DECEMBER 1916. Vol. XLI. No. 489. QUANTITATIVE MICROSCOPY. BY T. E. WALLIS B.Sc. (LoND.) F.I.C. (Read at the Meeting November 1 1916.) INTRODUCTION THE use of the microscope for determining the proportioiis of substances present in mixtures is generally regarded as an unreliable method of procedure and the results obtained have failed to carry weight as evidence in courts of law. The difficulties experienced in such work arise partly from the methods of manipulation that must be followed for microscopical work and partly from the nature of the substances examined. A common method of working has been to mix the powder with a fluid medium in a mortar transfer a drop to a microscope ,slide apply a cover-glass examine with the microscope and take a count of the number of certain characteristic structures seen in a particular number of fields.This result is then compared with that obtained by making similar counts of pre-parations made in an exactly similar way from powders of known composition 358 WALLIS QUASTITATiVE MICROSCOPY Such a process is liable to error for various fairly obvious reasons as for instance, the variation in the size of the drop of liquid taken up by a glass rod and the de-pendence of the thickness of the film of liquid examined upon the weight of the cover-glass the amount of pressure used in mounting and the nature of the fluid. Moreover no guidance is given as to the selection of the fields to be counted aiid no indication is provided as to the range of error to which the resulting figures we subject .Purther difficulties arise from the smallness of the quantities actually exanlined during %he process. For most ordinary work I have found that a fluid containing 0.2 grm. of substance in 10 to 20 C.C. is suitable for examination with a one-sixth inch (4 mm.) objective which it is necessary to use when one desires to count with precision. The depth of fluid between the cover-glass and slide must not exceed about 0.1 mm. and with a cover-glass of 19 mm. ($ inch) diameter the total volume of fluid is about one thirty-fifth of a cubic centimetre. Since 10 to 20 C.C. conti-tiia 0.2 grm. of the powder the amount of material under the cover-glass is from two to four sevenths of a milligram. The diameter of the field given by the one-sisth inch objective that I use is 0.53 mm.and its area 0.22 sq. mm. and the area of a circular cover-glass of 19 mm. diameter being 284 sq. mm. there are 1,291 fields under the cover-glass and each field will represent approximately a quantity of material varying from about two to five ten-millionth parts of a gram. I n tweiitF fields one is concerned with about one 250th to one 100th part of a mgrm. of material. and i t is upon a correct analysis of this minute quantity of the substance that the final result depends. When one considers this fact in addition to the uncertainty and lack of precision arising from the methods commonly adopted one cannot wonder that figures based upon microscopical methods are regarded with a certain scepticism and it is easy to understand the failure of such methods in the absence of any exhaustive investigation of their worth to carry weight as evidence of extent of adulteration.It has also been recommended in the case of mixtures of starches that photo-graphs of preparations from mixtures containing known percentages of the mixed starches should be made and that the proportion present in an adulterated starch should be estimated by comparison of a photograph of a preparation from the sample with the photographs of the standard mixtures. This method must inevitably be unsatisfactory since the ratio of the two kinds of starch grains to one another varies considerably from field to field of the same preparation and a true proportiolz can only be obtained by counting a sufficiently large number of fields. The accom-panying figures representing counts of potato and maize starch granules in a 50 per cent.mixture of the two illustrate fhis point. The mixed starches were rublml down in a mortar with dilute glycerol and the counts of ten fields selected accorriillg to the plan suggested below were as follows: Potato starch . . . . 28 18 28 21 25 19 18 18 34 22 Maize starch . . 185 140 171 186 195 183 158 188 1’74 173 If the number of potato starch grains in each field is represented by 100 the numbers representing the maize starch are 661 778 611 886 780 863 878 1,044 512 an WALLIS QUANTITATIVE MICROSCOPY 359 786 respectively figures which show a difference of 100 per cent. between the extreme values. The types of substance to be examined may be classed as follows: 1. Material consisting of portions all of t'he same kind and all varying in size within certain definite limits.such as starches pollen grains and spores. 2. Material that is all of the same kind-e.g. wholly cellulose or wood-but composed of particles of sizes varying between arbitrary limits depending upon the brittleness or toughness of the substance and upon the method of sifting or grading. Fibres pine-wood sawdust powdered coco-nut shells and olive stones, are examples. 3. Material presenting a variety of structures among which there are some, such as starch grains crystals stone cells etc. which are of diagnostic value. The majority of food-stuffs and drugs fall under this head. The difficulty of dealing with these types increases in the order in which they have been enumerated and although one may be able with a small amount of preliminary research to obtain results of sufficient accuracy with the more simply constituted materials it will be only after extended investigation that one can hope to decide upon the line of approach that will lead to the successful application of a reliable method of counting in the case of a substance exhibiting structures of many different types.The work recorded in this communication relates t o experi-ments whose aim has been to devise a general method of procedure that will give precision 60 c n m t s made mder the microscope and so to emble one to obtain, by the use of this instrument quantitative results which will carry conviction in much the same way as do figures based upon ordinary chemical processes.ADMIXTURE OF A SL~BSTANCE AS A STANDARD FOR COMPARISON. The plan adopted by bacteriologists for the counting of bacteria in a vaccine by mixing it with blood a,nd determining the ratio of bacteria to red blood-corpuscles suggested the idea that if one could add to powders a substance consisting of uniform grains corresponding to the corpuscles it would be possible to use a similar device in the case of powders. This procedure eliminates the errors due to variations in the size of the drops falling from the glass rod used in making the mount and renders it unnecessary to bring the volume of liquid to any exact measure. The difficulty arising from variation in the thickness of the film of liquid between the cover-glass and the glass slide is also removed.A substance suitable for admixture in this way must exhibit certain important characteristics : 1. It must consist of grains of uniform size and having dimensions comparable with those of starch grains. 