250 Observations on Locomotive Action. 



Tliese values make il easy to substitute I for A if it be 

 thought proper so to do. In my formulae for deriving / from 

 s, and 4> from <^', it is evident that \ and I are to be reckoned 

 equivalent. 



If we allow that a/ 1 + e' cos* (/ + §/) is equivalent to 

 \/ \ + e- cos^ /, we shall get by substituting the proper values 

 in the expressions of sin •\> and sin p', 



sin (/ + 8 Z ) = sin Z cos s' + cos I cos /* sin s' V \ + e'' 



f cos I sin /i 



sm jtx. = — ,, . V, • 



' cos (I -{• ol) 



In like manner, we obtain 



, sin /< sins' a/ 1 +«' cos (^ + S/) 



or, very nearly, 

 sin «' = ""'"/'"V — "V sin ju. sin s' tan {I + 11) sin (Z + 8Z). 



' cos («+«() 2 ' 



The advantage of my solution consists in its giving the ex- 

 act relations between all the quantities concerned, without 

 much calculation, and by means of expressions as simply as 

 the nature of the case will admit. Hence, in aj^plying it to 

 practice, it is easy to push the approximations to any required 

 degree of exactness. 



I remain, sir, yours, &c. 



April 5, 1825. Jasies IvoiiY. 



N. B. I observe that in the second formula, reckoning from 

 the top of p. 37, cos \(/ is printed for cos " ■i^. 



XLI. Observations on Locomotive Action^ ivitk reference to its 

 Differences in Skaiting and Walking. Bij A Correspon- 

 dent. 



T TPON what principle is it that the space gone over in skait- 

 ^ ing is so much greater than that gone over in the same 

 time and with the same exertion in walking? The answer to 

 this question would furnish curious hints as to an advantageous 

 application of force on rail-ways, &c. 



At first sight it might seem easy to answer, that the propel- 

 ling impetus communicated by the muscles of the leg behind 

 does not, in walking, carry the body beyond the spot where 

 the other leg is set down, but is checked and momentarily 

 stopped there by friction ; whereas in skaiting, this impetus not 

 only carries up the centre of gravity to that spot, but, owing 

 to tlie smoothness and slippcriness of the skait-irons and ice, 

 enables the body to glide forwards over a considerable space 



besides : 



