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Remarks on the Pennington proposal for a standard test of stereoscopic plotting instruments
211 REMARKS O N T H E P E N N I N G T O N PROPOSAL FOR A STANDARD TEST OF STEREOSCOPIC P L O T T I N G I N S T R U M E N T S by W. SCHERMERHORN,Delft, Holl~md. As aerial photogrammetry is more and more being applied to map production the demand for all kinds of plotting instruments has increased accordingly. Official and private organizations have not only to decide on a certain plotting method, but also on the instrument most suitable for their purposes. In view of the high costs of the instruments, attempts have been made to compare the various types of instruments; therefore literature is often consulted for indications as to their accuracy. Sometimes the future buyer is disappointed, as it proves impossible to make an objective comparison of the various accuracy indications, owing to the fact that the test conditions vary. It stands to reason, however, that attempts are made to compare the instruments on the ground of the accuracy of the results obtained. Especially during its period of development, i.e. till 1940, photogrammetry had to compete with terrestrial survey. The surveyor doubted whether the accuracy would be sufficient for his purposes: manufacturers and photogrammetrists tried to dispel his doubts by submitting accuracy indications. Therefore the accuracy always played an important role. Of course the evaluation of the accuracy of the whole method nearly always coincided with that of the instruments. Since then this attitude has not changed much and the question which of two instruments has the greater accuracy is still the main point. It is still believed that this accuracy can be objectively expressed by one or two figures applicable to all kinds of aerial surveys. If this assumption were correct, some very simple instructions might be drawn up for a final testing method. Application of this method to all kinds of instruments would provide a possibility of comparison. As shown below, the problem of comparing instruments is not quite so simple; even the accuracy, however important, only forms part of a total comparison. The second problem - - which only arises after an instrument has been taken into use - - is the regular control of the adjustment and of the optical-mechanical quality of the instrument. Actually these are two problems. Each manufacturer of instruments indicates a method of adjustment, although some differences in the instruments do not always entail a different method of adjustment. It is inappropriate and also undesirable to prescribe the same adjustment method for all instruments. It should be left to the manufacturer to indicate those adjustment instructions which he considers best. Furthermore there is the problem of loss of accuracy in the course of time. Although there are instruments, which even after 100,000 working hours still produce reliable results (thus when the instrument is carefully handled the loss of ~ecuracy can never become serious) there is no doubt that after some years their accuracy decreases. Besides, it is well known that certain differences in accuracy exist between instruments of the same type. It is gratifying that the fine-mechanical industry has succeeded in improving the precision of its instruments. Consequently
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the accuracy of instruments built during the post-war period is greater than those of the years 1930--1940. The statistical researches concerning the sources of errors of plotting instruments have of course greatly influenced the precision of the manufacturer's adjustment. Another contribution to this greater precision has been made by the general development of the fine-mechanical industry and the great improvement of resources. When comparing an old with a new instrument of the same type, it is obvious that one would like to apply the same test to both, in order to ascertain how great the difference in accuracy actually is. Even then the question remains open whether a test which is applicable to all types is also the best for one type only. Besides, is it of such importance for the user to know whether the method which he applies to compare an old with a new stereoplanigraph can also be used for other types? From these considerations the following conclusions may be drawn: 1) When adjusting the instruments the manufacturer's instructions must be taken into consideration; 2) A standardized test may be used for controlling the general accuracy of one instrument or for comparing the accuracy of various instruments of the same type. It is, however, not necessary to apply the same test to different types. 3) For the comparison of instruments of various types so many other considerations must be taken into account that the accuracy test need not in all cases be decisive. In order to evaluate Mr. Pennington's test proposal in its relation to other qualities, the different viewpoints which play a certain role when judging plotting instruments, should be mentioned systematically: 1 What survey material can be used in the instrument? It is possible to plot directly from original negatives or from contact copies on glass or on shrink~proof, nontransparent material? Is it necessary to make reductions of the original photographs on a smaller scale? 2) What difficulties will arise when plotting photographs taken with cameras of different focal length and size of image? What complications will arise if the distortion is to be eliminated to within a few thousandths of millimetres? 3) Is the instrument suitable for the plotting of terrestrial photographs as well as of aerial photographs? Is it possible to plot not only vertical photographs, but also oblique and converging photographs? H o w important are these various possibilities for the usefulness of an instrument in a certain case? 4) Are the images observed stereoscopically in transmitted light with optical enlargement or are the images projected and viewed in reflected light without optical enlargement? 5) Is the instrument suitable for all sorts of methods of relative orientation including the numerical method by which calculated adjustments are introduced or is it only possible to use optical-mechanical orientation? 6) Is it possible when orientating to read and adjust from the observer's seat? 7) Is the instrument built in such a way that continuous aerial triangulation with reading of the coordinates system form the observer's seat is possible? Is the instrument provided with a mechanical registration of the coordinates system? Is the instrument suitable only for graphical plotting of the aerial triangulation?
