TBANSACTIOKS OF SECTION A. 585 



as with the Amsler planimeter, but with the important advantage of a large dial 

 reading, there being only the simple difference that the pointer must in the sphere 

 planimeter be moved iu the opposite direction round the perimeter of the figure to 

 be measured. 



One feature of interest in the instrument is the use of the four guiding rollers, 

 ■which are in contact with the great circle of the sphere formed by the intersection 

 of the horizontal plane through its centre, and thus allow the sphere to turn with- 

 out resistance in any direction. To this end the rollers are carried in brackets, and 

 do not exert any pressure upon the sphere, but just keep it iu position in the frame. 

 They are pivoted on very fine centres, and they are of steel with polished edges, sa 

 that even when the sphere is moving in a direction causing its axis of rotation to 

 pass through one of these edges, the motion of the sphere is not appreciably re- 

 tarded bj' frictional resistance. Hence the planimeter is found to be correct up 

 to the limit of accuracy to which records can be read on the dial face. 



6. On Composition of Sensation and Notion of Space} By L. de la Rive. 



Notion of space is admitted to result from the association of our muscular 

 activity with the perception of visual or tactile sensation. On the other hand, 

 sensation of colour is a function of three variables, and muscular sensation is sup- 

 posed to be also a function of three variables. Then the three dimensions of space 

 are subjective. 



A theoretical law of composition or synthesis of sensation is found to be the 

 law of composition of forces. The principle applied to is — consciousness of two 

 simultaneous sensations is consciousness of the ratio of their intensities, of which the 

 well-known law of Fechner is a consequence. The differential equation of cosine 

 is obtained by considering the variation of intensity, which, being eventually posi- 

 tive or negative, gives rise to a quadruple field of specific variation continuous with 

 itself. The repetition numbered by 2^ for the double synthesis is by 2^ for the 

 treble in the case of the eight solid right angles composing the whole ternary specific 

 field, and would be 2^ for a hypothetical quadruple synthesis. 



The imiscular sense is supposed to have its nervous organ composed of all the 

 nervous fibres of an organ of mobility (the ocular globe, the arm) and the corre- 

 sponding nervous centre. According to the law of composition, the exercise of 

 muscular sense produces the notion of subjective spherical space thus defined ; the 

 notion of thejield of straight directions from a centre together tcith the notion of a 

 length from the centre. Hence the assertion that this notion is the muscular sense 

 has in its favour : First, each sense gives us a peculiar notion ; muscular sense is not 

 apparent as others because the quality it teaches to endow the external world with 

 is looked at as an absolute quality. Secondly, the fact of the blind possessing the 

 notion of geometrical space with the same thoroughness as the seeing shows that 

 the notion is neither visual nor tactile, but muscular. 



Association of a permanent cause of external sensation, or entity, with the 

 species in the ternary subjective field which, when acting, leaves undisturbed the 

 external perception is the localisation of the cause. Hence the formation of mono- 

 cular space. Any muscular sensation of the ocular globe is a rotation round an 

 axis, and the rotation round the direction of the luminous ray leaves undisturbed 

 the direct vision. A retinian angular field is produced by a similar process. 



A process of formation of tactile space is analysed in the case of a schematical 

 arm, with the humerus acting in the same manner as the ocular globe, and the 

 elbow giving by the variable angle of its articulation a variable radius to the 

 spherical surface described by the hand. The passage from a tactile point to 

 another with a minimum of sensation is given by a constant species in the ternary 

 field. Hence the geometrical definition of the straight line. Definition of parallels 

 is given by assimilating any tactile point to the centre. The hypothesis of sub- 

 jectivity of geometrical space may perhaps call the attention. 



' Published in extenso in the Memoires de la Suciete de Physique et d'Histinrs 

 Naturelle de Geneve, 1888. 



