ZOOLOGY AND BOTANY, MICBOSCOPY, ETC. 609 



action of the margin, so that the image shall fall on the axis and at 

 the same distance from the lens as the image formed by its central 

 portion. Suppose this correction to be made for the point B. Let 

 the mirror be tilted as described, so that a pencil of rays passes 

 through A to the left margin of the objective. This pencil makes a 

 smaller angle with the front surface than a pencil coming from B and 

 entering at the same place. Hence, the pencil from A will reach the 

 back surface of the lens at a point nearer the axis than would be 

 reached by the pencil from B. If then the pencil from B comes to a 

 focus on the axis, tbe pencil from A would cross the axis before 

 coming to a focus. This explains the displacement of the image a to 

 the right under the conditions given above. The image h of the point 

 B will not be affected, because the objective is corrected for a cone of 

 rays from B, and any pencil passing through B must coincide with 

 some element of the cone. It is not necessary to discuss the image c, 

 for it will be seen that it must be formed on the side of the axis 

 opposite to a." 



Phenomena of Motion.* — C. Nageli and S. Schwendener deal 

 with this subject as follows : — 



" The observation of the phenomena of motion under the Microscope 

 has led to many false views as to the nature of these movements. If, 

 for instance, swarm-spores are seen to traverse the field of view in 

 one second, it might be thought that they race through the water at 

 the speed of an arrow, whereas they in reality traverse in that time 

 only a third part of a millimetre, which is somewhat more than a 

 metre in an hour. It must not, therefore, be forgotten that the 

 rapidity of motion of microscopical objects is only an apparent one, 

 and that its accurate estimation is only possible by taking as our 

 standard the actual ratio between time and space. If we wish, for the 

 sake of exact comparison, to estimate the magnitude of the moving 

 bodies, we may always do so ; the ascertainment of the real rapidity 

 remains, however, with each successive motion, the principal matter. 



If a screw-shaped spiral object, of slight thickness, revolves on its 

 axis in the focal plane, at the same time moving forward, it presents 

 the deceptive appearance of a serpentine motion. Thus it is that the 

 horizontal projections of an object of this kind, corresponding to the 

 successive moments of time, appear exactly as if the movement were a 

 true serpentine one. As an example of an appearance of this nature 

 we may mention the alleged serpentine motion of Spirillum and 

 Vilrio. 



Similar illusions are also produced by swarm-spores and sperma- 

 tozoa ; they appear to describe serpentine lines, while in reality they 

 move in a spiral. It was formerly thought that a number of different 

 appearances of motion must be distinguished, whereas modern ob- 

 servers have recognized most of them as consisting of a forward 

 movement combined with rotation, where the revolution takes place 

 sometimes round a central, and sometimes round an eccentric, axis.f 



* ' Das Mikroskop,' English translation (in the press) pp. 258-60 (I fig.)- 

 t Cf. on this point Nageli, ' Beitrage,' ii. p. 88. 

 Ser. 2.— Vol. III. 2 R 



