t^ Mr Sang on the relatiwi which subsists 



cult of attainment. They are startled by the absurd distinction 

 which has been drawn between theory and practice, as if theory 

 were other than a digest of the results of experience; or, if they 

 overcome this prejudice, and resolve to dive into the arcana of 

 philosophy, they are bewildered among names and signs, ha- 

 ving begun the subject at the wrong end. That the attainment 

 of such knowledge is attended with difficulty is certain, but it is 

 with such difficulty only as can be overcome by properly di- 

 rected application. It would be, indeed, preparing disappoint- 

 ment, to buoy them up with the idea, that knowledge, even of 

 the most trivial importance, can be acquired without labour. 

 Yet it may not be altogether unuseful, for the sake both of 

 those who are already, and of those who are not, acquainted 

 with these principles, to point out the more prominent causes, 

 on account of which the performance of no model can, on any 

 occasion, be considered as representative of that of the machine. 

 Such a notice will have the effect of directing the attention, at 

 least, to this important subject. In the present state of the arts, 

 the expense of constructing a full-sized instrument is, in almost 

 every instance, beyond what its projector would feel inclined, 

 or even be able, to incur. The formation of a model is thus 

 universally resorted to, as a prelude to the attempt on the large 

 scale. An inquiry, then, into the relation which a model bears 

 to the perfect instrument, can hardly fail to carry along with it 

 the advantage of forming a tolerable guide, in estimating the 

 real benefit which a contrivance is likely to confer upon society. 



In the following paper, I propose to examine the effect of a 

 change of scale on the strength and on the friction of machines, 

 and, at the same time, to point out that adherence to the strictest 

 principles which is apparent in all the works of nature, and of 

 which I mean to avail myself in fortifying my argument. 



Previous, however, to entering on the subject-proper, it must 

 be remarked that, when we enlarge the scale according to which 

 any instrument is constructed, its surface and its bulk are en- 

 larged in much higher ratios. If, for example, the linear di- 

 mensions of an instrument be all doubled, its surface will be in- 

 creased four, and its solidity eight, fold. Were the linear di- 

 mensions increased ten times, the superficies would be enlarged 

 one hundred, and the solidity one thousand, times. On these 



