Angle of incidence

“ Frost makes the important point that the relative mortality is determined more accurately by case fatality than by case incidence, and that without a full and exact knowledge of the variations in case fatality, statistics of mortality are by no means translatable to terms of relative morbidity. ”

“ To show that the point scale units are even theoretically equivalent it would seem to be necessary to assume, on the basis of normal distribution of ability, that each unit of the deviation for each age distribution either equaled the same number of scale units or the same proportion of the total distance from lowest to highest ability at each age measured in the point-scale units. ”

“ Let us suppose that we desire to find the degree of correlation in variation, or deviation from the mean, between an organ A, called subject, and a second organ B, called relative. We first take all the individuals of one (subject) class; that is, individuals whose subject organ deviates from the mean by a constant quantity, p. We next find for those individuals the average deviation-from-the-mean of the organ B, and call it q. We then find the ration q/p; this is the partial index of correlation. ”

“ If an epidemic begin in a definite locality and spread from that locality, and if there is no loss of infectivity on the part of the organism, it is demonstrable that a similar proportion of the population should be attacked in each zone as the epidemic spreads outward. ”

“ When the observed area is found markedly greater than that determined by the ideal curve, the indication is that there is still infection in the wound.... A rather surprising and unexplained situation occurs frequently when the wound-surface heals more rapidly than the ideal curve would indicate ”

“ For example: if the thigh-bone of many persons deviate ‘very much’ from the usual length of the thigh-bones of their race, the average of the lengths of the corresponding arm-bones will differ ‘much,’ but not ‘very much,’ from the usual length of arm-bones, and the ratio between this ‘very much’ and ‘much’ is constant and in the same direction, whatever be the numerical value attached to the word ‘very much.’ Lastly, the trustworthiness of the Index of Correlation, when applied to individual cases, is readily calculable. ”

“ The similarities to the medical field cannot go unnoticed if we are to deal with the problem rationally and effectively. And like a disease, we need to predict the effects of the infection. What we have found in that area is as frightening. ”

“ Errors from Stating Deaths in proportion to Total Deaths.—There is nothing erroneous per se in stating the proportion of deaths at one age as a ratio of the total deaths at all ages, or the deaths from one cause as a ratio of the total deaths from all causes. ”

“ During the 19th century, the tendency toward statistical enumeration becomes more and more prominent, but the first statistical studies of real value to the epidemiologist were made in the epidemic of thirty years ago. Statistical study must begin with this last epidemic. ”

“ In this investigation no account is taken of the reaction time. The reasons for this will be explained later.
The general plan has been first to apply the test to normal persons, so as to derive empirically a normal standard and to determine, if possible, the nature and limits of normal variation; and then to apply it to cases of various forms of insanity and to compare the results with the normal standard, with a view to determining the nature of pathological variation. ”

“ In distributing the errors we must consider the general skill of the observer, the size of his theodolite relatively to the others, and the conditions under which his angles were observed; failing any particular reason to assign a larger error to one angle than to another, the_ error must be divided equally, bearing in mind that an alteration in the small angle will make more difference in the resulting position than in either of the other two, and as it approaches 30 (the limit of a receiving angle) it is well to change it but very slightly in the absence of any strong reason to the contrary. ”

“ The usual method of measuring the health conditions of any community, such as a city, town, county, state, or country, is to compute the general death-rate, as it is called; that is, the number of deaths occurring per 1000 population. ”

“ On the other hand the number of suicides in a certain month, the average length of life in a given place, the number of teams and pedestrians per day at a certain street corner, and the like, are also noticeably constant, each being an average from large groups of observations. But both kinds of numbers, which I shall temporarily denote as constants of natural science and statistical constants, are, as everybody knows, constant from different causes and with entirely different significance for the knowledge of causal relations. ”

“ The strain that produces an error of refraction is not the same as the strain that produces a squint, or a cataract,2 or glaucoma,3 or amblyopia,4 or inflammation of the conjunctiva5 or of the margin of the lids, or disease of the optic nerve or retina. ”

“ This gives an ideal solid, which may be called the stress figure, whose height shows the distribution of stress over the surface which forms its base. A line drawn from g, the centre of gravity of the stress figure, parallel to the ordinates Aa, &c, determines the point c, which is called the centre of stress, and is the point through which the resultant of the distributed stress acts. ”

“ Perhaps we shall ultimately be able to estimate the increase or diminution of any one motion, which by affecting all the motions in a part or in the whole body constitutes disease. When the disease arises from increased action we shall restore that normal quantity and quality of motion in the body, on which health depends, by decreasing the motion, or adding to the resistance to conversion; and when the disease arises from diminished action we shall obtain the same result, by increasing the motion, or lessening the resistance to conversion.—Ib. ”

“ It will be seen that the lower half of the authentic scale has the compass of a fifth, and the upper half the compass of a fourth; while the plagal scale has a fourth for the lower half, and a fifth for the upper. ”

“ These graphs represent the normal form of distribution usually expected when any fundamental ability is measured in a random group. If the number of cases at each unit of measurement are plotted by a point placed relatively as far above the scale, used as a base line, as the number of cases found at that unit of the scale, it will be discovered that these points arrange themselves in the form of a symmetrical curve high at the middle and flaring out 257along the base-line scale. ”

“ The normal groups have been studied for the purpose of determining the frequency and manner of occurrence among normal subjects of the various of abnormal reactions. It seemed best for this purpose to consider separately the records of those subjects who gave an unusually large number of individual reactions. Fifty-three records containing fifteen or more individual reactions were found after a fairly diligent search among our normal test records. ”

