Ill 



RULER, PARALLEL. 



RUMB. 



2U 



U beginner. Fur th* Utter w should state u follow! :-To find the 

 hypoUwmue at a right-angled triangle of which the two tide* are 

 reduce the two side* to the same denomination if Decenary 

 * 1 * of a foot, inchei and decimal* of an inch, *c., aa 

 O, multiply the unite in each aide by itself, add the 

 mulu. and extract the square root of the mm : thu (qiiare root U 

 the number of such unit* in the hypothenuse as were used in the 

 Biimieavm of the side*. 



If however many rules are to be learned, it would in all probability 

 be found more easy to learn the symbols of alegbra, that is, to learn to 

 read an algebraic expression and to use formula?, than to recur 

 frequently to rules. 



BULKS, I'AK.M.l.KL. A good form of this instrument is 

 tTrf4*"^ under MAB.QUOI'S RULERS, which U particularly applicable t<> 

 the ease in which numerous and related parallels or perpendiculars are 

 to be drawn. The ordinary instruments are of two kinds, which might 

 well be called parallel mien and parallel nJleri. 



The principle of the common parallel ruler is a parallelogram of 

 constant sides and changeable angles : one side being fixed and the 

 angles altered, the other side changes position, it and iU parallels 

 always remaining parallel to the first side and its parallels. Two 

 rectangular rulers are connected by two cross-bars of equal lengths, 

 which more on pivot* in the rulers in such manner that the four pivots, 

 two in each ruler, shall be the four points of a parallelogram. The 

 line joining two pirots on the same ruler U always made parallel to 

 the length of the ruler. One ruler being held fixed, and a line drawn 

 with the edge of the other ruler in any position, then any motion 

 giren to the other ruler by the rotation of the cross-bars gives, on the 

 edge of the moving ruler, a line parallel to the first line. The defects 

 of this construction are, that the four pivots may not make on accurate 

 parallelogram, in which case the instrument is worthless : and the 

 ride* of the two rulers, when the instrument is closed, may not be 

 parallel to one another, in which case all the lines must always be 

 taken off the same ruler. Moreover, one ruler remaining fixed, there 

 is but a small command of distance from it; so that, to gain the 

 parallel required, it may happen that the first ruler has to be advanced, 

 the second brought up to it, the first ruler advanced again, and so on. 

 Now, owing to the rotation of the pivots, this gives an oblique motion 

 to the instrument ; so that it often happens, by the time that the 

 required parallel is gained, that the point through which it is to be 

 drawn is off the ruler. To meet this disadvantage, and to give the 

 instrument more extent, three rulers are sometimes put together, each 

 connected with the next by cross-bars in such manner that the cross- 

 bars connecting the first and second have an opposite revolution to 

 those connecting the second and third. At its best however this 

 instrument is rather clumsy ; but, such as it is, it is safe and easily 

 earnt, when well made. 



The simplest kind of roller is the common round ruler, which, with 

 a little practice, will draw parallels for ordinary use very well. It is 

 good practice in the use of instruments to draw parallels in this way ; 

 the ruler being held in the middle and gently allowed to take its own 

 rolling motion. If a ring be well drawn round the ruler, it is good 

 practice in drawing perpendiculars to adjust the ruler so that the ring 

 may roll over the line to which perpendiculars ore to be drawn. But a 

 roller which is more easily used is sold in all the shops. It consists of 

 an ordinary ruler of rectangular form, both edges of which are 

 bevelled and divided into equal parts : one side into inches and tenths, 

 the other into inches and twelfths ; the inch divisions being made to 

 oome exactly opposite each other. A roller is let into a space cut out 

 of the middle of the ruler, in such manner as to project a very little 

 way from the under and upper faces of the ruler. When the instru- 

 ment is put down on the paper, either of the bevelled edges may be 

 brought down on the paper, or both may be clear of it. In this last 

 ease the roller (the efficient ends of which are toothed cylinders, the 

 middle part being in a frame) rolls easily, and additional stability is 

 given if, while it rolls, one of the bevelled edges be kept slightly on 

 the paper. The ends of the roller are graduated and a fixed index is 

 in the frame, so that by allowing equal numbers of divisions to pass 

 the index at each roll, a good approximation (though not quite with a 

 draughtman's accuracy) may be made to equidistant parallels. 

 Perpendiculars to a given line are drawn by adjusting the ruler so that 

 opposite divisions of the bevelled edges may travel on the given line. 

