653 



MEASLES. 



MECHANICAL POWERS. 



55* 



equally trustworthy, or that there is no circumstance which would 

 beforehand lead us to suppose that any one ia more likely to be true 

 than another. If this be not the case, no rule can be applied except 

 one which depends on the observer's judgment. He must make the 

 different observations reckon aa different nvjibers of observations, 

 allowing any one observation to count as mor>, than one, if he believes 

 it to be better than the rest. Thus, suppose three observations to give 

 26, 28, and 29, and that it is thought there is reason to prefer 28 to 

 the others, and 29 to 26, so that 28 ranks in the observer's mind as 

 being as good as a mean of eight observations, 29 of six, and 26 of four. 

 It must then be considered that there have been 8 + 6 -t- 4, or 18 obser- 

 vations, of which 8 have given 28, 6 have given 29, and 4 have given 

 26. These numbers, 8, 6, and 4, are called the weight* of the several 

 observations 28, 29, and 26, and the alteration in the preceding rule is 

 as follows : In forming the average, multiply each observation by its 

 weight ; add the result, and divide by the sum of the weights. Thus 

 8x28 + 6x29 + 4x26 = 502, which divided by 8 + 6 + 4, or 18, is 27'89, 

 the most probable result. In finding the probability of the truth lying 

 within given limits on one side or the other of this most probable 

 average, let the average be M as before, and the limits M + m and M TO; 

 take the difference between M and each of the results of observation, 

 multiply the square of each difference by the weight of its observation, 

 and add the results. Multiply 100 times the sum of the weights by m, 

 and divide by the square root of twice the sum just found ; take the 

 number nearest to the result in the column marked A, and opposite to 

 it in the column marked B will be found the number of chances out of 

 10,000 for the degree of nearness required. Thus if in the preceding 

 instance we ask what is the chance of the truth lying between 27'89 + 2 

 and 27-89 -2, we observe that 27'89 differs from the several results by 

 1'89, '11, and I'll, the squares of which multiplied by 4, 8, and 6, and 

 the results added together, give 21-7778, twice which is 43 5556, the 

 square root of which is 6'600. And 100 times the sum of the weights, 

 or 1800, multiplied by '2, is 360, which divided by 6'6 gives 54'6. 

 Opposite to 55 in column A we find 5633 in column B ; that is, we 

 have 5633 to 4367, or about 56 to 44 in favour of the truth lying 

 between the limits specified. 



The inverse problem ia as follows : given the observations, required 

 the limits of difference from the average between which it ia a given 

 chance, a to b, that the truth shall lie. In both cases the first process 

 is to turn a : (<i + b) into a decimal fraction of four places, and to take 

 the numerator of such fraction. 



Look for the numerator in column B, find the number nearest to it, 

 and take out the number corresponding in column A. Multiply this 

 by the square root used in the direct rule, and divide by 100 times the 

 number of observations, or, if they are not equally good, by 100 times 

 the sum of the weights. The quotient is the answer required. But 

 when, as most frequently happens, an even chance is the given chance, 

 use 47'7 instead of the number found in column A. 



In the first of the given instances it is required to know within what 

 limits it is 99 to 1 that the truth is contained. Here 99 : (99 + 1) is 

 9900, and looking for 9900 in column B we find 9899 opposite to 182 

 in column A. Multiply 182 by 1-203, which gives 218-946, which 

 divided by 700 gives -313, so that it is 99 to 1 that the truth lies 

 between 10-54 + '313 and 10-54 '313. 



In the second instance, required the limits within which it ia an even 

 chance that the truth is contained. Multiply 47'7 by 6'6, and divide 

 by 1800, which gives '175; and it ia an even chance that the truth lies 

 between 27'89 + '175 and 27'89-'175. 



The amount of departure from the average within which, on one side 

 or the other, it is an even chance that the truth shall lie, is called the 

 probable errrrr of the observation or average of observations to which it 

 refers. When the probable error of any one observation is given, that 

 of the average is found by dividing it by the square root of the number 

 of observations. Thus, if there be 100 observations, of each of which it 

 is an even chance that it is within "1 of the truth ; then the square 

 root of 100 being 10, and - l-=-10 being -01, it is an even chance that 

 the average of the hundred observations is within '01 of the truth. 



For further account of the matters contained in this article, see 

 PROBABILITIES, THEORY OF ; OBSERVATION ; RISK. For description of 

 methods without demonstration, see Lardner's Cabinet Cyclopiedia, 

 Essay on Probabilities, or Poisson on Probabilities. The tables may be 

 found to greater extent in the first article cited, and also in the Berlin 

 A.ttronomuiches JaMivfk for 1834. 



M KASLES (Morbilli, Jtubeota) is the popular name of a contagious 

 disease, characterised by an eruption on the akin, and affecting chiefly 

 children. 



The etymology of the word measles is uncertain, but its application 

 to the disease we are treating of was probably borrowed from an appear- 

 ance so denominated in pork, to which the eruption bears resemblance. 