213 ~8) What scale ratios are possible between aerial photograph and map? For instance between reductions of 3 • 1 up to enlargements of 1 : 10? 9) W h a t is the position with regard to the stability of the adjustment and what duration of life may be counted on if the instrument is regularly used and if there is no appreciable decrease in accuracy? 10) Is it possible to reestablish the original accuracy by means of a complete overhaul? After how many working hours would this become necessary and what would be the cost? 11) What is the price of the new instrument? Besides the planimetric accuracy obtainable with the instrument when transferring from photograph to map, the aforementioned considerations should be taken into account; they will, to a certain extent, influence the accuracy. For instance if the ratio of scale transfer is large, the mechanism of this enlargement will cause certain errors in the map. Another example is provided by the multiplex-like instruments where a certain inaccuracy ensues from the observation system. In both cases the aforementioned properties also influence the planimetric accuracy. Quite a number of these properties have nothing to do with the planimetric accuracy, yet they may be important when judging an instrument. Every buyer of an instrument should always be quite sure for what purpose he requires it. Small organizations, where all kinds of work have to be carried out on one instrument, should look for a machine with the greatest possible range of usefulness. If only vertical photographs of a highly cultivated and very detailed territory are desired, the plotting of oblique photographs will be less important than the capacity of the optical obser+ation system in the instrument. From these examples it is evident that a general comparison of plotting machines is a complicated matter, and that its value is entirely dependent on the special problems to be solved. Let us now examine more closely the accuracy control of a certain plotting machine. This may be done either by comparing it with the accuracy of other instruments of the same type, or by controlling the decrease of accuracy in the course of time. In order to obtain comparable expressions for this accuracy, it should preferably be expressed in the angular measure of the original image. When considering the European-Continental methods applied to this end by the manufacturers, it appears that all these procedures (with only one exception) resemble the Pennington proposal. For their own control of the instruments all manufacturers use grid plates. Galileo's grids for plates 18X18 have a mesh of 20 mm and for plates 235<23 meshes of 25 mm. The measurements are carried out on 25 of 81 points of intersection of the grids. Other firms use similar grid plates, mostly with 10 mm line distance. The mean error in the line position may be taken as 2-3 micron. See the publication on this subject by Fred. J. Doyle in this issue. Galileo, Wild and Zeiss start their adjusting by levelling both plate carriers independently, and by determining the zero points of the basis components. Then x and y are determined monocularly for a sufficient number of grid points. After setting a base length corresponding to the normal survey conditions, the 3 coordinates of at least 25 grid points are stereoscopically measured. This measuring is done by Galileo for two different h-values which are 3 f and 4 [; Wild measures h in three positions h, h + 0.2 h and h - - 0 . 2 h; Zeiss does it in
214 2 positions; h = 3 f and h = 5 f. Galileo repeats the setting of each grid point 5 times and introduces the mean as observation. The examination of the Stereocartograph Poivilliers/SO~M Model B is carried out by this firm according to a method which is considered best for this instrument. For adjustment and control the plate carriers are separated from the projection mechanism and the registration installation. The plate carriers are examined in a photogoniometer; the remaining mechanical part of the instrument is controlled with a view to the projective relation between the spatial direotion of the rays and the direction of their projection on x y and y z planes. No grids are used for the production and plotting of spatial photographs. Of course also on a Poivilliers SOM instrument it is possible - - after completion of the adjustment - - to carry out a grid measurement as control of the instrument, as is done for the abovementioned machines. When comparing these old test methods with the Pennington proposal it will be seen that this proposal resembles the conventional methods; the choice of h,ls measurements only being much smaller than usual. This raises a fundamental question. Mr. Pennington contends that when extensions are introduced, a standardized' test method becomes useless; the test for the applicability to all instruments becomes too complicated and the number of measured figures so large that an analysis and evaluation of these results would be too difficult. However, two purposes must be distinguished. If the user of an instrument requires a rapid working control, he will limit the number of his measurements as much as possible. If, however, a proper control is required to discover the various sources of error, or if the accuracy of an instrument as such is to be judged, the number of measurements proposed by Mr. Pennington is absolutely insufficient. The problem of properly testing a plotting machine cannot be simplified without greatly reducing the significance of this test. The best proof of the importance of such extensions is the fact that nearly all are to be found in the methods applied by the manufacturers. I shall therefore indicate and explain below certain necessary extensions of the Pennington proposal. 1) The accuracy in x and y is not only determined stereoscopically, but also monocularly. T o this end the two plate carriers are levelled, the principal distance and zero point are determined and the coordinates of the grid points are measured left and right. 2) It is necessary to execute the grid measurements at two or better still at three different heights, choosing the value in such a way that the whole plotting space is used. For a certain value of h the instrument may be adjusted in such a manner that the errors dx and dy are practically eliminated; thus the Pennington test might produce very good results, though at quite different heights the errors might be quite troublesome. For a control of the inner orientation it is absolutely necessary to adapt Mr. Pennington's proposal to industrial practice. If for a height a base length is set, the value of which is assumed to correspond to the angular field of the plate carrier and if the grid model is orientated stereoscopically - - as proposed by Mr. Pennington - - then for instance unequal errors in the setting of the principal distance might be eliminated by equal adjustment of tip; this latter adjustment will show only a slight deformation of the space model. With equal