 With a very little practice this is an instrument of great power and 

 accuracy. Before using it, draw a line with it, roll it away, and then 

 roll it up again to that line, and see if the coincidence is as perfect as 

 before. Various other modes of trial will suggest themselves : indeed 

 no one should use a parallel ruler at all until he has drawn pairs of 

 parallels across each other, and satisfied himself that he con get the 

 opposite sides quite equal 



A rough construction of this kind was (perhaps is) sold under the title 

 el ' BcnMngsr's Patent,' in which a round ruler of wood is sinn 

 nectd with a flat bevelled ruler, so as to carry it when it rolls. This 

 is meant to rule lines for writing, but it may be made to do good 

 service as a parallel ruler for other purpose*. , 



RUM is a spirit diitillcd from the sugar-cane, that is, from cane- 

 joios; or from the ncnmmings of the juice from the boiling-house or 

 from treacle or molasses; or from " dunder," the lees of former dUtil- 

 What is called pint-apple rum is not distilled from different 



ubstances : it is simply flavoured with slices of pine-apple put into the 

 puncheon. As the entire juice of the cane is not necessary for making 

 rum, the distillation is carried on in conjunction with the manufacture 

 of sugar. The best rum is made from the uncrystallised syrup 

 called molasses. [MOLASSES ] The proportion of molasses made in 

 crystallising a [cwt. of sugar varies! from 60 to 90 gallons, and 

 depends both upon the climate and the season ; being lowest in the 

 Leeward Islands, which have a dry climate, and highest in Demerara 

 and Trinidad. It is in the hitter that in fine seasons the proportion 

 reaches 90 gallons per cwt. Nearly one gallon of proof rum may 

 be made from one gallon of molasses. 



The nun consumed in the United Kingdom is entirely the produce 

 of the West Indies, and to a great extent of the island of Jamaica, 

 which is of a superior quality. For many years the home demand has 

 not taken off the whole supply ; and the surplus, which consists chiefly 

 of the Leeward Islands rum, and other kinds of inferior quality, is 

 exported. 



British spirits are said to be extensively sold for rum, the flavour 

 being imitated by the rectifier. 



The equalisation of the duties on East and West India sugar, 

 by 6 Wm. IV. c. 26, rendered it expedient to give a practical equality 

 to all the products of the sugar-cane, without which the cultivation of 

 sugar plantations in India could not have been so profitably extended, 

 as the molasses would have been comparatively wasted. The rum con- 

 sumed in the navy is exempt from duty. That which we re-export is 

 chiefly sent to Germany, Prussia, Holland, Italy, and Australia. After 

 various changes in the mode of arranging the duty, it was determined 

 in 1847 that rum should pay the same amount of Customs' duty as 

 British spirits paid of Excise duty. There still remained a few 

 anomalies, arising out of the excise duty being unequal in different 

 parts of the United Kingdom ; but this inequality was removed in 

 1858, and in 1860 the State was put in the receipt of 10*. 2rf. per 

 gallon on all rum, gin, whiskey, and British spirit of every kind, 

 consumed in the United Kingdom ; and an additional 3d. per gallon on 

 rum not the production of the country whence imported. 



The rum imported in four equidistant years will show the recent 

 progress of the trade : 



1844 



1849 



1854 

 1859 



3,120,010 gallon*. 



5,300,827 



8,625,907 



6,878,587 



The computed real value in 1854 (the first year in which such values 

 were calculated by the Customs), was 1,490,6612. ; from which the 

 values for the other years named may easily be calculated, sup, 

 the price to have remained unchanged. In looking at the above 

 numbers, it would seem as if rum had been rapidly increasing in con- 

 sumption in England about the year 1854 ; but such was not the case. 

 Of the whole quantity imported, only the following (in each year) was 

 retained for home consumption : 



1844 



1849 

 1854 

 1859 



2,198,592 gallons. 

 8,039,862 

 3,226,594 

 3,575,679 



The large excess beyond these quantities was either re-exported, or 

 consumed on shipboard. 



RUMB or RHUMB. Vitalis (' Lex Math.') calls this a Portuguese 

 word, and no doubt it might have been introduced into navigation by 

 the Portuguese, but we suspect it to be the Latin " rhombus ; " he 

 says it signified originally the meridian, or the principal meridian of a 

 map ; perhaps it came to signify this from such meridian being usually 

 ornamented by a distinctive rhombus, such as is added to the north 

 direction on a compass-card. However this may be, a rumb certainly 

 came to mean any vertical circle, meridian or not, and hence any point 

 of the compass ; so that, in modern phraseology, a rumb is one of the 

 thirty-two principal compass directions, and to sail on any rumb is to 

 sail continually on one course. Hence a rumb-line is a line drawn in 

 the sphere, such as would be described by a moving point which always 

 keeps one course ; it is therefore the spiral of Mercator's projection, 

 and is that which is also called the loxodromic spiral. 



The mathematical properties of the rumb-line maybe easily deduced. 

 Let r be the radius of the earth, A, and /, the longitude anl latitude of 



A,, and A, and 7, those of A,, A and I being those of any intermediate 

 point p : and let * be the length of A,P. If then we increase < by the 

 nfinitely small arc dt, increasing A and I at the same time by d A and 