“ We may take a horizontal line as an axis of abscissas, and lay off as an abscissa measured to the right of any origin, and erect as a corresponding ordinate, thus determining a certain curve. Again, taking a different origin, we may lay off as abscissas measured to the left, and determine a second curve by erecting the ordinates . ”

“ Farr, personally, as a vital statistician that invested with so much confidence the registrar-general's statistics, which shed so clear a light upon the black figures of our urban mortality statistics, and thus strengthened the hands of other workers in the field of sanitary reform. ”

“ Medical observation is ever incomplete, unless it take cognizance of all the functions, the aggregate adequateness of which, respectively ascertained, constitutes and is essential to health. The state of each should be accurately examined, however unconnected it may appear to be with the prominent derangement. Diligent scrutiny will often detect a morbid condition where it was unsuspected; and a negative should never rest on surmise wherever direct evidence is attainable. ”

“ There, for instance, the quantity of food is fixed, or increasing in a slow and only arithmetical ratio, and the proportion is limited by the same ratio. Supernumerary births consequently add only to your mortality. ”

“ The paradoxes of what is called chance, or hazard, might themselves make a small volume. All the world understands that there is a long run, a general average; but great part of the world is surprised that this general average should be computed and predicted. There are many remarkable cases of verification; and one of them relates to the quadrature of the circle. I give some account of this and another. ”

“ We may trust that ere long the concerted action of the entire medical profession will furnish us with a constant knowledge of the comparative prevalence of all disease. In the United States the want of such a system is in a manner compensated for by the periodical enumeration of causes of death at each national census. ”

“ On the whole, it seems to my mind, the burden of proof would be entirely on those who claim such a correlation between head-index, width of face, etc., and death-rate,—a correlation which I think is highly improbable, and which could be proposed only to sustain the theory of selection, not on account of any available facts. ”

“ In Fig. 7 curve H includes Gilbert's visual reaction time, Norsworthy's A and a-t tests, Carpenter's two A tests; curve I includes Gilbert's and Smedley's tapping tests; curve J is the median of the central tendencies of all 40 tests; curve K includes Norsworthy's two opposites and her part-whole and genus-species tests, the Pyle opposites, genus-species and part-whole tests; curve L is the same as D, curve M includes Smedley's strength of grip and ergograph tests and Gilbert's fatigue of tapping ”

“ In the present year, 1858, he read at the Epidemiological Society, and published in the Medical Times and Gazette, a repetition of his previous opinions, strengthening them by a statistical record, showing that the mortality of persons working at so-called offensive occupations is at certain ages lower, and at certain ages slightly higher, than in the general population. ”

“ There was an average loss of ·28 per cent in the weight-height-age relationship for the test group, and of 2·11 per cent for the control group. The average improvement of the test group in excess of the control group is, then, 1·83 per cent. The median improvement of test group over and above control is 4·00 per cent. The test group is more variable than the control in improvement. The greatest improvement, 8 per cent, is found in both groups.
TABLE IV Gain in Height—6 Months, 19 Pairs
The greatest loss, 10 per cent, is in the control group. ”

“ Broughton Brandenburg, Imported Americans, 208.
[18] This imaginary sketch adheres in every detail to the facts. The medical examiners and inspectors become exceedingly expert in detecting disease, disability, or deception. If an overcoat is carried over the shoulder, they look for a false or stiff arm. The gait and general appearance indicate health or want of it to them, and all who do not appear normal are turned aside for further examination, which is thorough. The women have a special inspection by the matrons, who have to be both expert and alert to detect and reject the unworthy. ”

“ Colossal statistics concur with the results of detailed inspection, to refer this disease, in common with many others that scourge our population, distinctly and infallibly, to the working of local causes—of causes susceptible of removal—of causes which it devolves on our Legislature to remove. ”

“ Imagine an epidemic in a hospital under such surveillance; the mortality is frightful even under ordinary circumstances. In acute cases, and in serious surgical cases, there is little or no chance for a successful result ”

“ Few people seem clearly to picture to themselves the meaning of a decimal plan in the percentage of death, and few clearly see that there are districts of England where the deaths at least in some years, and when no recognised epidemic occurs, are three times greater than in others. ”

“ The third rate, or the actual progression, is of course the most variable of all, being influenced by the greatest variety of causes. It is observable, that, while the checks, which produce the difference between the first rate and the second, have the property of retarding, and of taking away a part of the original rate of progression, still they are not connected with any limitation of its range, and their intensity is not necessarily increased in consequence of any actual increase of number. ”

“ If it is in excess, measures directed to bring it to the pathological norm should be instituted, but if the pressure found proves to be the pathological norm it is a bitter mistake to lower it, be the pressure what it may. ”

“ In all these things, as in the phenomena of symmetrical disease, we have proofs of the surpassing precision of the formative process, a precision so exact that, as we may say, a mark once made upon a particle of blood or tissue is not for years effaced from its successors. ”

“ Yet, in this respect, the prevailing notions are much less correct than they ought to be, and numbers are daily regarded as in perfect health, who, on a very slight examination, would shew evidences of such derangement of function, as only awaited an adequate exciting cause to be aroused into disease of the most intense activity. The habit too much obtains of ascribing the degree of severity of disease to the activity of the exciting cause. Much more truly would it be imputed to the state of constitution to which the exciting cause is applied. ”