204 



THE GRAMMAR OF SCIENCE 



As it is with change of size, so it is with change of 

 shape : we are really basing our system of measurement 

 upon conceptions, which enable us to describe and classify 

 perceptions, but are not real limits to perception. Change 

 of shape without change of size can be realised in the 

 following manner : Take a piece of woven silk or other 

 slightly elastic material, and draw a rectangle upon it 

 with sides a few inches long parallel to the warp and 

 woof. Then if such a rectangle be held firmly top and 

 bottom between two pairs of parallel pieces of wood, or 

 even between the two thumbs and their respective fore- 



FiG. 6. 



Fig. 7. 



fingers, a slide of the holders parallel to each other will 

 produce a change of form without change of size. Now 

 the extent of such a strain will depend on the amount by 

 which the warp and woof have changed their inclination 

 to each other, — that is to say, on the amount after strain 

 by which the angle between them differs from a right- 

 angle. But this change in angle only becomes of meaning 

 if we suppose the warp and woof to be straight lines. 

 In other words, to get a measure of the strain we replace 

 the perceptual warp and woof by a geometrical network. 

 Such a type of strain is termed a slide or shearing strain, 

 and all changes of shape without change of size can in 

 conception be analysed into slides.^ Further, it may be 

 shown that all changes of form whatever can be analysed 

 into stretches and slides,^ or into changes of length and 



1 Technically the slide is not measured by the change in angle or by the angle 

 bac in Fig. 7, but by the trigonometrical tangent of this angle, or by the ratio 

 of the length be to the length ha — in other words, by the ratio of the amount 

 the woof has been slid to the length of the warp. 



2 An elementary discussion of strain will be found in Clifford's Elements 

 of Dyna7nic, part i. pp. 158-90 ; or in Macgregor's Kinematics and 

 Dynamics^ pp. 166-84. The reader may also consult §§ 8 and 13, con- 