2. The grains should be fairly resistant to pressure and have strongly marked characters clearly differentiating them from all ordinary vegetable structures. 3. It should be unaffected by clearing reagents and stains used in microscopical work-that is i t must not be rendered invisible or be destroyed by such things as caustic soda chloral hydrate clove oil and strong hydrochloric acid. 4. It must be fairly easy to obtain the substance commerciall 360 WALLIS QUANTITATIVE MICROSCOPY It is soniewhat difficult to find a suitable material for admixture; but after a few trials I concluded that something which occurs naturally in uniform grains could be the only possibility.I finally decided to try lycopodium spores which are highly resistant to strong clearing reagents and have a diameter of from 2Op t o 28 p which is not larger than that of many stmarch grains. Their characteristically sculptured surface and tetrahedral shape makes them easy to identify and dis-tinguishes them clearly from all structures commonly found in vegeta,ble powders. A few experiments made it evident that t'hey fulfilled the requirements exactly. USE OF A SUSPENDING MEDIUM. T n my earlier experiments I tried working with the dry powders wit,hout any suspending fluid. The lycopodium and the powder under investigation were thoroughly mixed and then a small portion was taken with the point of a knife and placed upon a glass slide moistened with alcohol or in the case of a woody adulterant with a 1 per cent.solution of phloroglucinol in alcohol dilute glycerol or other iiiountant added the whole stirred with a glass rod and a cover-glass applied. The results were surprisingly exact; but every now and then a count which was obviously very far from correct would be obtained and this was due to the difficulty experienced in producing a perfect distribution of the constituents of the mixed powder. Such variations introduce an elenlent) of uncertainty and make it iixpoaaible 60 determinc the proportions c?f the materials in the mixtiire so satisfactorily that one would feel justified in reporting the figures found.To obtain a more complete mixing and to prevent the separation of heavier from lighter part'icles by tlhe liquid a number of suspending agents were tried. Such a substance should possess the following characters : 1. Its density should be less than that of lycopodium spores-i.e. less than 1.0S6-so that' all the material will tend to sink and not be separated into a flonting layer and a sediment consisting of entirely different materials. 2. The viscosity should be moderately high so that the suspended powders may sink slowly. 3. The medium should wet the powders readily and penetrate the substance of the walls of cellular structures so that air is excluded and the particles appear transparentl. 4. It must wet oily as well as dry and moist powders. 5 .It should prevent the deposition of the suspended matter or should allow the sediment to be easily shaken up to form an evenly distributed suspension. 6. It must mix readily with such reagents as alcohol and strong hydrochloric acid. There is no substance which satisfies all these conditions; But there are a few which show a near approach and by varying the details of working to meet special requirements one may hope to find a medium suited t o every case. Of the two common mucilages which immediately suggest themselves as sus-pending agents mucilage of acacia closely approaches the condition of a true solu-tion and for this reason behaves as a viscous fluid of considerable density. It i WALLIS QUANTITATIVE JIICROSCOPE' 361 not very suitable for microscopical work because i t completely separates a mixture containing lycopodium spores which after an interval of about twenty-four hours form a floating layer while starch and other matters collect as a sediment.The whole shakes up again fairly well but it is undesirable to use any medium which effects so complete a separation of the substances to be counted. Its stickiness and property of drying rapidly to form a hard brittle film when spread in a thin layer are also features which militate against the use of mucilage of acacia. Mucilage of tragacanth has an entirely different structure; it depends for its efficacy upon the presence of a fine network of cellulosic material distributed through an aqueous fluid. For this reason the mucilage tends to keep suspended particles in a more or less fixed position with respect to one another.That this is the case I have shown by making counts after suspensions have stood undisturbed during an interval of from three to five days when the proportions of lycopodium spores and of other particles have been found to remain constant. The suspending pro-perties of the mucilage are unaffected by alcohol and by strong hydrochloric acid. Mucilage of tragacanth is therefore a very efficient suspending agent and is most useful for quantitative work with the microscope. There are however certain drawbacks to the use of mucilage of tragacanth, such as the occurrence of a few granules resembling starch grains i t e lack of com-plete transparency and its unsuitability for use with oily powders. In the majority of cases the starch grains introduce no difficulty as they are only few in number and are readily distinguishable from aost othcr starches.The medium is rendered more transparent by using a mixture of 1 volume of glycerol and about 4 volumes of mucilage of tragacanth. If used for oily powders the fatty matter must be removed by a preliminary extraction with a suitable solvent. Oils such as olive oil and castor oil have proved extremely useful not only in the case of oily powders like mustard and pepper but also for general use with powdered