Machine and its Model. 265 



a full sized instrument is, in almost every instance, beyond what its 

 projector would feel inclined, or even be able, to incur. The forma- 

 tion 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 princi- 

 ples 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 in- 

 strument is constructed, its surface and its bulk are enlarged in much 

 higher ratios. If, for example, the linear dimensions of an instru- 

 ment be all doubled, its surface will be increased four, and its solidi- 



r 



ty eight fold. Were the linear dimensions increased ten times, the 

 superficies would be enlarged one hundred, and the solidity one 

 thousand times. On these facts, the most important which geome- 

 try presents, my after remarks are mostly to be founded. 



All machines consist of moveable parts, sliding or turning on others 

 which ace bound together by bands, or supported by props. To the 

 frame work I shall first direct my attention. 



In the case of a simple prop, destined to sustain the mere weight 

 of some part of the machine, the strength is estimated at so many 

 hundred weights per square inch of cross section. Suppose that, in 

 the model, the strength of the prop is sufficient for double the load 

 put on it, and let us examine the effect of an enlargement, ten fold, 

 of the scale according to which the instrument is constructed. By 

 such an enlargement, the strength of the prop would be augmented 

 one hundred times ; it would be able to bear two hundred loads such 

 as that of the model, but then the weight to be put on it would be 

 one thousand times that of the small machine, so that the prop in the 

 large machine would be able to bear only the fifth part of the 

 load to be put upon it. The machine, then would fall to pieces by 

 its own weight. 



Here we have one example of the erroneous manner in which a 

 model represents the performance of a large instrument. The sup- 

 ports of small objects ought clearly to be smaller in proportion than 