215 errors in principal distance right and left, no trouble will arise when measuring at one height; however, with different heights appreciable and constant errors will arise in the distance between successive grid projections. On account of this fact too, measurements at only one height must be considered insufficient. 3) For a thorough test of an instrument it is not sufficien~ to measure only with wide-angle setting. Precision survey with normal angle objectives with a basis proportion 1:3 should also be taken into account. 4) The number of grid points to be measured as indicated by Mr. Pennington is also insufficient. The study of the deformation diagrams which might arise on account of the residual distortions, shows that at least the observation of all grid points indicated by Mr. Pennington in his figure, is necessary. The measuring of more points, e.g. on both main verticals and on the main horizontal, is likewise required. Similarly, the measuring of points in the middle of the diagonals 1-4, 3-4, 8-9 and 8-11 could be recommended. If the middles of the diagonals 4-5, 4-7, 5-8 and 7-8 in Mr. Pennington's figure are also measured, we obtain exactly the 23 points measured by manufacturers for the control of the instruments. 5) When carrying out a standard test a continuous triangulation of 2 grid plates should be prescribed. This kind of triangulation provides a proper insight into the systematic errors which the instrument produces, even with a perfectly constant base length. An extension might be possible by executing this triangulation at a second height, i.e. with a different base length. This second value shows to what extent the base length influences the systematic errors in the triangulation. This is important for the question whether the user is obliged to triangulate with a constant base length. 6) We do n o t agree to the extension proposals mentioned by Mr. Pennington under 1). When judging the instruments it is important that the model be controlled up to the corners. 7) With regard to repetition of each observation, we would like to state the following: like Galileo, we may repeat each setting five times and introduce the mean of these readings as observation. It is, however, preferable to repeat each setting and its corresponding reading only once; the whole grid measurement as well as the grid triangulation should be executed twice at three different heights. Thus each base length would be used twice. Only such a number of measurements as would result in two different figures for each value of the grid coordinates, and provided sufficient conformity exists, would furnish an impression of the accuracy of the instrument. By the two settings executed for each point, the actual accuracy of measurement may be judged. The difference between coordinates of the same grid points - - resulting from both series of observations - - when compared with the accuracy of measurement, provides an impression of the sensitiveness and stability of the instrument. A comparison of the observed and actual values of the grid point coordinates finally shows the accuracy obtainable with the instrument. 8) If, after application of these repetitions and comparing the observed and actual values of the coordinates, the final result is desired in mean square . errors, the method of this calculation must also be indicated. Besides the aforementioned considerations regarding the accuracy of the
216 instrument, it is imperative to carry out another different test: determination of the resolving power of the instrument. This test should include the complete procedure from original negative to the image as observed when plotting the map. The simplest method is obtained by producing a number of photographic copies of the same test tables as are used for the determination of the resolving power of photographic objectives. It is advisable to copy these test tables at at least 15 points of the same diapositive plate. A provisional solution would be to stick 15 small diapositives of this plate in the proper position directly on to a blackened diapositive. Test tables with a slight contrast should be used for this purpose. Such a plate may be placed in the instrument to be tested and the number of lines per millimetre still visible separately, may be counted. For instruments necessitating a reduction of the original image, the plate with the 15 small images should be reduced accordingly and the result observed in accordance with the normal procedure on the instrument in question. Also for multiplex-like instruments we obtain by this procedure an objective possibility of comparison for the general resolving power of the whole plotting procedure. It is clear that besides the measurement of grid plates, where the resolving power plays only a minor role, the aforesaid indication of this resolving power is necessary for the total evaluation of a certain plotting machine. It should be considered, however, that also for the evaluation of the resolving power - - just as for the accuracy -- the work to be carried out by the instrument plays an important part. For the operator who has nothing else to do than to trace contour lines in hilly jungle terrain, the resolving power is of less importance than for the photogrammetrist who has to produce large-scale maps of highly cultivated areas and who has to plot very accurately frontier stones of 10X10 cm which are hardly visible in his original photograph. The qualities of the instrument, including the accuracy as obtained from grid measurements as well as the resolving power of the total procedure should never be considered in themselves, but always in connection with the problems to be solved. This is no simple matter which can be solved, by means of a few figures as indicated in Mr. Pennington's proposal, by organizations who wish to buy photogrammetric instruments, but who have not the necessary experience.