vegetable substances. Their densities axe slightly less than that of water, and hence all the suspended matters are deposited on standing and settling takes place slowly owing to their considerable viscosity. In the case of olive oil the sediment is easily shaken up again to form a uniform mixture; but with castor oil this is not effected so readily and consequently owing to its very high viscosity, castor oil is not so useful as a suspending agent.The great penetrating power of the oils causes them to mix readily with dry powders to displace air from cavities, and to render all the particles transparent. Oils are useful for starches especially when one wishes to use the polariscope to aid in distinguishing one kind of grain from another. The possibility of using soft paraffin suggested itself as the result of experience gained while examining an ointment composed of mucilage of starch and vaselinc. A few experiments demonstrated its utilit,y as a suspending medium and an examplc of its apphation is given under the heading of niustard among the experiments cited below.Soft paraffin is less generally useful than olive oil because more time and trouble are needed to obtain a satiefactory mixture of the powders and medium than is the case with the oil. Also when polariaed light is used the crystalline sbrncture of the paraffin produces a confused network of bright lines which tends t 362 WALLIS QUAh'TITATIVE MICROSCOPY obscure the objects to be counted. It is quite possible however that the occasion may arise when the peculiar properties of soft paraffin will indicate its employment in preference to any other suspending agent. Glycerol can be used successfully but its high density results in a complete separation of the lycopodiuiii as a floating layer after the preparation has stood for some hours and its great viscosity increases the difficulty of redistributing the materials evenly when the suspension is shaken up again.A mixture of alcohol and glycerol in equal volumes has been recommended for suspending such materials as mixed starches (" Admixture of Oatmeal with Barley Meal," by E. L. Cleaver, ANALYST 1877 I. 189); but alcohol decreases the viscosity to such an extent that one finds considerable difficulty in producing a uniform mixture of the powders with the fluid and in breaking up small groups of spores or starch grains. Mixing the powders first with glycerol and thinning with alcohol afterwards is also un-satiefactory . GENERAL STATEMENT OF THE METHOD OF WORKING. Expressed in general terms one proceeds in the following way: 1.Make a mixture of the pure substance with an equal weight of the adulterant whose amount it is desired to determine. The two substances may either be dried at 100" C. or preferably used air-dry; estimate the moisture present and apply the necessary corrections in the calculations. Mix 0.2 grm. or other convenient weighed quantity of this standard mixture with 0.1 grm. or other suitable amount of lyco-podium and sufficient of the suspending fluid to produce a liquid of which 1 drop, when mounted and examined with a one-sixth inch objective shall show from 10 to 20 lycopodium spores in each fiald. I n most cases this result will be obtained when the total volume is about 20 C.C. 9 drop of the suspension is transferred t o a slide by means of a glass rod and it cover-glass applied.Count the number of particles of adulterant and of lycopodium spores in ten fields selected according to the scheme detailed below. Mount a second drop on another slide and again record ten counts. Find for each set of ten counts the ratio of the number of lycopodium spores to the number of characteristic elements of the adulterant and express the results as the number of characteristic elements counted for every 100 lycopodium spores. The numbers found for the two sets of counts should not differ by an amount greater than 10 per cent.; should they do so fresh counts must be made. 2. Mix 0.2 grm. or other suitable amount of the sample in which the percentage of adulterant is to be determined with 0.1 grni.or other convenient amount of lycopodium and about 20 C.C. of suspending fluid. Xount a drop on each of two slides and count ten fields on each. Calculate the ratio of the number of spores of lycopodium to the number of characteristic elements of the adulterant and express the result in the same form as for the standard mixture. 3. The numbers obtained for the foreign substance in the two sections of work are directly proportional to the amounts present and a simple calculation gives the quantity sought. A correction must be appiied for moisture. Further manipu-lative details are given below in describing the experiments which were planned and carried out in order to illustrate and test this method of making quantitative determinations by means of the microscope WALLIS QUANTITATIVE MICROSCOPY 363 DISCUSSION OF DETAILS.The quantities of mixture and of lycopodium recommended for preparing the suspensions are such as have proved generally useful. In cases where the amount of inaterial to be counted is very small as in the determination of small percentages of powdered olive stones the proportion of mixture should be considerably increased ; and where the number of particles is very large as when one is dealing with a small-grained starch a greater propxtion of lycopodium must be used. Examples of these two cases will be found among the experiments. The powders used in preparing the 50 per cent. standard mixtures must be mixed very thoroughly by trituration in a mortar turning out on a tile or sheet of glass and mixing with a spatula returning to the mortar and repeating the process a few times until an intimate mixture is obtained.When dealing with powders in which woody structures are t o be counted the mixing should not be done on paper, since most paper contains woody tissue and a certain small amount of the fibres from the surface of the paper works up into the powder and causes errors in making counts of woody elements. A 50 per cent. mixture is recommended for use in most cases instead of the pure adulterant because difficulties that will arise in dealhg with the sample to be tested will also arise with the standard mixture and the operation of counting the sample will be facilitated and rendered more precise. There are occasidns when counts made with the pure substance are very useful as in the case of a mixture of