the study of Homer does not enter largely into the curriculum of Scottish schools.

In the Lower Grade of French the general style of the papers shows improvement, and the diminished per-centage of passes is chiefly due to the standard being somewhat raised, to meet the increased efficiency in teaching French in Scottish schools. The translation into French was not all that could be desired, although some candidates acquitted themselves well. The literature question was not well done and showed considerable signs of cramming. The commercial question was an almost total failure, as has also been found in previous years. On the whole the grammar gives evidence of careful teaching.

In the Higher Grade there were too many candidates who were totally unprepared. But on the whole the translation from French into English was good, as well as the grammar. Here also the commercial question gave no good results. In Honours the literature questions brought out some very sound knowledge, although the answers were often diffuse. The French essay was extremely creditable on the whole. This part of the examination affords abundant evidence that the study of French is advancing in the Scottish schools.

In this subject there is little to record in the way of retrogression or advancement, although on the whole the papers seem to reach a more uniform level. The per-centage of passes does not vary much from that of last year, but the standard which it was necessary at first to fix rather low has been slightly raised. The comparison between the translation from German into English and from English into German seems (although the results are not uniform in this respect) to correspond rather with the results in Greek and Latin than with those in French, that is to say, the German composition is, like the Greek and Latin prose, better than the translation from German into English. The grammar leaves a good deal to be desired; and the literature questions give too much evidence of unintelligent cram. A careful study of the papers which have been set in the past would convince teachers that

although no wide range of literary knowledge is expected, it must be knowledge at first hand, and not mere cram obtained from hand-books.

The Higher Grade papers show a gratifying amount of good work, and in particular the German composition was very satisfactory. In Honours the philological answers left much room for improvement, but the passage given for translation into German reached a higher standard than in previous years.

* No passes are reckoned in this per-centage unless the candidates have also obtained a certificate in mathematics.

The following are the remarks (based upon the reports of the various revisers) of the gentleman who took the chief part in this branch of the examination :

"The results of the examination were, as a whole, very creditable to the manner in which the elementary mathematical teaching is conducted. There is a progressive improvement in neatness and style, and the proportion of candidates who fall very far below the pass level is smaller. Fundamental principles seem generally understood, but there was often a tendency to hurry through the work, leading to carelessness and inaccuracy.

"HONOURS GRADE.

"Geometry. The work had evidently been well prepared by most of the candidates, although in the style of writing out and reasoning, there were wide and characteristic differences between various schools. An interesting feature was

found in the remarkably good work sent up by one or two small and remote schools. A point which deserves praise is the amount of ground covered by some of the candidates. The chief defect observed was a tendency to hurried and incomplete answering. A want of reasonable care in trying to grasp the full meaning of some of the questions was too often met, and the tendency to quote a result at least as remote as that asked for and to proceed to build a demonstration on this basis was still (though less general than last year) too common.

"The convention of signs, the properties of poles. polars, and harmonic section were apparently well understood; and almost all the definitions given were correct. Most of the work was carefully written and the figures were generally excellent; the most serious obstacle in most cases to the greater success of the pupils was a want of definiteness in statement and sometimes in reasoning.

Algebra.-None of the papers reached a high standard of excellence, though a few candidates showed a very satisfactory knowledge of the subject and some facility in dealing with problems. As a rule, very fair knowledge of the book-work of permutations, binomial theorem, roots of equations and complex numbers was shown. In some cases, however, the proof of the binomial theorem for fractional indices had been learned by rote without being fully understood. The majority of the candidates were somewhat unsuccessful in the solution of problems, and their analytical work was often wanting in elegance.

"Trigonometry.-In this paper the questions were evidently well within the reading of the candidates, but loss of marks occurred through carelessness and neglect of the meaning of the questions. That much of the teaching had been thorough was clearly shown by the generally good answers to the ordinary questions on book-work, while in some schools an excellent style was exhibited in the less ordinary pieces of work. On the other hand, it is a regrettable fact that in too many cases the known form of a result induced pupils to write down as inferences steps that either did not follow from their previous work, or were too remote to have been fairly grasped. The habit of reducing two sides of an identity to the same form, instead of working through from one side to the other, is responsible for much of this improper work.

