1 



KXTHKMK AND MKAX UATI<>. 



BYRE. 



in: I 



woape into the cavity of the abdomen, the remit u uniformly and 

 speedily fatal. If it insinuate itwlf into the cellular tissue in the 

 neighbourhood of the neck of the bladder or the urethra, the accident 

 is (till a very serious one, though it generally adiui to of cure if the 

 nature ol it be immediately recognised. The fluid, which i highly 

 deleterious, mart be promptly evacuated by free incisions, and care 

 must be taken to prevent further Infiltration. If thin be neglected, 

 unhealthy suppuration u sure to take place, accompanied by fever of a 

 typhoid character, and followed by extensive mortification. 



The most common causes of infiltration of urine are abacenes of the 

 prortato gland, and neglected or mismanaged strictures; and a very 

 frequent consequence u the establishment of a urinary fistula in the 

 perineum. [URMART GROANS.] 



It may be remarked that the bile is sometimes extravasated in the 

 tn way from the gall-ducts or bladder. If it escape into the abdomen, 

 it is followed by a similar fatal result from inflammation of the 

 txrHmatm. [CALCULI, BILIARY.] 



KEME AND MEAN RATIO. To cut a line according to 

 extreme and mean ratio, t Muu> tutpor no) nioot \ayan T<JUU>, is a phrase 

 of Euclid which it is not very easy to explain from the words of it. 

 The meaning is, to cut a straight line in such a manner that the whole 

 shall bear to the greater part the same ratio as the greater part to 

 the less ; or to make the greater segment a mean proportional between 

 the whole and the lees. Accordingly, the square of the greater segment 

 must be equal to the rectangle under the whole and the less segment ; 

 and Euclid shows how to make this section in the llth proposition of 

 the second book. 



If the whole line be called unity, and if x be the fraction which is in 

 the greater segment, we must have 



l-x=x*,arx=l */5-J. 



In the sense of Euclid, only the value 4 v'S 4 will solve the pro- 

 blem ; and the other root, with the sign changed, solves the following 

 problem : To produce a line in such manner that the part produced 

 may be a mean proportional between the given line itself and the line 

 made up of the given line and the port produced. Any one who 

 examines Euclid's construction will very easily see the formation of 4, 

 of 4 ^5, and the subtraction of the first from the second. 



The fraction x cannot be expressed arithmetically, and the segments 

 are incommensurable. But if a and 6 be any two numbers, of which a 

 is the less, and if we form a third by adding the two, a fourth by 

 adding the second and third, and so on, as in the series a, b, a. + b, 

 o + 26, 2a + 36, 8a + 6ft, 5a + 84, &c., it is demonstrable that the farther 

 we go the more nearly does the ratio of any one to the next represent 

 that of the less to the greater segment of a line divided in extreme and 

 mean ratio. If we begin with 1 and 1, we have the series 1,1,2, 3, 5, 8, 

 13, 21, 84, 55, 89, Ac. Ac. Thus, if 89 inches be divided into 34 and 

 55 inches, the division required is nearly made, for the rectangle has 

 89 *. 34, or 3026 square inches, and the square has 55 x 55, or 3025 

 square inches. This process gives us the results of turning 



1 ar=ar 3 , or *= _i- 

 1-r* 



into x = , Ac. [FRACTIONS, CONTINUED], and then making 



successive approximations. It is, perhaps, just worth noting, that the 

 nth number in the series 1, 1, 2, 3, 5, 8, Ac., is the number of ways in 

 which n can be made up out of odd numbers, differences of order 

 counting as different ways : thus, 6 can be made up in 8 ways out of 

 odd numbers. Accordingly, the greater n is taken, the more nearly 

 are the numbers of ways in which n and n + 1 can be composed of.odd 

 numbers in the proportion of the segments of a line divided in extreme 

 and mean ratio. 



The use of this division in elementary geometry is as a step to 

 dividing four right angles into five equal parts, as in the 10th propo- 

 sition of the fourth book. In fact, the half of 4 / 5 4 is the sine of 

 18, the fifth ]irt of a right angle. 

 I-:, IN OPTICS. [OPTICS.] 



EYE-PIECE, a combination of lenses for the purpose of examining 

 the image of an object formed by the object-glass, or by an achromatic 

 combination of lenses in the tube of a telescope or of a compound 

 microscope. Eye-pieces are usually of two kinds, the JJuyjmiati <>r 

 Htgativt, and Haaudcn'i or positive ; but the former is most commonly 

 used. It consists of two plano-convex lenses, with their convex sur- 

 faces towards the object-glass. The one nearest the eye is known as 

 the eye-ylau, while the other is called the fiM-glau, its function being 

 to increase the field of view. Between the two lenses is a perforated 

 > or diaphragm, for the purpose of cutting off the extreme rays that 

 ht disturb the perfection of the image. 



n's eye-piece also consists of two plano-convex lenses ; but 



the ficld-plam has ito convex surface turned upwards instead of down" 

 wards. The punitive eye-piece is chiefly used with the micrometer- 

 [MICHOSCOPK; TELESCOPE; DOUBLET*; MICROUKTER, Ac.] 



