262 Prof. Forbes on the Muscular Effort required 



hours in a day. This estimate does notdifler much from that 

 of the guides at Chamouni. My own experience would give 

 results somewhat greater, and the constant must of course be 

 determined by each individual for himself. For heights not 

 exceeding 5000 or 6000 feet I find 1500 feet per hour to cor- 

 respond to the most moderate sustained muscular effort, and 

 which might be long kept up ; the only kind of observation of 

 any value, since excessive exertion puts all calculation at de- 

 fiance. 



1 long since proposed to myself to find an expression for 

 muscular exertion in walking which should mclude inclined 

 planes of all inclinations, and consequently a horizonal road 

 as a particular case, where the preceding reasoning becomes 

 inapplicable, since the distance corresponding to a given 

 height is infinite. During the prosecution of experiments at 

 great elevations already partly before the Royal Society of 

 Edinburgh, I have had an opportunity of extensively consi- 

 dering this practical question. My practice when in Switzer- 

 land in 1832, was to measure from time to time the inclination 

 of the path with a kiinometer, and to note the times elapsed, 

 making observations when necessary for the total height with 

 the barometer. The continued and equable ascent of some of 

 the carriage passes of the Alps afforded a good opportunity of 

 observing at small inclinations when the horizontal component 

 became relatively great, whilst long experience gave me per- 

 fect confidence in the uniformity with which I walked day 

 after day, at the rate of four miles an hour, on level ground. 

 These experiments seem to indicate about 700 vertical feet of 

 ascent per hour at an angle of 3j°, from 1000 to 1100 feet 

 at 7°, and nearly 1500 feet per hour from 10° to 20°, without 

 much variation, but rather indicating that the higher angles 

 were the more advantageous. 



For inclinations greater than 25°, there is a deficiency of 

 directly comparable observations. Coulomb could not per- 

 suade a labourer to ascend a stair cut in the rock, through a 

 height of 9000 feet in a day, at the usual wages. The angle 

 may be supposed equal to 30° or 35°. This may be consi- 

 dered to indicate a diminution of useful effect, and confirm 

 the existence of a maximum advantage between 20° and i)0°. 



At very high angles the tread-mill affords some curious re- 

 sults. It appears from the statistical tables* that though the 

 velocity of tread-wheels varies much, as well as the total work 

 done in a day, yet there is more uniformity in the hourly 



• See Parliamentary Reports, and particularly Prison Discipline Society's 

 Report for 1823. 