two pawders b3th containing woody elements or other diagnostic structures of which a particular kind is to be estimated.Some confusion may tend to arise between those proper to the powder a.nd those belonging to the adulterant, and a useful check may be obtained by counting the pure adulterant against lyco-podium as well as counting a 50 per cent. standard mixture. Close agreement between these two results will greatly strengthen one’s reliance upon the accurMy of one’s judgment in distingaiahing the woody elements starch grains or other striictures similar in type but different in origin. Before adding the liquids to the weighed quantities of lycopodium and other substances these powders should be thoroughly mixed in a dry state by rubbing them together upon a sheet of glass with a spatula.This thorough trituration distributes the constituents much more evenly and breaks down any little collec-tions of adhering spores or starch grains. These mixinga may be carried out in a mortar provided that the trj turation is gentle ; otherwise the lycopodium spores will be largely broken. Mixing in a mortar presents no advantage and on the whole the use of a plate and spahula as described is to be preferred since it is almost impossible to break the spxes by this means and the mixing is quite satisfactory. CHOICE OF THE FIELDS TO BE COUNTED. In selecting the fields to be counted care must be taken to avoid the possibility of counting the same field twice and the positions of the fields chosen should be evenly distributed over the whole preparation.Their positions must also be fixed arbitrarily by soms previously axepted arrangement so as to avoid the errors that u!iiatsntionslly anise iii selscting fidds which one thinks suitable for counting 364 WALLIS QUANTITATIVE MICROSCOPY This selection can only be made by the use of a mechanical stage having graduaticns on the two movements at right angles to one another. For an jnstiuEcnt havir-g a plain stage one can use one of the very satisfactory forms of attachable mechanical stage. The position of the fields to be counted is best fixed by choosing positions at certain distances from the middle point; if the slide is then placed on the stage so that the lens is over the centre of the cover-glass one can note the reading for the position of the right-hand near corner of the Elide on the two scales of the mechanical stage and then move it precisely into the positions required for making the counts.For my own experiments I have counted ten fields on each slide and the positions selected are shown in the accompanying diagram all distanccs being D~a~eaiv SHOWING THE Posrrross OF TILE FIELDS C o c s m ~ . Tlie numbers indicate distances in millimetres from the centre of the cover-glass. given in millimetres from the centre of the cover-glass. To make the actual counts it is necessary to use an eye-piece micrometer ruled in squares and to count regularly along each line of squares in succession until the whole field has been covered. The number of fields to be counted will depend upon the intimacy of the mixing.If perfect mixing could be secured a very few counts-say three-would be suffi-cient; but since each field contains only about one four-millionth of a grm. of sub-stance and half that amount of lycopodium it is very difficult and in my experience, impossible to obtain by ordinary means so complete a mixing. One must therefore continue until so many fields have been counted that the counting of an additional one will not appreciably alter the ratio obtained. In actual practice I have found 20 fields give a reliable result ; and if these are counted in two sets of 10 upon different slides one set acts as a check upon the other and so adds to the precision of the operat ion WALLIS QUANTITATIVE MICROSCOPY 365 R,ECORD OF EXPERIMESTS.The following examples will serve to illustrate the method employed the kind of difficulties that arise in the course of such work. and the way in which modifica-tions may be introduced in order to meet special conditions. The mixtures chosen for experiment are such as have been reported as occurring in actual practice and consist of materials which cannot be determined quantitatively by other than microscopical methods. used as a suspending agent was prepared from the dry powder at the time of mixing; 0-2 grm. of the mixed flours 0.1 grm. of lycopodium and about 0.12 grm. of powdered gum tragacanth were carefully mixed together and put into a cylindrical weighing bottle of about 40 C.C. capacity. About 1.0 C.C. of alcohol was added and shaken with the powders; 20 C.C.of water were poured in rapidly the stopper replaced, and the whole shaken vigorously for two or three minutes. The counts made were MIXTURES OF WHEAT FLOUR AND CoRNFLOUR.-The mucilage Of tragacanth as follows : Mixture of Wheat ten fields: Maize starch L yc opodium . . Flour 50 per Cent. and Cornflour 50 per Cent.-B'irst set of 14 15 7 11 11 5 4 13 12 10 = 102 43 T4 53 33 61 39 25 38 57 59 = 482 Lycopodium spores - 100 Maize starch grains 473' Ratio - - _ _ - - - -Second set of ten fields : Lycopodiurn . . 11 11 11 7 12 7 4 9 9 12 = 92 Maize starch . . 51 45 57 52 63 28 23 37 47 36 = 439 Lycopodium spores - 100 Ratio - - -Maize starch grains 477' Lycopodium spores - 100 Maize st&rch grains - 475.Average ratio - -: Mixture of Wheat Flour 62.2 per Cent. and CornJlour 37.8 per Cent.-B%st set of ten fields : L y c opo dium . . 13 10 14 20 21 11 4 14 16 12 = 135 Maize starch . . 48 38 42 87 64 26 24 43 77 49 = 497 Lycopodiuni spores - 100 Ratio - -_ Maize starch grains 368' Second set of t,en fields: Lycopodium . . 11 6 5 8 12 5 8 8 14 6 = 8 3 Maize starch . . 30 23 34 46 26 17 18 11 44 40 = 294 Lycopodium spores - 100 Maize 'starch grains 354' Ratio Lycopodium spores - 100 Maize starch grains 361' Average ratio - - - - -Amount of cornflour found = 361 x-50 = 38.0 per cent. 47 366 WALLIS QUANTITATIVE MICROSCOPY Mixture of Wheat Flour 90 per Cent. and Cornjlour 10 per Cent.-Counts of ten fields on eaoh of two slides gave the ratios: 109 100 and -=--100 96.1 * Lycopodium spores - 188 - 100 Maize starch grains 187 99.5 101 92.7' -__ _- ~ - _ - _ With an average of Amount of cornflour found- 9 z L 3 0 = 10.1 per cent.470 N.B.