of four zones, and then substitute successively the values obtained in the equation 1 (36) Ome=45o.- cos? ✓7213,2+1-1 -1) which is easily deduced from the equation of the ellipse, putting Imz for the radius vector, we get as the angles to which the mean radii vectores of the several zones of equal area correspond H'=28 51' (37) A,'=52° 33' 0,' =6723' 8,'=82° 20' If, now, we were to place a mirror at each of these angles, both above and below the horizontal axis, but only on one side of the vertical diameter, then for a source having an intensity curve identical with the assumed ellipse, the mean value of the intensity from the eight mirrors, obtained by dividing the sum of the intensities from the mirrors by eight, would exactly equal the mean spherical intensity of the source, provided, of course, that the surface of distribution of intensity is a figure of revolution around the vertical axis. This is never the case, and since, in general, when the maximum curve is on one side of the arc the minimum curve is on the other side, hy placing eight other mirrors on the other side of the vertical diameter at the same angles as those already located, the mean intensity in the complete vertical plane is obtained, which will be more nearly equal to the mean spherical value than the value obtained from mirrors on one side of the vertical diameter only. In order to obtain mean spherical values of any considerable accuracy the mean of a great number of determinations of the mean vertical intensity must be taken. In a similar manner mean hemispherical determinations can be made if the surface of the sphere is divided into an even number of zones, as was pointed out above in the discussion of the Matthews instrument. The typical curve of the open arc does not correspond exactly with such an ellipse as assumed in the preceding discussion, but the errors in arc-light photometry are in other respects necessarily so large that the difference between the true mean value for a vertical plane and that given by the mirrors arranged to satisfy the ellipse distribution will in general be much smaller than the other errors incident to the measurement. If a closer agreement between the integral and summational values of the arc is desired without increasing the number of mirrors, it would be necessary to investigate in detail the typical curve of the arc, and from this curve to compute the angles corresponding to the true distribution of mirrors, In order to determine the magnitude of the error that would arise if the form of intensity curve differed to any extent from an ellipse, the distribution of mirrors satisfying the ellipse was applied to the two curves, (38) To=sin 6 and (39) To=cos The true integral means of these are, respectively, [eq. (24)] whereas the values given by one-fourth of the summations of the sines and cosines, respectively, of the angles of eq. (37) are Ime =.7976 which are in error by 1.6 per cent and 0.1 per cent, respectively. V. APPLICATION OF THE RUSSELL-LÉONARD PHOTOMETER TO INCANDESCENT LAMPS. In the application of the Russell-Léonard photometer to incandescent lamps the problem is just the same as in the application to arc lamps, except that here we seek the distribution of mirrors that will satisfy the three intensity curves Any distribution of mirrors which will satisfy these three cases will yield very small errors when applied to any actual curves. Moreover, since any distribution of mirrors in zones of equal area will satisfy case I, we simply have to determine the distribution most nearly satisfying cases II and III. The true integral values for cases II and III, respectively, are [eqs. (10) and (41)] Imx=.7854 Im=.5000 If we divide the surface of the sphere into twelve zones instead of eight, the distribution of mirrors satisfying case II, as determined by evaluation of eq. (28) for each of the twelve zones, after putting for f(a) its value sin 0, gives an error of 1.0 per cent when applied to case III. Similarly the true distribution for case III gives an error of 0.7 per cent when applied to case II. If, however, we take a distribution of mirrors intermediate between the two true distributions, i. e., if we take 4 = 22° 47' 0,=41° 14' 4,= 54° 15' (42) 0,= 65° 14' 4. = 85° 8' the error is divided between the two cases, so that the summational values for cases II and III are, respectively, Im=.7883 I=.5025 the corresponding percentage errors being 0.4 percent and 0.5 per cent. We have divided the surface of the sphere into 12 zones in this case, as compared with 8 in dealing with are lamps, because in the first place a higher accuracy is obtainable in the photometry of incandescent lamps, and, secondly, if the incandescent lamp is rotated, 12 zones demand only 12 mirrors which can be arranged around the whole circle, whereas 8 zones demand 16 mirrors in the arc-light photometer,--S mirrors on each side of the vertical diameter. Thus, for incandescent lamp work, 12 mirrors, each ti inches broad, can be arranged in a circle of 3 feet diameter, and yield a result accurate to within