to ascend Planes of different Inclinations, 263 



vertical ascent than might be expected. The reliefs being 

 more frequent when the velocity is great, the work done varies 

 in summer and winter, but may generally be stated at from 

 1400 feet per hour. 



The most remarkable circumstance is the high angle of 

 elevation at which this effort is performed, and which I doubt 

 not might be advantageously modified if ceconomy of the la- 

 bour of prisoners should ever become an object. I have ex- 

 amined the operation of the tread-wheel in Edinburgh, and 

 find that the angle of ascent is about 80°, and sometimes al- 

 most vertical. It is not to be supposed that this angle is as 

 favourable as a smaller one, though the work done is greater 

 than in some cases already considered ; this being a punish- 

 ment and considered as hard labour, the other (the ascent of 

 mountains) being only equivalent to an active man's common 

 daily work. The viev/ in making the angle of ascent of tread- 

 wheels so great is, no doubt, to secure the greatest effective 

 leverage of the man's weight; but by duly increasing the ra- 

 dius this leverage might be attained at any other angle, and 

 the stepping-boards instead of being prolongations of the 

 radii should form an angle with them such as to make them 

 horizontal at the part of the wheel where the moving power is 

 applied, which should be when the radius forms an angle 

 perhaps not greater than 40° with the vertical. 



The tread-wheel observations are the most satisfactory at 

 high angles, since when ladders are used (as in the Cornish 

 mines, and those which communicate with the village of AI- 

 binen near Leuk in the Valais.) powerful assistance is afforded 

 by the arms. 



In the want of decisive observations, we shall assume 1100 

 feet per hour as the ascensional effort at the extremity of the 

 scale when the ascent is vertical, or the horizontal component 

 null; being somewhat more than two thirds of the maximum 

 effect. This must be considered, however, as in some mea- 

 sure conjectural, and to be corrected by future experience. 

 I would also add, that it is distinctly to be kept in view that 

 the effort which we mean to represent is not an extraordinary 

 but an ordinary due ; not what by a certain degree of exertion 

 might be accomplished for a single day, much less the maxi- 

 mum effect attainable, but an amount of labour which may be 

 continued for eight hours aday at least, and for many days 

 together *. 



Since we propose to include in a formula both distance and 



* As an example of the necessity of attending to this, and also of the 

 usual method o^ observing, I quote my observations during the ascent of 

 the Rigi, a hill of comparatively small height, and particularly accessible : 



