all alike, the standard in the ordinary subjects is necessarily low, the chief difficulty being found in the Grammar paper. The standard in the Additional Subjects is, of course, higher; and it is important to remember that a minimum of marks must be obtained in every paper, or the candidate will not pass. After this examination, candidates for honours are not called upon again by the University until the time of their tripos. But for poll men the General Examination occurs about the end of the second year of residence. The subjects are-(1.) The Book of the Acts of the Apostles in Greek. (2.) One of the Latin classics. (3.) One of the Greek classics. (4.) Elementary Algebra. (5.) Elementary Mechanics. (6.) Elementary Hydrostatics. (7.) English Prose Composition. (8.) Latin Prose Composition. The last two papers, however, are not compulsory, but the marks obtained in them are added in to the sum total, which determines the order in the list. This, when published, is divided into four classes, the names being arranged alphabeti cally. After passing this examination there lie open to the student five different subjects in which he may obtain his B.A. degreei.e., in theology, law, moral, natural or mechanical science; and the University desires, in thus extending their range of the final or, as it is called, Special Examination, to enable a man to read in his last year those subjects which may be most useful to him in after life. This examination is held at the end of the third year of residence; and the list, when published, is divided into two classes, of which the first only is arranged in order of merit. The theological branch consists of papers in(1) A book of the Old Testament in English. (2) One of the Gospels in Greek. (3) Two of the Epistles in Greek. (4) The History of the Church of England down to 1688. The moral science branch is divided into the three heads of moral philosophy, history, and political economy; and the candidate must pass in one of these heads. The law branch consists of papers in(1) Justinian's Institutes. (3) Lord Mackenzie on Roman Law. (3) Malcolm Kerr's abbreviated edition of Blackstone. The natural science branch is divided into four heads, in one of which the student must pass-viz., chemistry, geology, botany, and zoology. The mechanical science branch consists of papers areas, is called Cross Multiplication. In theory it is the same as the method of duodecimals, but the operation is arranged in a rather different form. of a foot, which is an of a prime, called a Primes, seconds, and The dimensions used are:-A foot; inch (sometimes also called a prime); second; of a second, called a third. thirds, etc., are denoted by one, two, or three, etc., accents respectively written above the numbers, and a little to the right. Thus, 5 feet 2 inches (or primes) 4 seconds and 25 thirds would be written 5 ft. 2' 4" 25"'. EXAMPLE. (1.) Find the area of a rectangular board 12 ft. 7 in. long and 4 ft. 3 in. wide. 9" is 144, or 5 x 12 square inches. of a square foot, or 9 square inches. Hence, to reduce the square primes and seconds in the product to square inches, multiply the primes by 12, and add the seconds to the product. Hence the result is 53 square feet 69 square inches. 10. It will be seen from the above that feet X feet give (square) feet, feet X primes give (square) primes, feet X seconds (square) seconds, and so on. Primes x primes give (square) seconds, primes X seconds (square) thirds, seconds X seconds give (square) fourths, and so on. Hence we see that, in multiplying any denominations together, the denomination of the product is got by adding together the accents placed above each number which we multiply, observing that the numbers expressing feet have no accent or index above multiplier under the corresponding terms of the multiplicand. Multiply each term of the multiplicand by each term of the multiplier separately, beginning with the lowest denomination in the multiplicand and the highest in the multiplier, and placing the first figure of each line one place to the right of that of the preceding line, under its corresponding denomination. Finally, add the several lines together, carrying 1 for each 12 both in multiplying and adding. The sum will be the answer required. EXAMPLE.-(2.) Find the area of a board 9 ft. 7′ 2′′ long, and 3 ft. 4' 7" wide. We now subjoin some other examples connected with square and cubic measure, such as are of frequent occurrence, not confining ourselves to the method of duodezimals. EXAMPLE.-(3.) Find the cost of carpeting a room 24 ft. 6 in. long by 18 ft. 4 in. wide, with carpet which is of a yard broad, and costs 3s. 9d. a yard. 24 × 18} = number of square feet in the floor, and the breadth of the carpet is of a foot. Therefore the length of carpet in feet x ft. = area of floor in sq. Therefore the number of feet of carpet required EXAMPLE. (4.) What is the height of a room which contains 223 cub. yds. 7 cub. ft. 624 cub. in. of air, the area of the floor being 41 sq. yds. 12 sq. in. ? Since the cubical contents are obtained by multiplying the three dimensions of length, breadth, and height together, and the area of the floor is obtained by multiplying the length and breadth together, we shall evidently get the height of the room by dividing the cubical contents by the area of the floor. 223 cub. yds. 7 cub. ft. 624 cub. in. = 602893 cub. ft. 41 sq. yds. 12 sq. in. = 36912 sq. ft. Hence required = height in feet 602813 = 369 12 4129 = 217021 17716 39861 39861 = 602813 cub. ft. ÷ 4429. necessary to complete the covering of the floor, and its cost at 5s. per square feet; what is its length? 