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the accuracy of instruments built during the post-war period is greater than those of the years 1930--1940. The statistical researches concerning the sources of errors of plotting instruments have of course greatly influenced the precision of the manufacturer's adjustment. Another contribution to this greater precision has been made by the general development of the fine-mechanical industry and the great improvement of resources. When comparing an old with a new instrument of the same type, it is obvious that one would like to apply the same test to both, in order to ascertain how great the difference in accuracy actually is. Even then the question remains open whether a test which is applicable to all types is also the best for one type only. Besides, is it of such importance for the user to know whether the method which he applies to compare an old with a new stereoplanigraph can also be used for other types? From these considerations the following conclusions may be drawn: 1) When adjusting the instruments the manufacturer's instructions must be taken into consideration; 2) A standardized test may be used for controlling the general accuracy of one instrument or for comparing the accuracy of various instruments of the same type. It is, however, not necessary to apply the same test to different types. 3) For the comparison of instruments of various types so many other considerations must be taken into account that the accuracy test need not in all cases be decisive. In order to evaluate Mr. Pennington's test proposal in its relation to other qualities, the different viewpoints which play a certain role when judging plotting instruments, should be mentioned systematically: 1 What survey material can be used in the instrument? It is possible to plot directly from original negatives or from contact copies on glass or on shrink~proof, nontransparent material? Is it necessary to make reductions of the original photographs on a smaller scale? 2) What difficulties will arise when plotting photographs taken with cameras of different focal length and size of image? What complications will arise if the distortion is to be eliminated to within a few thousandths of millimetres? 3) Is the instrument suitable for the plotting of terrestrial photographs as well as of aerial photographs? Is it possible to plot not only vertical photographs, but also oblique and converging photographs? H o w important are these various possibilities for the usefulness of an instrument in a certain case? 4) Are the images observed stereoscopically in transmitted light with optical enlargement or are the images projected and viewed in reflected light without optical enlargement? 5) Is the instrument suitable for all sorts of methods of relative orientation including the numerical method by which calculated adjustments are introduced or is it only possible to use optical-mechanical orientation? 6) Is it possible when orientating to read and adjust from the observer's seat? 7) Is the instrument built in such a way that continuous aerial triangulation with reading of the coordinates system form the observer's seat is possible? Is the instrument provided with a mechanical registration of the coordinates system? Is the instrument suitable only for graphical plotting of the aerial triangulation?
