The following means are recommended to ascertain if an eye has the defect now de scribed. The person should attentively con template for some time and with attention a cross, three or four lines in size, made of fine wire and fixed in a frame. If affected, he will see the horizontal lines differ in thickness and blackness of tint from the vertical.
To determine the focal length which the lenses should have, a person whose sight is preshyopic in one direction should take bi sphero•convex lenses which enable him to see distinctly at the ordinary distance the lines which otherwise appear indistinct: he can deduce the focal distance of the cylindrico convex glasses. A person myopic in one direction should do the same with regard to bi-sphero-concave lenses. The convex glasses should be chosen of one or two numbers stronger.
VITAL STATISTICS.—The duration of human life, with a consideration of the princi pal causes by which it may be lengthened or curtailed, is a subject which evidently belongs both to the domain of physiology and to that of statistics. It belongs to physiology, in asmuch as the duration of human life is the final effect of the operation of natural causes brought to bear on the healthy human frame ; and it belongs to statistics, whether we use that term in the less exact sense of a branch of human knowledge largely indebted to the use of numbers, or in the more accurate sense of a department of science, having an im portant bearing on the interests of the public.* ' In this place it is proposed to take only a limited view of the subject of Vital Sta tistics, and to examine the scientific methods which have been suggested and employed for determining the true duration of human life in communities and classes of men; in other words, to do for this important branch of statistics what has been done elsewhere the statistical or numerical method.* Flaying already insisted on the precautions to be ob served in the use of numbers as a scientific instrument, it remains to determine the pre cise value of those measures of the duration of life which are in common use for scientific and practical purposes.
On a superficial view of the subject, it might seem sufficient, in order to determine the mean age attained by a given class of persons exposed to a given class of influences., to collect the ages, at death, of a certain number of persons belonging to that class, to add those ages together, and to divide the sum by the number of persons. But it must be evident, on further consideration, that an average so obtained may furnish a very im. perfect measure of the longevity of the class, and of the force of the influences brought to bear upon the individuals of whom it is com posed.
In order to build up a science of Vital Statistics— in other words, in order to deter mine the true influence of external agents on the duration of human life, we must make use of such materials as happen to be ready to our hands. These materials do not always
present themselves in the same shape, nor do they all possess the same value. Sometimes they are simple averages ; at other times they are complex calculations based upon the same, or similar facts, but moulded into new forms by means of certain necessary corrections. A few preliminary observations on these mate rials will be found to answer several useful purposes. They will serve, at one and the same time, as a test of the value of the prin ciples sought to be established, and as a check to the tendency with which the statist is often reproached to exaggerate the value of inferences drawn from numerical data.
Several methods are in use for measuring the duration of human life. Of these, the best known and most commonly employed are the following: 1. The mean age at death ; 2. The rate of mortality ; 3. The expectation of life ; 4. The mean duration of life ; and 5. The probable duration of life. Other terms, such as the specific intensity of life, and other methods, such as the ages of the living, are occasionally employed.
1. The mean age at death. — The mean, or average age at death, is the sum of the ages at death, divided by the number of deaths. Thus, if five persons die at the respective ages of 20, 30, 40, .50, and 60, their mean, or average age at death is 20+30+10+50+60, 5 or 40 years ; and if a second group of five persons die at the respective ages of 20, 35, 50, 65, and 80, their mean age at death is 20+35+50+65+80 ' or 50 years. Now, if 5 these two groups of five persons were each exposed during their lives to a peculiar set of influences, the mean age which they respec tively attained would be a measure of the force of those influences. But such a mea sure would be open to the serious objection that the number of facts from which the averages are calculated is insufficient. Let us, however, suppose this objection to be set aside by increasing the number of deaths in each case to several hundreds or thousands, so as to embrace either the entire number of deaths of the classes submitted to comparison, or such a considerable proportion of deaths taken without selection as would give satis factory results in accordance with the strictest requirements of the numerical method, the question still presents itself, Is the mean age at death a safe measure and standard of com parison? The answer to this question must be in the negative. The mean age at death is not always a safe and sound standard. Its employment would often lead to very erro• neous inferences. It will therefore be neces sary to discriminate between those cases in which it may be employed with safety, and those in which its use would lead to fallacious results.