16. Find the cost of carpeting a room 17 ft. 6 in. long by 13 ft. 9 in. wide, with carpet yard wide, at 4s. 8d. a yard. 17. If a cubic foot of water weighs 1000 ounces, what must be the depth of a rectangular tank, which is 35 ft. long and 10 ft. broad, that it may just contain 1000 tons of water? 18. A roller being 6 ft. 6 in. in circumference and 2 ft. 3 in. wide, makes 12 revolutions as it moves from one end of a grass-plot to the other, and passes 10 times from one end to the other; find the area of the grass-plot. 19. What length must be cut off a plank 13 ft. broad and 9 in. deep, in order that it may contain 11 cubic feet? 20. A block of wood in the form of a rectangular parallelopiped* measures along its edges 181 ft., 51 ft., and 3 ft. respectively; And its value if a cubical block of the same wood, whose edges are all 11 in. long, is worth 3s. 6d. 21. On laying down a bowling-green with sods 2 ft. 6 in. long by 9 in. wide, it is found that it requires 75 sods to form one strip the whole length of the green, and that a man can lay down one strip and a quarter each day; find the area laid down in 8 days. 22. If a cubic foot of water weighs 1000 oz., find to what depth a ton of water will cover an acre. 23. A square foot of paper weighed 104.68 grains, and when 320 figures had been written on it, weighed 105 155 grains. If a strip of this paper 5 inches wide be taken to have written on it the circulating period of 10010s (which contains 100102 figures) in two lines at the rate of 5 figures in an inch, find the weight of the whole, and the length of the paper, and express this act in terms of the height of Salisbury spire, which is 400 feet. Errata. In page 142 of this vol., col. 2, line 40, for "24" read ";" line 41, for "1: 1:4," read "1:1:1;" and in line 42, for "7 lbs. of the third," read "5 lbs." SKETCHING FROM NATURE.-IV. THEORY OF SKETCHING. THE previous lessons upon Sketching from Nature have been almost entirely devoted to the practice; we must now say something upon the theory, and offer our pupils some advice upon the course they must pursue amongst the difficulties they will find in the principles and application of the art. During their progress they will meet with many perplexities, for which technical rules car. afford but little assistance, because the theory of art depends upon laws of quite a different nature. The rules we have given will help them over grammatical difficulties and assist them in the work of construction, and for these reasons they cannot be dispensed with; but they are incapable of giving those charms to a picture which it is the province of theory to impart, founded upon a right feeling for the beauties and effects of nature. Our pupils have now at their command a sufficient supply of geometrical information, as well as directions where to find it in these pages, and of which we hope and trust they will make good use; it will prove to be the best and most solid foundation whereupon EXERCISE 63.-EXAMPLES IN SCALES OF NOTATION, DUO- to build other principles to be derived from a close observation DECIMALS, CROSS MULTIPLICATION, ETC. 1. Transform 12345678 from the decimal to the duodecimal scale, and also to the scale of 7. 2. Transform 58367 from the decimal to the duodecimal scale. 3 Transform 57:39 from the duodecimal to the decimal scale. 4. Transform 67535 from the scale of 8 to the scale of 6. 5. Transform 79e658 from the duodecimal scale to the scale of 8. 6. Transform tetet from the duodecimal to the decimal scale. 1 ft. 10 in. wide ? 7. How many square feet are there in a board 15 ft. 7 in. long, and 8. How many cubic feet are there in a block 18 ft. 5 in. long, 4 ft. 2 in. wide, and 3 ft. 6 in. thick? 9. Find the area of a space 16 ft. 3' 4" by 6 ft. 5' 8" 10". 10. Find the area of a space 18 ft. 0' 5" 10" by 4 ft. S' 7" 9". 11. What will it cost to plaster a room 20 ft. 6 in. long, 18 ft. wide, and 10 ft. high, at 6d. a square yard? 12. How many bricks 8 in. loug, 4 in. wide, and 2 in. thick, will make a wall 50 ft. long, 10 ft. high, and 2 ft. 6 in. thick ? 13. Find the cost of carpeting the following rooms: (a) 18 ft. 4 in. long, 13 ft. 6 in. broad, with carpet of a yard wide, at 2s. 9d. a yard. (b) 14 ft. 6 in. long, 10 ft. 4 in. broad, at 10s. 6d. a square yard. (c) 16 ft. 11 in. long, 13 ft. 3 in. wide, with carpet 2 ft. 3 in. wide, at 4s. 7d, a yard. 14. A Turkey carpet 11 ft. 6 in. long by 9 ft. 8 in, wide is laid down in a room 14 ft. long by 12 ft. 6 in. wide; find the amount of oil-cloth of nature, and from a careful study of the numerous works of subject appears preferable to another. It may be the composition of the subject, or perhaps the display of colour it exhibits; or it may be owing to the effect of light and shade. Each of these circumstances is sufficiently important to create a preference. When we sit down to draw an out-door scene, the first questions that occur to us are: Does it compose well? Are the principal lines of the subject harmoniously arranged and connected with each other? Do any of the less important parts obtrude in such a way as to offend the eye with their masses and angles, to the detriment of other parts of greater consequence? These questions, and others of a like nature, will suggest themselves; and in the course of our experience we shall find out that we have the liberty, or licence, as it is termed, to modify the composition in such a way as to make it agreeable, without sacrificing the