196 Reviews. ; [Jan 
by our author for the determination of the proportions of gearing, 
shafts, or any other portion of mill work, the fact transpires, that the 
mathematics have been fitted to the practice, and not the practice to 
the mathematics. Nor is this peculiar to Mr. Fairbairn; on the con- 
trary, a similar tendency has pervaded the work of our best engineers, 
so that it has almost come to be believed by some, that a great mathe- 
matical capacity is inconsistent with unusual mechanical ability. 
Though this is a question of much interest, we do not propose to 
discuss it here, but merely remark, in passing, that Mr. Fairbairn’s 
work is certainly another and weighty argument put into the mouths 
of those who hold that the great masters in the mechanical craft have 
ever used pure mathematics as a very humble kind of servant, treating 
her mainly as a custos rerum, or a means of making the results of their 
great natural intuition and observation common property for their 
inferiors or successors. 
The second and recently published volume of the work opens with 
Section 4, and contains an elaborate investigation into the wide subject 
of the machinery of transmission. Amongst one of the most important 
general conclusions on this subject, towards which Mr. Fairbairn con- 
ducts the reader, is that of the superiority of toothed gearing over straps 
or other wrapping connectors for purposes of transmission. It is well 
to have our attention called to this point at a time when the example of 
American engineers has produced a strong feeling in favour of strap- 
ping as compared with gear, and Mr. Fairbairn does good service in 
pointing out the superiority of wheelwork. The advantages which can 
be claimed for straps are smoothness of motion, noiselessness of action, 
and perhaps smallness of first cost; but they are cumbrous, frequently 
out of repair, destructive in their effects on the journals, and wholly 
inapplicable in cases where the motion requires to be transmitted in a 
constant ratio. One of the drawbacks to a freer use of toothed wheels 
has hitherto been found in the great expense of truly shaped and fitted 
gears; but the introduction of the wheel-moulding machine, with its 
consequent improvement in the truth of teeth in cast-wheels, is likely 
to bring wheelwork into more extensive use than at present. 
The chapters on the teeth of wheels would be little more than a 
recapitulation of the ordinary mathematical demonstration of their true 
form were it not for the introduction of a most useful series of practical 
tables, from one or other of which, as if from a ready reckoner, every 
problem concerning any required wheel may be instantly solved, 
whether it relate to the strength, pitch, thickness, depth, clearance, 
or horses’ power to be transmitted through a particular tooth.* 
* Among the drawings given of various forms of teeth is one which, like the 
table just referred to, illustrates the very practical nature of this treatise. Our 
mechanical readers are, of course, aware that in most demonstrations of the Epicy- 
cloidal tooth that particular form having its flanks formed by hypocycloids, which 
are also radial lines, is almost exclusively dealt with. Now this is a tooth which, 
notwithstanding the simplicity of its delineation, is rarely used in practice, because 
of its inherent weakness ; so, although we get, as usual, some prominence given 
in the demonstration to the radial hypocycloid, Mr. Fairbairn’s practical bent does 
not permit him to leave his reader without giving a figure of the “teeth of a large 
wheel, traced from one of my own patterns, to exhibit the form which practice has 