-Where the counts of the individual fields are not given each ratio from a set of ten counts is expressed in two forms; the first fraction has for numerator and denominator the sum of the ten actual counts of lycopodium spores and starch grains or other characteristic elements respectively while the second fraction has in every case 100 for the numerator representing the lycopodium spores and for the denominator the corresponding number representing the starch grains or other structures. By dividing the numbers in the first fraction by 10 one has immediately the average number of grains or particles counted in each' field.treated in the same way as the mixtures of wheat flour and cornflour. fields on each of two slides gave the ratios: MIXTURES OF POTATO STARCH AND MAIZE STARcH.-These mixtures were Mixture of Potato Starch 50 per Cent. and Maize Starch 50 per Cent.-Counts of ten Lycopodium spores- - 58 - 100 R,nd -= 40 100 Maize starch grains 338 583 - - - - - 218 545. 100 With an average of ~- 564' Mixture of Potato Starch 90 per Cent. and Maize Starch 10 per Cent.-Counts of ten fields on each of two slides gave the ratios : Lycopodium spores- 108- 100 72 100 - and - = - Maize starch grains 117-108 84 117' 100 With an average of -. 113 113 x 50 564 Amount of maize starch found= - - -~ = 10.0 per cent. ilkfixture of Potato Starch 95 per Cent.and Maize Starch of ten fields on each of two slides gave the ratios: 144 - and - Lycopodium spores - 11 1 - 100 Maize starch grains 63 56-8 82 _-_-With an average of 56.9 x 50- Amount of maize starch found& ~ - 5-1 . 564 5.0 per Cent .-Counts 100 56.9 ' 56.9 * . 100 per cent. The method of making the mucilage of tragacanth at the moment of mixing has its advantages in aiding the even distribution of the constituent powders; bu WALLIS QUANTITATIVE MICROSCOPY 367 if the drops of suspension are mounted and examined immediately currents are produced owing to the continued swelling of the gum. If a few hours are allowed to elapse until the mucilage has properly formed this difficulty does not arise and the counts are easily made.It may be suggested that where a mixture of two starches is being dealt with, the addition of lycopodium is unnecessary because the ratio of the two kinds of granule to one another can be obtained. Although this is true it is preferable to add lycopodium because by doing so a greater precision is secured. It is impossible to mistake lycopodium spores for starch grains whereas if a few grains of one kind of starch are mistaken for those of a second sort a double error results since what is added to one side is subtracted from the other. So large an error cannot possibly occur when lycopodium is used; time also is saved because it is much easier to count the spores than to count starch grains. Up to this point no account was taken of the moisture present in tbe starches, and since the powders used in the various mixtures were identical with those used in the standard mixtures no error was introduced.In ordinary practice it would be necessary to make corrections for moisture; hence in the remaining experiments moisture was always estimated and the corrections applied. MIXTURES OF MUSTARD PLOUR AND CoRhTFLouR.-The mixtures were made with cornflour dried a t 100" C. For the standard mixture the mustard was also dried but for the 26 per cent. mixture the ordinary air-dry powder was used. In place of mucilage of tragacanth the 0.2 grm. of mustard and 0.1 grm. of lycopodium were mixed with olive oil by working them with a spatula upon a piece of glass until a thick paste was formed; this was further gradually diluted to the consistence of thin cream.The fluid was then transferred to a weighing bottle and more olive oil added until the volume was about 20 C.C. The whole was well shaken and a drop mounted for examination. Mixture of Dried Mustard 50 per Cent. and Dried Cornjlour 50 per Cent.-Counts of ten fields on each of two slides gave the ratios: Lycopodium spores- 194 - 100 and - 100 - - Maize starch grains 1289-664 645' 100 With an average of - 655' Mixture of Air-Dry Mustard 75 per Cent. and Dried Cornflour 25 per Cent.-The mixture was dried before weighing out and mixing with the lycopodium Counts of ten fields on each of two slides gave the ratios : Moisture= 6.67 per cent. and oil. Hence dry substance= 93.33 per cent. 87 100 and __ = ~ Lycopodium spores- 66 - 100 Maize starch grains 261 395 307 353' 100 With ail average of ~ 374' - - - ~ 374 x 50- Amount of cornflour found in the dry substance = - 28.5 per cent.655 Or in air-dry substance = 26.6 per cent 368 11' ALLIS QUANTITATIVE MICROBCOPY I n order to test the possibility of replacing olive oil by soft paraffin fresh counts were made for the mixture containing 25 per cent. of cornflour. The weighed quantities of the powders were thoroughly incorporated with about 6 grms. of soft paraffin by means of a spatula and glass plate. A small amount of this strong mixture was diluted wit#h more paraffin until examination under the microscope showed that a mixture containing a suitable proportion of the powder had been produced. Counts of ten fields on each of two slides gave the rafios: LYcoPodium 82 - loo and __ 96 - 100 Maize starch grains 303 370 371 390' 100 380' With an average of 380 x 30 Amount of cornflour found in the dry substance - - -- = 29.0 per cent.65a Or in air-dry substance = 27.1 per cent. The remaining experiments were made with air-dry powders; this was done because dry vegetable powders are very hygroscopic and may take up appreciable quantities of moisture during manipulation. The use of air-dry powders also results in a reducttion of the time required for the whole operation. MIXTURES OF WHEAT FLOUR AND POTATO STARcH.