truthfulness of the whole. To apply these remarks, let us suppose we are about to draw a scene of which the view is limited; in other words, there is very little choice of position from which to take it. For instance, it might be a the subject-rather the contrary. It is admitted to be correct in principle and in practice to make the sky subservient to the rest of the picture, as it is capable of every variety of change in form, light and shade, and in colour, and yet it need not be false to nature. Besides, a sky can be made exceedingly service. able in giving effect, by increasing the mass of dark in a picture where it is required, or as a background to throw up objects that are in light. For instance, after a shower, when the sun has broken out, and its rays are lighting up buildings and objects in the distance, the retiring dark mass of clouds, as they dip below the horizon, give, by contrast, additional brilliancy to the effect of the sunlight. Fig. 6 is an example of the right-angular form, of which a line in the direction from A to B (taking the lines of the hills and the trees) forms the hypothenuse; the ground, the base, and the upright trees on the right, form the perpendicular. In a subject like this the above arrangement assists the perspective, and many artists do not hesitate in the least to make such alterations in the disposition of the parts, that they may be able to tower or ruin, having its most interesting part concealed by trees. The licence we speak of would permit that the position of the trees might be changed, or their branches directed another way; or they might be thinned or cut out so as to admit a view of the part we wish to preserve. Much of this may be done without in the least altering the character of the subject. We give this simply to supply an instance where the taste and judgment of the artist must be exercised. One of the most pleasing forms of arrangement in the composition of a subject is that of a right-angled triangle. Whether we employ this form to include the whole subject, as in Fig. 6, or in parts or in groups, as in Fig. 7, certain it is that it affords an opportunity for great contrasts, with an harmonious blending of intermediate forms and proportions to combine them. With regard to preserving the triangular form of composition, if desirable, much may be done by slight alterations to make the picture more effective. The growth of a particular tree may be improved, and another, much in the way, may be carried back in the picture. Sometimes the massing of clouds in certain parts will assist; and we may observe here that clouds and skies in general are great resources when difficulties arise in the composition of a landscape, because many liberties may be taken with their arrangement which cannot in the least interfere with preserve this character. If a couple of poplars stood in the foreground, at c or d, of the same height as the tree on the right, and on the same plane, they would either leave them out, or put them further back with different heights; or, with the help of the sky as a background, modify their prominence, so as not to destroy the general character of the composition. Some will even venture to remove trees and buildings to other situations altogether. It was the frequent practice of an eminent English landscape painter to take great liberties with his subjects in this respect. He would remove a large group of trees to the opposite side of a river, rather than they should interfere with the lines he wished to preserve; and especially if they were useful in their new position to give additional improvement to his picture. But a wholesale interference with the true portraiture of the landscape is dangerous without long previous experience; in youthful hands it may act prejudicially in the practical part of the work. It is only they who know well what they are about who can venture to such an extent as we have just mentioned. At first, let our pupils bear in mind that they must proceed step by step; copy Nature closely until they can copy her well; then afterwards they may be able and at liberty to adapt or alter as they find necessary, or as their improved taste and judgment may dictate. Mr. John Burnet shows what a master-mind is capable of, in a passage to be found in his work upon landscape painting in oil. It is thus:-"In examining the pictures of Claude Lorraine, and especially the work of the Liber Veritatis,' containing prints from these pictures, we are struck with the various ways in which his studies from nature were applied and dovetailed in, as it were, to the composition of a complete work. The connecting links which his own taste made necessary for this purpose, give us a clear insight into the mode of generalising his ideas. The strong passages from nature are interwoven and toned down in their harshness by the extension of the forms in more delicate lines, and their abruptness swallowed up by bringing the softening influence of shadow to come in contact with them." In our choice and treatment of a subject, we must bear in mind that there should be always one leading object to form the central attraction of the composition, and we must devote sufficient care and attention to its character and details, that the eye may have something to rest upon at once, before it is allowed to wander off to other parts. It is a practice, or rather a habit of which few are aware, but all follow without any predetermination, first to look for something upon which the eye may repose; and, however interesting the details