22 



KNOWLEDGE & SCIENTIFIC NEWS. 



[Feb., 1904. 



each maker, whether En,L;lish or foreit^n, is a law unto 

 himself, and the list of cover-f^lass corrections is a most 

 torniidable one. But it follows that any variation in 

 cover-glass thickness from that for which the objective 

 was originally corrected necessitates a readjustment 

 either of the lenses of the objective, by means of a " cor- 

 rection collar," or by adjustment of the length of the 

 microscope tube. In the latter case, of course, we have 

 at once a variation of initial magnifying power, but the 

 converse also applies, i.e., that an arbitrary variation of 

 tube-length affects the corrections, and consequently the 

 performance of the objective. We can at once see the 

 limitations, therefore, of the ordinary suggestions as to 

 varying the magnification by drawing out or pushing in 

 the draw- tube of the microscope. With low powers of 

 small angle the difference in performance is not marked, 

 and would e\en need a trained eye to detect it, but it 

 becomes more- and more marked with an increase of 

 angular aperture, which generally coincides with higher 

 powered objectives. Broadly speaking, therefore, we 

 must use our objectives with the tube-length for which 

 they were originally constructed. 



The part played by the ocular — at least by the Huy- 

 ghenian type of ocular which is generally used and with 

 which we need only concern oursehes here — is twofold. 

 It consists of a field-lens and an eye-lens, with a dia- 

 phragm between. The field-lens may really be con- 

 sidered almost as part of the objective, for its action is to 

 draw in the image rays and bring them to their final focus 

 in the plane of the diaphragm just mentioned. Then the 

 eye-lens merely magnifies this image and brings it to a 

 focus suitable for the eye. 



It is important to note, therefore, that the magnification 

 of any unadjustable ocular is always a fixed quantity, but 

 that the magnification of an objective (perfection of image 

 apart) will vary according to the tube-length. In spite of 

 this, many Continental and some English makers persist 

 in treating the two magnifications as if it were the ocular 

 magnification which varied, thus giving rise to no little 

 confusion. I have seen lists in which elaborate tables 

 have been made of the combined magnifications of objec- 

 tives and oculars used with a 6i inch tube, in which the 

 ocular has been treated as the varying quantity, and I 

 have seen calculations of magnifications of objectives in 

 one and the same table in which an inch or other objec- 

 tive is treated as magnifying 10 times and in another 

 7 times, at 6i inches distance, the real fact being that the 

 oculars are not of the powers they profess to be. All this 

 is, of course, very confusing to the beginner. 



Now, focuses do not represent " working distance." 

 This merely represents the clear space between the cover- 

 glass and the front surface of the objective, and can be 

 measured by a carefully made wedge of wood which is 

 inserted when the objecti\e is focussed, marked, and then 

 measured. 



Nor is it necessary for us to work out with mathemati- 

 cal accuracy the exact equivalent foci of objectives, which 

 are made up of complicated systems of lenses. This would 

 be a difficult matter. It will be sufficient for us to obtain 

 the approximate equivalent focus — approximate because 

 the centre of the system cannot be readily obtained. If 

 we set up conjugate foci at equal distances from the centre 

 of the lens, the object and image will l)e of the same size, 

 and conversely if the object and the image are the same 

 size the distances of the conjugate foci are identical. 

 This, of course, means that object and image are both 

 beyond the principal focus ; in fact they are at a distance 

 just as much again as is the principal focus, i.e. they are 

 on each side twice the distance of the principal focus from 

 the centre of the lens. Therefore, the equivalent focus 



can be obtained by projecting the image of a brightly 

 illuminated object upon a screen at such a distance that 

 both image and object are equal, and dividing the total 

 distance by four. Having obtained the equivalent focal 

 length, we can easily calculate the magnification with any 

 tube-length. 



It is, however, with the magnifying power that the 

 microscopist generally needs to concern himself, and this 

 known, the equivalent focus can be easily obtained. 

 Perhaps the easiest method of obtaining this is that 

 mentioned in Carpenter. A micrometer slide ruled in 

 hundredths and thousandths of an inch, or in tenths 

 and hundredths of a millimetre, is placed upon the stage 

 of the microscope, and the latter inclined to the hori- 

 zontal position. A strong light is transmitted through 

 the microscope, and the room darkened. The micro- 

 meter lines are then focussed sharply upon a piece of 

 white cardboard placed five feet (60 inches) behind the 

 front lens of the objective. The divisions on the screen 

 are measured with an ordinary foot or millimetre rule 

 and the result divided by 6, which gives, of course, their 

 size at 10 inches from the objective. The value of the 

 original stage micrometer divisions being known defi- 

 nitely beforehand it is easy to calculate the resulting 

 magnification. Suppose the distance between the micro- 

 meter rulings of two i-iooo of an inch to measure ij- 

 inches at 5 feet distance with a nominal i inch objective. 

 Then at 10 inches distance they would measure -2083 inch, 

 which is equivalent to an initial magnification of nearly 

 lol times. A millimetre scale or rule can be used on 

 the basis of 25-4 millimetres to an inch. Magnifications 

 are always expressed in diameters, or linear measure- 

 ments, not in areas. A considerable distance such as 

 the above is taken so as to reduce the amount of error 

 due to the fact that the measurements should really be 

 taken from the principal posterior focus of the objective, 

 which in a compound system cannot easily be found. 

 But by measuring from the front lens as above a very 

 small margin of error is left. It is best to take the 

 mean of several micrometer divisions as they are not 

 quite accurately ruled. 



Combined magnification of objective and eye-piece is 

 calculated by a similar method except that there is not 

 the same necessity for taking a longer distance, and the 

 image of the micrometer must be accurately projected 

 exactly 10 inches from the eye-lens of the eye-piece. 

 This may be done either direct by means of a photo- 

 graphic camera or otherwise, or at right angles by means 

 of a Beale's camera lucida, to a piece of paper placed on 

 the table, the microscope being raised if necessary to the 

 requisite height so as to get the exact distance of loinches 

 from the eye-lens. Short-sighted observers may therefore 

 need to use spectacles in ordertoseethelinesonthe paper. 



The eye-piece magnification is readily calculated by 

 dividing the combined magnification by the initial mag- 

 nification of the objective, independently determined. It 

 will be noted that the result, as calculated, gives the 

 magnification with a lo-inch tube; any other length is 

 easily calculated — a 7-inch tube giving an initial magni- 

 fication of 7-ioths of the result as above obtained, and 

 the eye-piece mat;nification remaining constant for each 

 eye-piece. One further explanation is perhaps necessary. 

 We have hitherto been dealing with a total magnification 

 calculated for a visual distance of 10 inches from the eye- 

 lens, this being the normal visual distance, but it is as 

 well to bear in mind that in actual practice an abnormal 

 eye will form its image nearer or further away, according 

 to whether the eye be short or long sighted. This will, 

 of course, proportionately affect the magnification of the 

 eye-piece, and, in consequence, the magnification of an 