-It is generally easy to distinguish grains of wheat starch fliolil those of p t a t o starch; b u t there is 8 number of grains forming about 10 per cent. of the potato starch which it is difficult? to distinguish with certainty.With the polariscope wheat starch polarises feebly, whereas potato starch grains show a strongly marked cross. These differences are very clearly shown when the starches are mounted in oil and for this reason olive oil was used as the mountant for the mixtures and the counts were made with the polariscope using crossed Nicols. Although the majority of wheat starch grains polarise feebly one finds here and there one which shows a brilliant effect owing to the fact that the grain is on its edge. These grains are however distinguisha,bIe, because the potato starch grains always show a cross formed by the intersection of two lines whereas in the case of grains of wheat starch turned upon their edges the " cross " is composed of five lines of which four are arranged in pairs bifur-cating from the ends of the fifth line thus >-<.Some few potato starch grains show a circular outline and a cross formed by the intersection of two diameters, much as one finds in wheat starch. Such grains may be distinguished from brightly polarising grains of wheat starch by the fact that in potato starch the lines forming the cross are usually thicker towards the circumference and taper off to the pointJ of intersection which is clearly marked while the lines on wheat granules becoiiie wider as they approach the centre which is itself marked by a darker circular area. Keeping these points in mind it is possible to make an accurate count of potato starch mixed with wheat flour.I n each case 0.2 grm. of the substance was mixed with 0.1 grm. of lycopodium, and the powders worked up wit'h olive oil in the manner described above for the mustard mixtures WALLIS QUANTITATIVE MICROSCOPY 369 Jfizture of Wheat Flour 50 per Cent. and Potato Starch 50 p e r Cent.-;\iloisture Hence the mixture contains 39-62 per cent. of potato starch dry at 100" C. in t'he potato starch = 20.76 per cent. Counts of ten fields on each of two slides gave the ratios: 108 100 Lycopodium spores - 86 - 100 Potato st-arch grains 68 791 85 78.7 * 100 Wit'h an average of - - 78.9 ' and -= --,Mixture of Wheat Flour 80 per Cent. and Potato Starch 20 per Cent.-Counts of t e n fields on each of two slides gave the ratios : 154- 100 Potato starch grains 51 33;s 56 36.4 Lycopodium spores- - 151 - 100 and - ~~ 100 35.1 With an average of - --.39.62 x 35.1 = 17.6 or __-78.9 Hence percentage of dry potato starch in the mixture = 82.2 parts of air-dry starch. MIXTURES OF WHITE PEPPER AND GIXGER.-h this case the powders were mixed with castor oil using a spatula and a sheet of glass; the oil was added until a suitable dilution was obtained. I n each experiment 0.2 grin. of the mixture and 0.1 grm. of lycopodium were used. Mixture of White Pepper 50 per Cent. and Ginger 50 per Cent.-Noisture in the ginger= 13-91 per cent. Hence the mixture contains 43-05 per cent. of ginger dry a t 100" C. Counts of ten fields on each of two slides gave the ratios : Lycopodium spores- 81 - 100 68 100 Ginger st'arch grains 247 305 206 303' and- =--100 With an average of - 304 ' Mixture bof White Pepper 90 per Cent.and Ginger 10 per Cent.-Counts of ten fields on each of two slides gave the rat>ios: 135- 100 Lycopodium spores- - 343- 100 and -Ginger starch grains 234- 62- 87 64.4' 100 66.3 a With an average of 66.3 x 4 3 ~ 0 5 ~ 9.4 or 10.9 per 304 Hence percentage of dry ginger in t,he inixt>ure = -cent. of air-dry ginger. siiisll grains and judging from the relative size of maize starch grains it seemed probable that for a preparation containing starch and lycopodium in the propor-fion of 0.2 of the former to 0.1 of the latter the number of grains to be counted in each field would approach 2,000 which is too large a number for comfortable working. The proportions were accordingly altered and for this set of experiments MIXTURES OF WHITE PEPPER AND RICE STARCH.-RiCe starch Consists Of Ver 370 WALLIS QUANTITATIVE MlCROSCOPY 0.2 grm.of I~-copodium was niixecl with 0.05 grm. of starch or pepper. Olive oil was used as the fluid medium and the volunie was made up to about 20 C.C. as before. I n addition to counting a standard mixture of pepper and rice starch pure rice starch mixed with lycopodiuin was also counted. This was done to accustom the eye to the size and appearance of the rice starch and also to give a ratio that would act as a check upon the remainder of the work. To count ri2e starch in the presence of pepper is not so difficult as might be anticipated and that for two reasons. In the first place by far the greater part of the pepper starch occurs in angular masses so that the number of loose grains is small; and secondly pepper starch grains vary in size from 0 4 p to 5 0 p while rice starch grains vary from 5p to 8p in diameter so that if one omits all starch grains having a diameter less than half that of the larger rice starch grains the count obtained will represent the rice starch.Pure Rice Starch-Moisture in the rice starch = 15-96 per cent. Counts of ten fields on each of two slides gave the ratios: 181 - 100 and ---. Lycopodiuni spores- 218 - 100 Rice starch grains 5853 2686 5135 2836 .- - -. -100 With an average of -~ 2761' Mixture of White Pepper 50 per Cent. and Rice Starch 50 per C'ent.-This mixture Counts of ten fields on each of two slides gave the ratios: contained 42.02 per cent.of rice starch dry a t 100" C. Lycopodium spores- 211 - 100 141 100 ~- - and -=-Rice starch gramins 2670 1266 1703 1208' 100 With an average of ~ 1237 * Mixture of White Pepper 80 per C'ent. and Rice Starch 20 per Cent.-Counts of ten fields on each of two slides gave the ratios: 265 100 and - = - Lycopodium spores - 200 - ~ 100 Rice starch grains 921 460.3 1232 465' 100 463 With an average of Hence percentage of dry rice starch in the mixture = 463 42*02 = 15.72 or 1237 18-71 per cent. of air-dry rice st,arch. The figure 1237 for the rice starch in the 50 per cent. mixture is about 10 per cent. smaller than the figure 1380 obtainable by calculation from the pure starch. This is due to one's anxiety to avoid the inclusion of pepper starch in the counts, and the consequent omission of some of the smaller rice starch grains.This fact also emphasises the desirability of using a mixture for the standard rather than to base the calculations upon a figure obtained from counts of tlhe pure adulterant WALTAIS QUANTITATIVE MICROSCOPY 371 NIIXTURES OF GENTIAN ROOT AND COCONUT SHELL.-The powdered gentian root was an ordinary commercial sample and the coconut shell was a No. 80 powder prepared in the laboratory. In t,he case of the pure coconut shell the 50 per cent. and the 5 per cent. mixtures the mixed powder and lycopodium were rubbed together on a glass plate with about 1-0 C.C. of a 1 per cent. solution of phloroglucinol in alcohol until nearly dry; 1.0 C.C. of strong hydrochloric acid was next added and the mixing continued; 3 C.C.of glycerol were then incorporated and the volume adjusted by gradually adding mucilage of tragacanth. The whole was transferred to a weighing bottle and well shaken. For the 29.3 per cent. and the 8.5 per cent'. mixtures about 0.12 grm. of powdered gum tragacanth was added and all the powders were thoroughly mixed in the dry state. They were then treated with phloroglucinol hydrochloric acid and glycerol as described above. The thin paste thus produced was transferred to a weighing bottle water was added and the whole shaken vigorously until a uniform mixture resulted; the suspension so formed was very satisfactory. No attempt was made to count the individual stone cells present; any portion or group of stone cells was counted as one unit.The bright rose-pink colour assumed by the woody elements of gentian helped in distinguishing them from the coconut shell which nearly always takes a yellowish-red colour. Pure Powdered Coconut Shell.