"ADDITIONAL SUBJECTS.

"Higher Dynamics.-The papers worked in this subject cannot be considered satisfactory, for in a large proportion of cases there were serious errors in fundamental points; for instance, after quoting Newton's third law of motion correctly, candidates proceeded to state that the action and reaction between the masses in Atwood's machine differed. The proof of the parabolic motion of a projectile was only occasionally free from error, and the problem on impact was generally wrongly worked. To these defects there were, in some schools, striking exceptions; and in at least one case the full appreciation of elementary points had not been sacrificed to the hasty covering of a wider field. The general style of the writing and figures was creditable.

"Analytical Geometry. The work was in general well done, in some instances very well done. A considerable number of the candidates showed a highly satisfactory grasp of the subject as distinguished from merely being able to remember and apply formula.

"Geometrical Conics.--The answering was in general satisfactory, both in writing out propositions and in working deductions, the differences between the work of the various schools depending principally on the amount of the subject read. In some schools this was limited to the properties of the Parabola; in others those of the Ellipse had also been studied; while a fair number showed a satisfactory knowledge of the properties of the Hyperbola as well. A small number of candidates knew how to deduce the focal properties of the curves from the fact that they are sections by a plane of a right circular coue or cylinder.

"Elementary Dynamics.-The work of the better class of schools was uniformly good, showing careful teaching and diligent preparation. In some schools, however, the teaching had evidently been inadequate, and many pupils were presented who had no real knowledge of the subject. Neatness and brevity should be more aimed at: long rambling answers are often given by candidates who have only a superficial knowledge of the principles of the subject.

"HIGHER GRADE.

"Geometry.--The bookwork was generally well done, but the candidates, with a few exceptions, failed in the deductions, frequently from not paying attention to the conditions laid down, and still more frequently from making unwarranted

assumptions, sometimes equivalent to what they were required to prove. In spite of the instruction that candidates were not expected to attempt every question, many endeavoured to do so, and in consequence failed to give all the steps of their work. The writing was fairly good, though in a few schools it is still defective.

"Algebra.-On the whole the papers were well done and showed evidence of careful preparation. The handwriting was as a rule distinct, and the arrangement of the work neat. Considerable skill was shown in the manipulation of equations, particularly in that of the biquadratic, which was solved by a variety of ingenious devices. A large proportion of the candidates sent in correct solutions of the problems. The answers to the question on cube root were less satisfactory, many candidates guessing the answer and pretending to have extracted it, though they broke down in trying to reproduce the evolution-process. Horner's method seems by no means generally used, and to be very seldom contracted in such a way as to bring out its superiority. In the higher parts of the subject, though much good work was sent up, formulæ and results appeared to have been too often unintelligently learnt by rote.

"Arithmetic. The questions on numeration, resolution into factors, fractions both vulgar and decimal, and stocks, were in the majority of cases answered satisfactorily, and the work as a rule was fairly neat. In many cases candidates failed to take into consideration the reasonableness of their answers; thus one candidate estimated the cost of papering a room at over four million pounds.

"Trigonometry.-This paper proved to be well within the range of the candidates' powers, and showed that the general knowledge of the subject as defined in the Note as to Mathematical Papers is satisfactory. It is, however, to be regretted that a certain amount of guesswork of an improper kind occurred; in some cases ingenuity had been exercised to dovetail correct results into entirely wrong premises. Such faults generally run through a school. Bearing in mind that the candidates were expressly told that every question need not be attempted, a great loss of marks from haste, incompleteness, careless reading of the questions, and inaccuracy in work took piace. A few words of praise may be added for some of the remote schools where careful teaching of a few pupils produced good results.

"LOWER GRADE.

"Geometry. On the whole the answering was excellent, the figures carefully drawn, and the reasoning neatly and clearly expressed, though in this respect whole schools differed considerably. Numerical references to previous propositions on which the proofs depended were often correctly given, but frequently the references to the more important were omitted, while the less important (dealing, for instance, with details of construction) were given. Riders were freely attempted, and in many cases correctly solved.

"Algebra.-On the whole the paper was well answered, particularly the questions involving the elementary rules in which the candidates had been well grounded. Most of the candidates failed in the questions requiring simplification, and very few had been taught the proper method of establishing identities. The problems were often tried, but not with much success. In point of neatness the work was, as a whole, below the average of former years, and some papers were in a rather dirty condition.