about 0.5 per cent for lamps of various intensity curves, whereas the Matthews instrument, as at present constructed, gives an error of over 2 per cent (Tab e II) when applied to the lamp having the intensity curve l. = cos A. It has not been the intention, in this discussion of the RussellLéonard photometer, to make the treatment exhaustive, but rather to suggest the method which can be applied to locate the mirrors in the zones after the uses to which the instrument is to be put and the consequent general dimensions of the instrument have been determined. ·THE TESTING OF CLINICAL THERMOMETERS. By C. W. WAIDNER and L. A. FISCHER. Soon after the organization of the Bureau of Standards work preparatory to the testing of clinical thermometers was taken up. At the same time all of the prominent manufacturers of clinical thermometers were requested to submit samples of their product in order that the Bureau could determine what accuracy might be expected and what defects were most common. The design and construction of the apparatus required for this purpose was undertaken with two main objects in view: first, that the highest accuracy should be obtained, and second, that the tests could be made so rapidly that the fees for testing would be reduced to a minimum. The apparatus finally adopted has been in use for some time, and the methods of testing have been subjected to exhaustive trials. As both the apparatus and methods used by the Bureau have been the subject of numerous inquiries, it is deemed advisable to publish a full description for the use of those interested and also an account of the experiments upon which the regulations finally adopted are based. The first tests made showed that many of the clinical thermometers had errors as large as 0.5° or 0.6° F., and in some cases even larger error's were found. Moreover, a study of groups of thermometers suggested that the standards used were in error. The manufacturers were accordingly requested to submit their standards to the Bureau for examination. Without exception this request was complied with, and, as suspected, the conclusion that the standards were in error was confirmed. « The work was begun in the section of weights and measures under the direction of Mr. Fischer, and was subsequently transferred to the section of thermometry, upon its organization, under the direction of Dr. Waidner. CLINICAL STANDARD THERMOMETERS. Some of the standards submitted were found to be radically defective in construction. Some were so constructed that when used in the water bath for the pointing of ordinary clinical thermometers the stems projected above the surface of the bath by amounts corresponding to 60 F. and even more. Since changes of 20° F. or more occur in the temperature of rooms where clinical thermometers are graduated, and since the temperature of the exposed portion of the stem is largely controlled by the temperature of the room, there is here presented a possible source of error of about 0.1° F. Another defect common to most of the clinical standards submitted was the absence of the ice point (32° F.) from the scale. The presence of this point is important, since it enables one immediately to detect any change in the indications of a thermometer by determining the ice point in a mixture of finely crushed pure ice and distilled water. If any change is detected in this point the reading of the thermometer may then be corrected. It is true that most of the standards used by manufacturers are quite old, and hence changes in these thermometers would probably be small. Nevertheless changes might occur on account of the development of minute air bubbles or other causes, which, as before stated, would be readily detected by a determination of the ice point. A form of clinical standard well adapted for the pointing or testing of clinical thermometers is shown in fig. 1. Immediately above the ice point is an enlargement of the bore, which makes it possible to obtain on a short stem the ice point and also the range of temperature required in clinical thermometry. Above the enlargement there are graduations corresponding to 0.1 and covering the range 90- to 110° F. In ordinary use these standard thermometers are immersed in the water bath to about the 93 mark, so that not more than 17 is emergent from the bath, and hence the variations in the temperature of the room may be neglected. The corrections to these thermometers are carefully determined by comparing them with the primary standards of the Burean. These latter are made of the usual thermometric glasses, namely, French hard glass or Jena 1611 normal glass, and are artificially aged, before final filling, by exposing them to a temperature of about 850 F. for at least 60 hours, after which they are allowed to cool slowly. When treated in this manner subsequent time changes are extremely small. The graduations on these thermometers are very fine, whereas some of the standards submitted to the Bureau for examination were only graduated into 0°.2 F., and the graduation lines were nearly as wide |