-Moisture in the coconut shell = 12.42 per cent. The quantities used were Coconut she!! 0.2 gr". and ljxopdiurn 0.1 grm. Counts of ten fields on each of two slides gave the ratios: 230 100 and __ =- Stone cells 197 = 83.8 191 83.0' 100 With an average of -83.4' Lycopodiuni spores - 235 100 -~ ~~ ~ Mixture of Gentian Root 50 per Cent. and Coconut Shell 50 per Cent .-This mixtme The quantities used were Mixture 0.2 grm. and lycopodium 0.1 grm. Counts of ten fields on each of two slides gave the ratios : contained 43.79 per cent.of coconut shell dry at 100" C. Lycopodium spores - 164- 100 and 160 __ 100 100 With an average of -41.05' - __- - Stone cells 71 43.3 65- 38.8 ' Mixture of Gentian Root 70.7 per Cent. and Coconut Shell 29.3 per Cent.-The quantities used were Mixture 0.4 grm. and lycopodium 0.05 grm. Counts of ten fields on each of two slides gave the ratios : Lycopodlum spores-65- . - 100 and 76 - ~ 100 Stone cells 55 84.6 67 88.2 100 86.4 - With an average o 372 WALLIS QUANTITATIVE MICROSCOPY If the quantities used had been the same as for t>he 50 per cent. mixture the value 86.4 would become 86.4 +- 4 = 21.6. Hence percentage of dry coconut shell in the mixture= 21D6 ~ 43*79- - - 23.04 or 41.05 26.3 per cent. of air-dry coconut shell. quantities used were Mixture 0.4 grm.and lycopodium 0-05 grm. Mixture of Gentian Root 91.5 per Cent. and Coconut Shell 8.5 per Cent.-The Counts of ten fields on each of two slides gave the ratios: Lycopodium spores - 109 - 100 and 135 =- LOO Stone cells 33 -303 41 30.4' 100 With an average of __ 30.35' -___ -- . __ . . -If the quantities used had been the same as for the 50 per cent. mixture the value 30.35 would become 30.35 +- 4 = 7.6. 7.6 >c 43.79 - Hence percentage of dry coconut shell in the mixture= -<- - 8.1 or 9.25 41.05 per cent. of air-dry coconut shell. tities used were Mixture 0.8 grm. and lycopodium 0.05 grm. Mixture of Gentian Root 95 per Cent. and Coconut Shell 5 per Cent.-The quan-Counts of ten fields on each of two slides gave the ratios : Lycopodiuni __________- spores- - 118- 100 and 136- 100 100 31.2 ' Stone cells 38- - 32.2 41 - 30.15' With an average of If the quantities used had been the same as for the 50 per cent.mixture the value 31.2 would become 31.2 -+ 8 = 3.9. Hence percentage of dry coconut shell in the mixture= 3*9 43*79= 4.2 or 4.8 41.05 per cent. of air-dry coconut shell. When examining mixtures such as this of coconut shell and gentian root it would ordinarily be necessary to determine by measurement and by comparison with standard powders the degree of disintegration to which the powdered substance to be counted had been reduced and to make the standard mixtures with a similar powder. Also where the amount to be determined is very small the dried crude fibre could be worked upon instead of using the original substance WALLIS QUANTITATIVE MICROSCOPY 373 CONCLUSION.For the purpose of reviewing as a whole the results obtained by the method described I have arranged them in tabular form : z 2 3 4 5 6 7 8 9 10 11 12 -Substance. Wheat flour 7 9 ? 9 Potato starch , 9 , Mustard WGat flour White pepper Gentian root 2 9 9 , Y ? Aditiix ture. Name. Cornflour 7 ,, Y , PotLio starch Ginger Rice starch Coconut shell Amount Present per Cent. 37.8 10.0 10.0 5.0 25.0 25.0 20.0 10.0 20.0 29.3 8.5 5.0 -~ A moan t Found per Cent. 38.0 10.1 10.0 5.1 26-6 27.1 22.2 10.9 18.7 26.3 9.3 4.8 Suspending Agent. Powdered gum traga-canth Glycerol Powdered gum traga-canth Powdered gum traga-canth Olive oil Soft paraffin Olive oil Castor oil Olive oil Powdcrcd gum traga-canth and glycerol Powdered gum traga-canth and glycerol Mucilage of tragacanth and glycerol A study of the figures in the table shows that a high degree of accuracy is attain-able.The errors may be taken to represent such as one may expect to find in every-day practice. It is difficult to draw any general conclusion as to the magnitude of error because the.conditions of working vary so largely in the different experi-ments and a degree of precision attainable with one type of mixture is not always possible with another. The table shows however that one may generally anticipate that the error of working will not exceed 10 per cent.on the amount present while in many cases it should be much smaller. Even when the larger errors occur one could reduce them by increasing the nvmber of counts made or by repeating the work. In each instance one can gain a very good estimate of the probable error in the working by preparing a mixture containing the materials in the proportions found and then determining its composition microscopically ; this additional work is a wise precaution to take in many cases as for instance where the problem includes a determination of the degree of disintegration of a powdered substance. The time required to make one set of ten counts varies from about fifteen minutes to as much as an hour and a half in exceptional cases; the average time s about half an hour 374 WALLIS QUANTITATIVE MICROSCOPY This method of working conqtitutea a process of general applicability and makes it possible to obtain precise quantitative results by means of the microscope.The use of lycopodium enables the observer t o attack successfully many problems that it has been hitherto impossible to solve with any approach t o certainty and in the case of such mixtures as that of two starches where the counting method has already been applied with only an approximate accuracy the error of working is reduced to such an extent as to give the results a real value subject to only a small error. DIscussroN. The CHAIRMAN (Mr. J. H. B. Jenkins) in inviting discussion remarked that the lycopodium presumably simply served as a unit for calculation and one