In

“ Arithmetic.—On the whole a satisfactory average standard was reached, and the work of the candidates from the majority of the schools was good in respect of the methods used, but the calculations of a considerable proportion of the candidates contained a number of numerical errors. Points which seem to require more attention in a good many schools are-(1) Accurate knowledge of tables of weights and measures; (2) Elementary rules for finding small factors of numbers, especially in calculation of least common multiple and in reduction of fractions; (3) The principles of determining areas and volumes in rectangular surfaces and solids. regard to this last point it may be mentioned that a good many candidates, in answering a question on the cost of painting the inside of a tank, found instead the cost of filling the tank with paint. There are indications that in some parts of the subject the teaching is often too mechanical. Thus a large number of candidates who were well acquainted with the manipulation or fractions failed altogether to answer a simple question as to how many men were left in an army after a certain part of the whole had died of disease, and a certain part of the rest had been killed in battle. In many cases the answers to problems were deficient in necessary explanation, only figures being given where a few words were required to indicate or to justify the method of solution employed. Some candi

dates did not attend properly to the rule that the fair copy of the work must contain all the detailed work. Others wrote out a second copy of all their work unnecessarily, and lost time which was required for the rest of the paper. The number of candidates who were quite unfit to cope with the examination was less than in previous years, and there was also a great improvement in the matter of giving the details of the work fully. Many absurd mistakes would probably ne avoided if the candidates were taught always to read over their result in connexion with the question asked before proceeding to the next question.

"BOOK-KEEPING AND COMMERCIAL ARITHMETIC.

"Candidates were examined from 54 schools with the following result :-

"Book-keeping.-The candidates were required to frame a complete set of books for a manufacturer's business. Only a few transactions were set for each book, and these were generally of a simple nature. They were also required to draw up a balance sheet and a profit and loss account to show the results of the trading. The paper thus included all the transactions of a manufacturer who does not use bills, and in whose business no difficulties occur; and finding its correct answer involved a good knowledge of elementary book-keeping. The answers were, on the whole, fairly well done, and showed an improvement on former years. Many were very good indeed, and in some cases ail the candidates in a school obtained high marks. Insufficient attention appears to be given to the cash book. In many answers the balances brought forward and carried down were omitted, and the book consequently did not give the balance in the cash-keeper's hands, to show which is one of the principal reasons for keeping a cash book. A considerable number of candidates were presented without sufficient preparation.

"Commercial Arithmetic.--The answers showed that the greater number of the candidates possessed a good knowledge of the tables of weights and measures, and facility in working questions which involve the direct application of the ordinary rules of arithmetic. They were, however, less successful with questions which required much thought. Some of the papers sent in were excellent, reflecting credit both on teachers and scholars. On the other hand, a few of the candidates were quite unprepared for the examination and should not have been presented."

There is one point to which I desire to call special attention. Considerable doubt arises with regard to the certificate in arithmetic. A complaint, for which there appears to be considerable foundation, has been made, that the lower certificate in arithmetic may be used somewhat unfairly when a comparison is instituted between the number of certificates gained by different schools. That certificate does not, it is urged, give evidence of what is properly called secondary education, although a sound and practical knowledge of arithmetic is a necessary and indispensable basis of any higher mathematical training. Your Lordships have always avoided any comparison between the results of the Leaving Certificate Examination in particular schools, and have expressed regret that such comparisons should be instituted. But it is hardly possible to prevent such comparisons being made between different schools which publish the statistics relating to their own scholars; and it is obviously unfair that a school in which a large proportion of the candidates was presented in lower arithmetic should be able to show apparently better results than one in which the presentation was chiefly in more difficult subjects. It would not, perhaps, be expedient to abolish the certificate in lower arithmetic altogether, as it gives to many schools a useful interest in the examination, and reasonable proficiency in this subject is made one of the conditions of the issue of a certificate in lower mathematics. But intimately as this part of the examination is bound up with the whole scheme, it is very doubtful whether the lower arithmetic certificate ought to bear the name of a leaving certificate, or whether a school should be entitled