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therefore, the angle must vanish to producean equal thickness, hence a mathematicalshould be substituted for a heavy flexibleline, that is, one which has no weight.

Nature, in respect to the tenacity of thematerial she has given for chain bridges,and in respect to the limits as to form whichshe has prescribed for them, has measuredher bounty by the possible wants of man ;and she has left it to the industry andtalents of any one to display that bountyand define her laws, in respect to the oneand the other, which the author has at-tempted to do. But she has left it only toa few to display her bounty in practice,.and, inasmuch as they approach those limitswhich she has prescribed, they bring intoview her glory, and extend their own fame.It is for them duly to study the principleswhich are herein attempted to be soughtafter, and which hold in all machines and inall animal bodies, and to keep within the cer-tain limits, “ in regard to magnitude, which“ not only in all machines and artificial“ structures, but also in natural ones, sup-“ posing them made of the same matter,