290 



THE POPULAR EDUCATOR. 



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 to- 

 gether. 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 " Ad- 

 ditional Subjects," as well as in the ordinary subjects, which 

 are common to all, and consist of the following, viz. : 



The accidence of Greek and Latin Grammar. 



One book or more of some Latin classic. 



The same of some Greek classic. 



One of the four Gospels in the original Greek. 



Paley's " Evidences of Christianity." 



Euclid I., II., HI., VI. 119 and A. 



Arithmetic. 



Elementary Algebra. 



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 



Algebra and Logarithms, ) / 



Elementary Trigonometry, > or < French and German. 



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 af the Acts of the Apostles in Greek. (2.) 

 One of the Latin classics. (3.) One of the Greek classics. (4.) 

 Elementary Algebra. (5.) Elementary Statics. (6.) Elemen- 

 tary Hydrostatics. (7.) Elementary Heat. (8.) English Prose 

 Composition. (9). Latin Prose Composition. (10.) A Play of 

 Shakespeare. 



The last three 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 alphabetically. 



After passing this examination there lie open to the student 

 six different subjects in which he may obtain his B.A. degree 

 i.e., in theology, moral science, law and modern history, natural 

 science, mechanism and applied science, music ; 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.) Selected books of the Old Testament in English. 

 (2.) One of the Gospels in the original Greek. 

 (3.) One or more of the Epistles in the original Greek. 

 (4) The History of the Church of England down to 1830, 

 and selected subjects or periods of English Church 

 History. 



The moral science branch is divided into the two heads of 

 logic and political economy ; and the candidate must pass in 

 one of these heads. 



The law and modern history branch is divided into two 

 heads, in one or other of which the candidate must pass : 



Law. (1.) Lord Mackenzie on Eoman Law, or the elements 

 of Hindu and Mohammedan Law. (2.) Blackstone's 

 Commentaries. 



History. (1.) Outlines of English History from the Norman . 

 Conquest to the Accession of George IV. (2.) Hallam's 

 Constitutional History. (3.) A specified period of 

 European History. 



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 on the practical application of mechanics, hydrostatics, 

 hydraulics, heat, electricity, magnetism, etc. 



It will be useful for the student to have previously attended 

 a course of lectures on 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 paper 

 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 encouragement of successful competitors. 



LESSONS IN ARITHMETIC. XLIV. 



CEOSS MULTIPLICATION. 



9. A METHOD much used in practice by workmen in finding 

 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. 



The dimensions used are : A foot ; faot & foot, which is an 

 inch (sometimes also called a prime) ; fa of a prime, called a 

 second ; fa of a second, called a third. Primes, seconds, and 

 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 



5ft. 2' 4" 25"'. 



EXAMPLE. (1.) Find the area of a rectangular board 12 ft. 7 in. 

 long and 4 ft. 3 in. wide. 



12 ft. r 

 4 ft. 3' 



50 

 3 



53 sq. ft. 5' 9" 



The reason of the above process will be seen by exhibiting it 

 in the following form : 



12 ft. r - 12 ft. + A ft. 



4 ft. 3' = 4 ft. + A ft. 



Now, first * multiplying the multiplicand by 4 feet, we get 



4 ft. x A ft. = ?| sq. ft. = 2 sq. ft. -5- A sq. ft. 

 and 4 ft. x 12 ft. = 48 sq. ft. 

 Adding these together, we get 



(1) 50 sq. ft. + A sq. ft., or 50 4' square feet. 

 Again, multiplying the multiplicand by ^ feet, we get 

 A ft- x A ft. = & sq. ft. = A sq. ft- + T?J sq. ft. 



and A ft. x 12 ft. = 3 sq. ft. 

 Adding these last together, we get 



(2) 3 sq. ft. + A sq. ft. + r? sq. ft. or 3 1' 9" square feet. 

 Adding (1) and (2) together, which must give the whole area, 

 we get 



53 sq. ft. + A sq. ft. + T !i sq. ft., 



which is 53 5' 9" sq. ft. 

 5 here are A of a square foot, 

 that is, A x 144, or 5 x 12 square inches. 



9" is r* of a square foot, or 9 square inches. 

 Hence, to reduce the square primes and seconds in the pro- 

 duct 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 'onds (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 

 them. 



The above remarks will sufficiently explain the following 

 Rule for Cross Multiplication. Place the several terms of the 



* We speak here, for shortness, of multiplying feet by feet ; but let 

 the reader refer to, and bear in mind, the observation following Art. 7, 

 in Lesson XXII., Vol. I., page 380. ^ 