213 ~8) What scale ratios are possible between aerial photograph and map? For instance between reductions of 3 • 1 up to enlargements of 1 : 10? 9) W h a t is the position with regard to the stability of the adjustment and what duration of life may be counted on if the instrument is regularly used and if there is no appreciable decrease in accuracy? 10) Is it possible to reestablish the original accuracy by means of a complete overhaul? After how many working hours would this become necessary and what would be the cost? 11) What is the price of the new instrument? Besides the planimetric accuracy obtainable with the instrument when transferring from photograph to map, the aforementioned considerations should be taken into account; they will, to a certain extent, influence the accuracy. For instance if the ratio of scale transfer is large, the mechanism of this enlargement will cause certain errors in the map. Another example is provided by the multiplex-like instruments where a certain inaccuracy ensues from the observation system. In both cases the aforementioned properties also influence the planimetric accuracy. Quite a number of these properties have nothing to do with the planimetric accuracy, yet they may be important when judging an instrument. Every buyer of an instrument should always be quite sure for what purpose he requires it. Small organizations, where all kinds of work have to be carried out on one instrument, should look for a machine with the greatest possible range of usefulness. If only vertical photographs of a highly cultivated and very detailed territory are desired, the plotting of oblique photographs will be less important than the capacity of the optical obser+ation system in the instrument. From these examples it is evident that a general comparison of plotting machines is a complicated matter, and that its value is entirely dependent on the special problems to be solved. Let us now examine more closely the accuracy control of a certain plotting machine. This may be done either by comparing it with the accuracy of other instruments of the same type, or by controlling the decrease of accuracy in the course of time. In order to obtain comparable expressions for this accuracy, it should preferably be expressed in the angular measure of the original image. When considering the European-Continental methods applied to this end by the manufacturers, it appears that all these procedures (with only one exception) resemble the Pennington proposal. For their own control of the instruments all manufacturers use grid plates. Galileo's grids for plates 18X18 have a mesh of 20 mm and for plates 235<23 meshes of 25 mm. The measurements are carried out on 25 of 81 points of intersection of the grids. Other firms use similar grid plates, mostly with 10 mm line distance. The mean error in the line position may be taken as 2-3 micron. See the publication on this subject by Fred. J. Doyle in this issue. Galileo, Wild and Zeiss start their adjusting by levelling both plate carriers independently, and by determining the zero points of the basis components. Then x and y are determined monocularly for a sufficient number of grid points. After setting a base length corresponding to the normal survey conditions, the 3 coordinates of at least 25 grid points are stereoscopically measured. This measuring is done by Galileo for two different h-values which are 3 f and 4 [; Wild measures h in three positions h, h + 0.2 h and h - - 0 . 2 h; Zeiss does it in
214 2 positions; h = 3 f and h = 5 f. Galileo repeats the setting of each grid point 5 times and introduces the mean as observation. The examination of the Stereocartograph Poivilliers/SO~M Model B is carried out by this firm according to a method which is considered best for this instrument. For adjustment and control the plate carriers are separated from the projection mechanism and the registration installation. The plate carriers are examined in a photogoniometer; the remaining mechanical part of the instrument is controlled with a view to the projective relation between the spatial direotion of the rays and the direction of their projection on x y and y z planes. No grids are used for the production and plotting of spatial photographs. Of course also on a Poivilliers SOM instrument it is possible - - after completion of the adjustment - - to carry out a grid measurement as control of the instrument, as is done for the abovementioned machines. When comparing these old test methods with the Pennington proposal it will be seen that this proposal resembles the conventional methods; the choice of h,ls measurements only being much smaller than usual. This raises a fundamental question. Mr. Pennington contends that when extensions are introduced, a standardized' test method becomes useless; the test for the applicability to all instruments becomes too complicated and the number of measured figures so large that an analysis and evaluation of these results would be too difficult. However, two purposes must be distinguished. If the user of an instrument requires a rapid working control, he will limit the number of his measurements as much as possible. If, however, a proper control is required to discover the various sources of error, or if the accuracy of an instrument as such is to be judged, the number of measurements proposed by Mr. Pennington is absolutely insufficient. The problem of properly testing a plotting machine cannot be simplified without greatly reducing the significance of this test. The best proof of the importance of such extensions is the fact that nearly all are to be found in the methods applied by the manufacturers. I shall therefore indicate and explain below certain necessary extensions of the Pennington proposal. 1) The accuracy in x and y is not only determined stereoscopically, but also monocularly. T o this end the two plate carriers are levelled, the principal distance and zero point are determined and the coordinates of the grid points are measured left and right. 2) It is necessary to execute the grid measurements at two or better still at three different heights, choosing the value in such a way that the whole plotting space is used. For a certain value of h the instrument may be adjusted in such a manner that the errors dx and dy are practically eliminated; thus the Pennington test might produce very good results, though at quite different heights the errors might be quite troublesome. For a control of the inner orientation it is absolutely necessary to adapt Mr. Pennington's proposal to industrial practice. If for a height a base length is set, the value of which is assumed to correspond to the angular field of the plate carrier and if the grid model is orientated stereoscopically - - as proposed by Mr. Pennington - - then for instance unequal errors in the setting of the principal distance might be eliminated by equal adjustment of tip; this latter adjustment will show only a slight deformation of the space model. With equal