did not know to what extent the weighing of a definite quantity of it was essential.So long as it simply functioned as unity it did not seem to him to make much difference what quantity of it was present. Professor H. G. GREENISH said that a good deal of work had been done in this direction but he had never seen the problem attacked by the method which Mr. Wallis had used. All who had tried to determine the proportion of a substance like coconut shell or almond shell when mixed with gentian root liquorice root etc. must have felt that the results of their examination were very uncertain amounting rea,lly to little more than an approximate guess. In cases like the first four in Mr. Wallis’s table one could probably attain a fair degree of precision without the use of lycopodium ; but with mixtures of mustard and wheaten flour pepper and rice or gentian root and coconut shell the problem was very much more difficult.In the casc of say gentian root and coconut shell it became a question of making the standard mixture with coconut shell reduced to about the same degree of fineness as the powder under examination by measuri’ng the particles of coconut shell and endeavouring by some suitable method of grinding to produce particles of the same size for use in making the standard inixture. To succeed as Mr. Wallis had in determining the proportion of coconut shell in such a mixture within 10 per cent. either way was more than he should have thought possible. Mr. W. PARTRIDGE said that in counting the bacteria in a vaccine the bacterial emulsion was mixed with normal human blood in a known proportion the slide was dried and stained and the bacteria and blood corpixscles counted against one another.This method by which the different elements were fixed in situ and stained where it could be adopted seemed preferable to counting the particles in a liquid medium. With a liquid medium the Thorna-Zeiss counting chamber designed for counting the red and white cells in blood might be used with advantage. The cells were counted in a standard volume of liquid the height being that mentioned by Mr. Wallis namely one-tenth of a millimetre. The fields counted were moreover squares which made the counting easier than with circles as there was no difficulty with regard to particles occurring on the edges; those touching the top and right edges could be included and those on the bottom and left ignored or riceuersa.B4r. C. REVIS said that in counting milk cells diluted with red blood corpuscles he had experienced very great difficulty with circular fields but this was obviated by the use of a square diaphragm. He had had no experience with larger particles but when red blood corpuscles were used as a “diluent ” of larger cells of the size of whit WALLIS QUANTITATIVE MICROSCOPY 375 corpuscles he had found i t very difficult to get a properly proportioned mixture of the two. With larger particles i t would probably be less difficult to get a satisfactory mixture. Mr. A. CHASTON CHAPMAN remarked that sodium nucleate might be useful in some cases as a suspending medium.Solutions containing about 1 to 2 per cent. of sodium nucleate were quite limpid whilst solutions containing about 5 per cent. (of the gelatinising variety) were almost solid so that varying degrees of viscosity could be obtained. One objection was that the solution was very apt to froth and the sodium nucleate would of course be decomposed by some of the reagents used in making the microscopical preparations. Mr. C. C. ROBERTS suggested that it might be worth while to photograph the fields counted in order to preserve a record of them for use as evidence. Mr. E. T. BREWIS asked whether Mr. Wallis had considered what was generally meant by say a No. 80 powder. It meant a powder which had passed through a sieve having meshes of the size indicated but such a powder might consist of particles of any degree of fineness from No.80 to still finer and the question was what effect any such variations in fineness might have upon the counting. In the case of the first four items of Mr. Wallis’s table all the particles would be of approximately the same size; but in the case of the white pepper or the gentian root the ultimate particles of pepper or of gentian root would be different in size and also possiblyin shape and would have a ten-dency to sift apart. Again before the actual examination was begun the question would arise as to whether. the sample worked upon was a fair average portion of the few ounces constituting the sample submitted which again would perhaps be taken from a bulk weighing some hundredweights or tons.Mr. WALLIS in reply said that although the mixtures referred to in the table were actual binary mixtures it did not matter how many substances were present. The counting in each case had reference to one constituent only so that all mixtures were binary mixtures from that point of view. He had found that weighing was necessary in order to get accurate results. At first he thought that weighing might be dispensed with and had made a number of experiments in which everything was measured with, in some cases-mixtures of ground olive stones with pepper for instance-very good results; but that method was bad in principle. The only cases to which it could be satisfactorily applied would be cases in which the different constituents were of almost the same density. The question of the counting of particles a t the edge of a field. was a little difficult. He used a squared micrometer and the particles a t the edges were averaged as fairly as possible. The particles could not very well be fixed as in bacterio-logical work. He was not quite sure whether sodinm nucleate would be a satisfactory suspending medium because of the possible action of reagents upon it. Alcohol for instance might create some diffixdty ; but i t would be well worth trying. The No. 80 powder was prepared by sifting through a No. 80 sieve and of course contained particles of varying sizes. He had not made any attempt to investigate the difficulties that might be caused by such variations but he thought that with patience it would be pos-sible to obtain correct results. As to how far the 0.2 grm. worked upon was represen-tative of the bulk this would probably depend upon the care taken in mixing before weighing out. If the samples he had worked upon had not been representative none of his experiments would have succeeded