may be, the principal object will certainly be the last the eye rests upon before it leaves the picture. This being the case, the theory of composition teaches us to provide for this result. Very frequently a few figures will give an interest to the subject, and afford an opportunity for concentrating the attention of the spectator upon the picture. A view which an inexperienced eye would pass by without any especial remark, may be made exceedingly interesting. Let us go out and sketch a view on a common; there may be nothing much in it; it may be very dull and flat; but something, we trust, will turn up as we proceed to make Fig. 7. it more lively. The one we have chosen has no trees upon it, except one, old and dead, possessing only a few angular and leafless branches. Its trunk, almost totally stripped of the bark, has still clinging to it a piece of ivy; and even that is weak and straggling. On the left of the tree, and at about the centre of the picture, is an unused gravel pit, in which we perceive the leavings and rubbish of a recent gipsy camp. These are the principal features, and we might have passed it by, but as we have sat down to draw it we will try to make a picture out of it. We begin by marking in the general lines of the gravel pit, place the position of the tree on the right of the picture, and indicate its trunk and branches. We also arrange some of the lines of the furze, brambles, and other wild shrubs, whose forms, wave-like, rise and fall, gradually blending both in form and colour into the distance, until the eye is arrested by a low line of far-off hills. This is the arrangement. Now we must trust to details in the drawing to make up the rest, re-commencing with the gravel pit, the top of which makes an incline from the tree, and dips into a hollow partly out of sight. The left slope of the pit is covered with brambles and honeysuckles, and we now perceive for the first time a stream of water, running under the shelter of some dock-leaves and foxgloves. Whilst we are drawing these a donkey approaches, and stations itself upon the bare spot under the old tree, and its foal lies down by its side. These are valu able additions to our picture. Two ragged children, wondering what we are about, come out of curiosity to watch our proceedings. Soon finding no amusement in this, they go into the gravel pit, and turn over the rubbish the gipsies have left. These afford other suggestions, and are added to our picture. Some ducks, from off the common, come and dabble in the little stream amongst the dock-leaves. We take advantage of these also. We then devote our attention to the mid-distance, amongst patches of purple heath and yellow furze; and here we avail ourselves of the pictorial licence already mentioned by removing a cottage, partly surrounded by apple-trees, which is placed beyond the limits of our picture. We see only its white gable, pierced with one small window, and its thatch and chimney; but this is enough, and we place it peeping above the furze in the mid-distance. This object helps to break a long monotonous line, and adds another idea to the whole. Beyond this some peatgatherers have lit a fire, and its curling smoke amongst the dark heather affords another kind of contrast. The whole surface of the scene is broken up by passing lights and cloud-shadows, which, as they float along, bring out alternately brilliant bits of colour, backed up by shades of various tones to relieve them. Thus a sameness is avoided, and what is very important, they assist the perspective. The sky also helps us; its patches of blue, broken up by a few dark clouds, with their thousands of semi-tones and white masses, form an excellent background, against which we put in the sharp and carefully drawn tendrils and leaves of the ivy on the old tree. We finish with the weeds and wild flowers in the foreground, brighten up the children's dresses, put a few more brilliant touches to the ducks, the sparkling water, and the most prominent of the leaves and branches of the brambles, tone down the shadows on and near the donkeys, and having finished our sketch, we exclaim, "All this comes of a dead tree and a gravel pit !" A repetition of extreme contrasts must be avoided. They would render the picture, if in outline, angular and harsh; if in colour, or light and shade, the result would be "patchy." Such effects are startling, but they are not pleasing when repeated. They must be accompanied by middle tones of various grades. Black and white in juxtaposition are not agreeable; but place combinations of them in conjunction with the extremes, and a very different effect is produced. The same may be said of colours without their combinations; lines also. Suppose a perpendicular line cuts an horizontal one (and where there is a repetition of these the effect becomes worse), it will be necessary to take off the harsh effect they produce by adding inclined lines (see Fig. 7, where the stooping and inclined figures unite the two extremes, the one on the ground and the upright figure). We must now say something about the introduction of figures and other objects, all of which contribute largely to the interest of a picture. If we draw a view of a river and its surroundings, and there is a towing-path at the side, there ought to be boats and barge-horses. A farm-yard is not complete without cattle and pigs; or a sea-coast without its boats and fishermen. In short, whatever may be the character of the landscape, the character of the figures must be in unison. To qualify, there |