 Measles is ushered in by more or less fever, a running from the nostrils 

 and eyes, with some inflammation of the latter, sneezing, hoarseness, a 

 dry coui{h, difficulty of respiration, and occasionally slight soreness of 

 the throat. From four to six days after the commencement of these 

 symptoms a rash begins to appear, which first shows itself in distinct, 

 red, and nearly circular spot*), having some resemblance to flea-bites : 

 these spots gradually coalesce and form small slightly elevated patches 

 of an irregular figure, but approaching nearest to that of semicircles or 

 crescents. The patches first show themselves on the forehead and 



face, and gradually extend downwards to the trunk and extremities 

 At the commencement of the eruption the catarrhal symptoms and 

 fever are somewhat augmented, and during its height the whole face is 

 often swollen and the eyelids thereby closed ; on its decline, which 

 begins on the fourth or fifth day, the fever ceases, and from those 

 parts of the body previously covered by eruption the cuticle separates 

 in small bran-like scales. A diarrhoea now commonly supervenes, and 

 affords relief to the other symptoms. This, however, is the period 

 when the danger, which is a consequence rather than a concomitant of 

 measles, commences. The cough, which has continued throughout the 

 active period of the disease, now assumes a more serious character ; the 

 expectoration, which hitherto has been simply mucus, indicative of the 

 inflammation being confined to the mucous membrane of the bronchial 

 tubes, becomes bloody, or mixed with pus, showing either that inflam- 

 mation has attacked the proper substance of the lungs, or that tuber- 

 culous deposits have taken place in these organs, constituting pulmonary 

 consumption. If the patient happily escape these dangers, others, less 

 fatal indeed, but scarcely less to be dreaded, not unfrequently show 

 themselves, among the most severe of which are obstinate ophthalmia 

 and inflammation of the internal parts of the ear, the former not 

 unfrequently terminating in partial or total loss of vision, and the 

 latter in deafness. It must be confessed, however, that this is a pic- 

 ture rather of what may and occasionally does happen than of what 

 takes place in the majority of instances ; such severe terminations of 

 the disorder are confined chiefly to the ill-fed and ill-clad children of 

 the poor, and to the more sickly ones of the opulent. 



Measles frequently occurs as an epidemic, in this country usually at 

 the beginning of spring. These epidemics vary considerably in character, 

 being sometimes benign, at other times very fatal, and occasionally they 

 are observed to prevail in conjunction with small-pox ; like the litter 

 disease, measles rarely attacks the same individual twice. Experiments 

 have been made to determine how far inoculation with the blood of 

 the parts on which the eruption appeared might succeed in moderating 

 the violence of the disease thus artificially produced ; but the cases in 

 which it was tried were not sufficiently satisfactory to warrant its 

 general adoption. Measles, before the outbreak of the rash, may be 

 mistaken for severe catarrh ; the eruption itself is liable to be con- 

 founded with that of roseola, scarlatina, strophulus, lichen, urticaria, 

 incipient small-pox, &e. ; but the crescentic shape of the patches and 

 the catarrhal character of the other symptoms can hardly fail to remove 

 any doubt as to the nature of the disease. 



With respect to the treatment, little is 'required during the eruptive 

 stage of the disorder, which is seldom attended with danger. It is 

 chiefly necessary to open the bowels, to confine the patient to a light 

 vegetable diet, with cold acidulated aqueous drinks, and to maintain a 

 cool temperature in the room, which should be moderately darkened. 

 Where the skin is dry and hot, sponging it with cold water has been 

 recommended and practised with benefit. The old practice of confining 

 the patient in heated chambers, and covered with an overwhelming 

 quantity of bed-clothes, is now justly abandoned : the free use of the 

 lancet during the eruptive period of the disease is likewise laid aside, 

 and its employment restricted to those cases in which any of the vital 

 or important organs are threatened or attacked by inflammation. 

 Cases in which the vital powers, are low, to which the name rubeola 

 putrula has been applied, of course will require an opposite mode of 

 treatment, aa the exhibition of bark, the mineral acids, and wine, 

 together with a nutritious diet and a pure atmosphere : these, too, are 

 the remedies which prove moat serviceable in checking the diarrhrca, if 

 injuriously protracted. 



MEASURE. One number or magnitude is said to measure another, 

 when the first is contained an exact number of timea in the second. 

 [INCOMMENSURABLE ; PROPORTION.] 



MEASURES. [STANDARDS; WEIGHTS AND MEASURES.] 



MECHANICAL POWERS ia the name given to certain simple 

 machines or engines, for these worda are applied indifferently, either of 

 which is occasionally used by itaelf in moving bodies or raising weights, 

 or any of which are combined together in the formation of the complex 

 constructions which are employed in manufactures and the arts. 

 Frequently however, in investigations relating to statical equilibrium, 

 the properties of the mechanical powers are introduced when no 

 machine is contemplated ; aa when, at some part of a plane surface, 

 the effect of a pressure at another part is determined by the ratio of 

 the distances from a supposed point of support. 



The several machines to which the name of mechanical powers is 

 applied are the LEVER, the WHEEL AND AXLE, the INCLINED PLANE, 

 the WEDGE, the SCREW, and the FUNICULAR MACHINE. 



The object proposed in every machine ia to transmit a force from 

 the point at which it is immediately applied to that at which some 

 resistance is to be overcome or some operation to be performed ; and, 

 in the transmission, the intensity of the motive power is to be increased 

 so that effects may be produced which could not be accomplished by 

 that power alone. The increase of the power ia obtained by causing 

 part of the resistance which is to be overcome to rest on the machine 

 or on the fixed points which serve for its support, so that only the part 

 which remains is opposed to the motive force. Thus, if it be required 

 to raise a heavy body to a certain height from the ground, no exertion 

 of human or animal strength may be sufficient, if directly applied, to 

 accomplish the end ; but if a plane inclined to the horizon and extend- 



