365 



former writers, the author instituted several sets of experiments ; some 

 calculated to determine the forces required for dragging bodies of 

 various kinds along a horizontal surface, and others for measuring 

 the angle at which a plane was required to be inclined to the horizon 

 in order to admit of the body sliding down it, attention being paid 

 to the circumstances of pressure, extent of surface, time of previous 

 contact, and velocity of motion. 



The following are the principal conclusions which the author de- 

 duces from his experiments. The friction of ice rubbing upon ice 

 diminishes with an increase of weight ; but without observing any 

 regular law of increase. When dry leather is made to move along a 

 plate of cast iron, the resistance is but little influenced by the extent 

 of surface. With fibrous substances, such as cloth, the friction di- 

 minishes by an increase of pressure, but is greatly increased by the 

 surfaces remaining for a certain time in contact ; it is greater, ceeteris 

 paribus, with fine, than with coarse cloths ; the resistance is also 

 much increased by an increase of surface. With regard to the 

 friction of different woods against each other, great diversity and ir- 

 regularity prevail in the results obtained ; in general the soft woods 

 give more resistance than the hard woods : thus, yellow deal affords 

 the greatest, and red teak the least friction. The friction of different 

 metals also varies principally according to their respective hardness ; 

 the soft metals producing greater friction under similar circumstances 

 than those which are hard. Within the limits of abrasion, however, 

 the amount of friction is nearly the same in all the metals, and may 

 in general be estimated at one sixth of the pressure. The power 

 which unguents have in diminishing friction, varies according to the 

 kind of the fluidity of the particular unguent employed, and to the 

 pressure applied. 



The paper is accompanied with drawings of the apparatus used ; 

 and the details of the experiments are given at length in a tabular 

 form. 



An Attempt to rectify the Inaccuracy of some Logarithmic Formula;. 

 By John Thomas Graves, of the Inner Temple^ Esq. Communicated 

 by John Frederick William Herschel, Esq. V.P. Read December 

 18, 1828. [Phil. Trans. 1829, p. 171.] 



The discovery made by Poisson and Poinsot during their recent 

 researches on angular sections, of errors in trigonometrical formulae 

 usually deemed complete, drew the attention of the author to an 

 analogous incorrectness in logarithmic series. He accordingly pro- 

 poses in the present paper to exhibit in an amended form two fun- 

 damental developements ; the principles employed in the establish- 

 ment of which admit of application in expanding by different methods 

 various similar functions, and tend also to elucidate other parts of 

 the exponential theory. 



He then enters into an analytical investigation of the equation 

 a*-=.y, and exhibits correct developements ; first, of y in terms of 



