450 Royal Society. 



were introduced into Cornwall very early in the last century, and soon 

 superseded the rude machinery which had, till then, been employed 

 for raising water from the mines by the labour of men and of horses. 

 The terms of Mr. Watt's patent in 17G9, which secured to him, until 

 the year 1800, the receipts of one-third of all the savings in fuel, re- 

 sulting from the adoption of his improvements in the construction of 

 the engine, rendered it necessary to institute an accurate compari- 

 son between the efficiency of his with former engines. A copy of the 

 report drawn up on this occasion, in October 1778, is given in the 

 paper; but as the dynamic unit of one pound avoirdupois, raised 

 through a height of one foot, by the consumption of one bushel of coal, 

 had not yet been established as the measure of efficiency, the author, 

 proceeding upon the data furnished by that report, calculates that the 

 duty performed by Watt's engine on that occasion was 7,037,800. 

 In the year 1 793 an account was taken of the work performed by 

 seventeen engines on Mr. Watt's construction, then working in Corn- 

 wall. Their average duty was 19,.56!),000, which exceeds the perform- 

 ances of the former atmospheric engines in the standard experiment 

 in the proportion of 2"78to 1. Someyears afterwards, disputes having 

 arisen as to the real performance of Mr. Watt's engines, the matter 

 was referred to five arbiters, of whom the author was one ; and their 

 report, dated in May 1 798, is given, as far as relates to the duties 

 of the engines. The general average of twenty-three engines was 

 17,671,000. Since that period, so great have been the improvements 

 in the economy of fuel, and other parts of the machinery, that in De- 

 cember 1829, the duty of the best engine, with a cylinder of eighty 

 inches, was 75,628,000, exceeding the duty performed in 1 795 in the 

 proportion of 3-865 to 1, and that of the atmospheric engine of 1778 

 in the proportion of 10v5 to 1. 



The remainder of the paper relates to the friction in machinery, 

 and the different modes of obviating its effects. With a view of re- 

 ducing the amount of friction, the author is led to consider what are 

 the most proper forms for the teeth and cogs of wheels, and through 

 what intermediate steps a given increase of angular velocity may be 

 most advantageously communicated. E(juability of velocity is ob- 

 tained, though at the expense of some degree of sliding friction, when 

 the outline of the teeth of tlie wheels are involutes of circles. Friction, 

 on the other hand, is wliolly prevented when their form is logarithmetic 

 spiral ; but the angular velocities will then be variable. Hence these 

 two advantages are incompatible with one another ; but, on the whole, 

 the author gives the preference to the involute, which produces an 

 equability of angular motion. The most advantageous mode of in- 

 creasing velocity by a series of wheels, is to adjust them so that the 

 multiplication of velocity shnll proceed in a geometrical progression. 



April I. — " Statement of the principal circumstances respectingthe 

 united Siamese Twins, now exhibiting in London." By George Buck- 

 ley Bolton, Esq. member of the Royal College of Surgeons. Commu- 

 nicated by the President. 



The twin brothers, of whom an account is given in this paper, were 

 born of Chinese parents, in 1811, at a small village in Siam, distant 



about 