KYi:.S, PROPAGATION BY. The power of propagating plant* 

 by any other means than seeds depends entirely on the pro*-! 

 leaf-buds or " eyet," as they are technically called by gardeners. A 

 plant may in fact be regarded as a congeries of individuals, and each 

 leaf-bud is an individual capable of maintaining an independent exist- 

 ence. Though this is generally true, the buds of all plants will not 

 grow when removed from their parent stock. Many, however, admit 

 I their buds being removed from one branch and placed 

 another, which constitutes the process of budding. [BUODINU.] Others 

 admit of a branch being removed and placed in the ground, when the 

 eaf-buds upon it will develop, and tho wood of the branch form roots. 

 Such branches are called cuttings. [CUTTING.] A few plants admit 

 of single buds being taken and planted in the earth, when they will 

 grow and produce plants in the same manner as seeds. It must, how- 

 ever, be borne in mind in this case that the individual and not the 

 species, as is the case with seeds, is propagated. The plants which are 

 most frequently propagated by eyes are the potato and the vine. It 

 appears that for plants to grow in this manner, the bud requires that 

 a due supply of nutriment should be stored up in the branch or part 

 of the stem to which it is attached. This is undoubtedly the case in 

 ;he potato, where a large quantity of amylaceous matter is stored up 

 n the tubers, so that a bud cannot be token without carrying away 

 fragments of its alimentary secretions. Mr. Knight observed, with 

 regard to the buds of the vine, that those grew with most rapidity and 

 strength which were in contact with the largest quantity of alburnum, 

 which he regards as the nutritious matter of the young buds. Tho 

 provision, however, of alimentary matter may be in some cases, 

 as has been pointed out by Dr. Lindley, disadvantageous by pro- 

 moting too great a development of stems and leaves. According to 

 theory, the more nutritive matter there is for the eyes, the greater 

 crop there will be ; and thus it would seem that it would be more 

 advantageous to plant whole potatoes than portions of the potato or 

 sets. Dr. Lindley proved by a series of numerous experiments, that 

 the weight of potatoes per acre is greater under equal circumstances, 

 from sets than from the whole tubers by upwards of from seven cwt. 

 tu three tons per acre, and considerably more on comparison of the 

 clear produce after deducting the weight of sets employed in l<;li 

 cases. He supposes " the rankness of the vegetation from the whole 

 tubers to be the cause of the diminished crop ; for the stems were 

 unable to support themselves, and were blown about, laid, and broken 

 by the wind." A curious fact with regard to the growth of the 

 eyes on different parts of the potato has been pointed out in th 

 ' Gardener's Magazine.' It is well known to the cultivators of potatoes 

 in Lancashire that different eyes germinate and yield their produce at 

 very different times, some being ripe or fit for use as early as the 

 middle of May, and others not till June or July. It is found that it 

 is the seta which are nearest the extremity of tho potato which ripen 

 soonest ; and these are planted in Lancashire in warm places, in March 

 or the beginning of April, and are ready for the market by the middle 

 of May. The produce of the next sets are ready a fortnight aft- 

 that from the root end still Liter. 



In propagating the vine by this moans on eye is token with a small 

 portion of the stem adhering to it, and is placed in earth with a 

 bottom heat of 75 or 80". It should be kept in a damp atmo.-i 

 when it speedily shoots upwards into a branch, and at the same time 

 establishes iteelf in the soil by the development of roots. In order to 

 ensure the success of this operation, it is necessary that the bud should 

 be dormant at the time it is removed, and that a small piece of well- 

 ripened wood should be separated with it. 



There is another mode of propagating plants resembling this, and 

 that is by planting the abortive branches, called ' Knaurs,' and ei 

 buds. This plan is pursued in Italy for the propagation of olive 

 trees. These knobs or abortive branches are produced by other trees 

 besides the olive, and might be made use of for the same purpose. 

 The beech, the poplar, the cedar, and many other trees produce these 

 knobs in abundance in this country. 



EYRE (from the old French eyre, a journey), the court of the 

 justices itinerant who were regularly established, if not fir 

 liy the parliament of Northampton, A.D. 1176 22 Hen. II. with a 

 delegated power from the king's great court, or Aula Regis. They 

 were first appointed to make their circuit round the kingdom once in 

 seven years, but by Magna Charta, c. 12, it was provided that they 

 should be sent into every county once a year. (4 Inst. 184.) These 

 itinerant judges have been long superseded by the modem 

 assize. There was also a court so called which was held before the 

 chief justices of the several forests, under the old Forest Laws. 

 [FOREST LAWS.] 



END OF VOLUME IIL 



im.LUBVHY AND EVANS, rHIKItlU, WUITETBIAU. 