215 errors in principal distance right and left, no trouble will arise when measuring at one height; however, with different heights appreciable and constant errors will arise in the distance between successive grid projections. On account of this fact too, measurements at only one height must be considered insufficient. 3) For a thorough test of an instrument it is not sufficien~ to measure only with wide-angle setting. Precision survey with normal angle objectives with a basis proportion 1:3 should also be taken into account. 4) The number of grid points to be measured as indicated by Mr. Pennington is also insufficient. The study of the deformation diagrams which might arise on account of the residual distortions, shows that at least the observation of all grid points indicated by Mr. Pennington in his figure, is necessary. The measuring of more points, e.g. on both main verticals and on the main horizontal, is likewise required. Similarly, the measuring of points in the middle of the diagonals 1-4, 3-4, 8-9 and 8-11 could be recommended. If the middles of the diagonals 4-5, 4-7, 5-8 and 7-8 in Mr. Pennington's figure are also measured, we obtain exactly the 23 points measured by manufacturers for the control of the instruments. 5) When carrying out a standard test a continuous triangulation of 2 grid plates should be prescribed. This kind of triangulation provides a proper insight into the systematic errors which the instrument produces, even with a perfectly constant base length. An extension might be possible by executing this triangulation at a second height, i.e. with a different base length. This second value shows to what extent the base length influences the systematic errors in the triangulation. This is important for the question whether the user is obliged to triangulate with a constant base length. 6) We do n o t agree to the extension proposals mentioned by Mr. Pennington under 1). When judging the instruments it is important that the model be controlled up to the corners. 7) With regard to repetition of each observation, we would like to state the following: like Galileo, we may repeat each setting five times and introduce the mean of these readings as observation. It is, however, preferable to repeat each setting and its corresponding reading only once; the whole grid measurement as well as the grid triangulation should be executed twice at three different heights. Thus each base length would be used twice. Only such a number of measurements as would result in two different figures for each value of the grid coordinates, and provided sufficient conformity exists, would furnish an impression of the accuracy of the instrument. By the two settings executed for each point, the actual accuracy of measurement may be judged. The difference between coordinates of the same grid points - - resulting from both series of observations - - when compared with the accuracy of measurement, provides an impression of the sensitiveness and stability of the instrument. A comparison of the observed and actual values of the grid point coordinates finally shows the accuracy obtainable with the instrument. 8) If, after application of these repetitions and comparing the observed and actual values of the coordinates, the final result is desired in mean square . errors, the method of this calculation must also be indicated. Besides the aforementioned considerations regarding the accuracy of the
216 instrument, it is imperative to carry out another different test: determination of the resolving power of the instrument. This test should include the complete procedure from original negative to the image as observed when plotting the map. The simplest method is obtained by producing a number of photographic copies of the same test tables as are used for the determination of the resolving power of photographic objectives. It is advisable to copy these test tables at at least 15 points of the same diapositive plate. A provisional solution would be to stick 15 small diapositives of this plate in the proper position directly on to a blackened diapositive. Test tables with a slight contrast should be used for this purpose. Such a plate may be placed in the instrument to be tested and the number of lines per millimetre still visible separately, may be counted. For instruments necessitating a reduction of the original image, the plate with the 15 small images should be reduced accordingly and the result observed in accordance with the normal procedure on the instrument in question. Also for multiplex-like instruments we obtain by this procedure an objective possibility of comparison for the general resolving power of the whole plotting procedure. It is clear that besides the measurement of grid plates, where the resolving power plays only a minor role, the aforesaid indication of this resolving power is necessary for the total evaluation of a certain plotting machine. It should be considered, however, that also for the evaluation of the resolving power - - just as for the accuracy -- the work to be carried out by the instrument plays an important part. For the operator who has nothing else to do than to trace contour lines in hilly jungle terrain, the resolving power is of less importance than for the photogrammetrist who has to produce large-scale maps of highly cultivated areas and who has to plot very accurately frontier stones of 10X10 cm which are hardly visible in his original photograph. The qualities of the instrument, including the accuracy as obtained from grid measurements as well as the resolving power of the total procedure should never be considered in themselves, but always in connection with the problems to be solved. This is no simple matter which can be solved, by means of a few figures as indicated in Mr. Pennington's proposal, by organizations who wish to buy photogrammetric instruments, but who have not the necessary experience.