30 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Jan. 



the same p'.tcli. Xow it has long been known that involute teeth have this 

 property, but the objections to tljese teetli on the score of the obliquity of 

 their action have operated fatally against their introduction. I sliall now 

 therefore explain a metliod of impartiuc; to epicycloidal teeth tliis property, 

 and that without making them deviate very much from the gencial form 

 winch has been establislicd by practiee. 



" To effect this it is merely necessary to employ a proposition well known 

 and stated by almost every writer on the subject, namely, if there be two 

 pitch circles touching eacli other, then an epicycloidal tooth formed by caus- 

 ing a given describing circle to roll on the exterior circumference of tiie one 

 will work correctly with an interior epicycloid formed Ijy causing the same 

 describing circle to roll on the interior circumference of the other. This 

 proposition liaving been already demonstrated, it is unnecessary for me to 

 dwell upon it longer than to remark that our author (Buchanan) like all other 

 writers on tlie sidiject, has passed from it to recommend for practice that 

 particular case of it in which tlie describing circle lieing made equal in dia- 

 meter to tlie radius of the pitch line, the interior epicycloid becomes a radial 

 straight line, the inconveniences of which practice I have shown. The fol- 

 lowing corollary is I believe new, and constitutes the basis of the system I 

 projiose to explain. 



" CoROLL.VRV. — If for a set ofii'/ieels nf the same pitch a constant describ- 

 ing circle be taken and emploi/ed to trace those portions of the teeth ichich 

 project beyond each pitch line, tjy rolling on the e.rterior circumference, and 

 those which lie vnthin it, by rolling on its interior circumference, than any 

 two irheels of this set will work correctly together. 



" For in the first place it is well known, and can be sliown from general 

 principles, that the portion of tootli within the pitch line of a driving wlieel 

 works only with the portion that lies beyond the pitch line of its follower, 

 and that its action is confined to tlie approach of the point of contact to the 

 line of centres, .\fter the point of contact of the teeth has passed that line, 

 then the case is reversed, and the portion of the driving tooth which lies be- 

 yond the pitch line is in contact only with that part of its follower's tooth 

 which lies within its pitch line. Now as a constant describing circle is used 

 for the whole set, it is clear that the proposition will apply to any pair of 

 wheels both liefore and after the teeth have passed the line of centres, for in 

 each case we have an exterior epicycloid working with an interior epicycloid, 

 and both have been drawn by tlie same describing circle, that is, by the con- 

 stant circle of the set. 



" To carry this scheme into practice it only remains to settle the propci 

 diameter to be given to this constant describing circle, wliich may be done by 

 considering the effect of this (its) diameter has upon the form of the tooth. 



" Let B C ?j be a pitch circle 

 whose centre is O, then upon this 

 system tlie flank of the tooth or 

 that portion which lies within the 

 pitch circle will be an arc of an 

 interior epicycloid (or hy|)0cy- 

 cloid) m' n or m n. Now if the 

 describing circle be of half the 

 diameter of the pitch line, the 

 flank will become a straight line 

 coinciding with the radius O n. 

 If the describing circle be of less 

 than half the diameter of the 

 pitch line, the flank m n will be 

 concave, and the base of the tooth 

 will spread. But if the describ- 

 ing circle he more than half the 

 diameter, the flank m' n will be 

 convex, and the base of the tooth lessen inwards, a form manifestly unpractical 

 and useless. Hence the describing circle must not be greater than half the 

 diameter of the pitch line. 



" On the other hand if the diameter be too small the base of the tooth will 

 spread inconveniently, and the curvature of the exterior epicycloids be inju- 

 riously increased, therefore on these grounds it should lie made as large 

 as it can, consistently with the limitation just stated, so that we finally obtain 

 this rule for fimling the diameter of the constant describing circle for a set of 

 wheels. 



" Make it equal to the radius of the least pitch circle of the set. 

 '■ .\ud as pinions sliould never have less than 12 or It teeth, it would be 

 well to establish one of these numbers as the least pitch circle. 



■■ The proposition and corollary being perfectly general, will apply to racks 

 which must be considered as (portions of) very large wheels, and also to an- 

 nular or internal wheels. Accordingly, if the constant describing circle be 

 employed in tracing their teeth, they will work correctly with any wheel of 

 the set." 



In page ll'.\ Professor Willis describes a moile of drawing the 

 teetli of wheels by means of compasses, that will work upon the pre- 

 ceding principles, and which, though not inatheniaticaUv exact, is 

 suthciently so for practical purposes. We shall endeavour to describe 

 this metliod without the aid of a diagram. 



First describe the pitch circle — draw a diameter, and from the ex- 

 tremity of the diameter, with a radius of one-fourth of llie diameter, 

 set oil' an arc of the pilcli circle. The point of iutersectiuu is the 

 centre from wliicli with the same radius, tliat part of the side of the 



tooth extending beyond the pitch line is to be swept. To describe 

 that portion of the tooth within the pitch line, draw a line through the 

 extremity of the diameter, which makes an angle of 7.5^, with the line 

 of centres, and fix upon a point in this line suilicientlv low down to 

 give a moderate concavity to the inner portion of the tooth when 

 swept from that point as a centre. In the description of this method 

 in page 1-19, the word "radius" is twice put for the word "diameter." 

 There are various similar mistakes in other parts of tlie work. 



The Appendix B on Roofs, by Mr. James Nasmyth, is a highly in- 

 teresting paper, it explains the great utility of the lathe with the slide 

 rest, and its importance to engineers. 



The plates attached to the work are for the most part excellent, 

 they exhibit several splendid specimens of machinery to be found in 

 tlie manufactories of government and mechanical engineers of the first 

 class. The typography is of the very first quality, and reflects much 

 credit upon the parties concerned in the production. Notwithstanding 

 the imperfections we have pointed out, the work will, we are confident, 

 meet with an extensive sale. The subject of niillwork is an important 

 one, and there is no better treatise upon it than this edition of Bu- 

 chanan's essays. 



The Companion to Ihi .Almanac, lS-1'2. 



Our Christmas companion always affords us much pleasure, contain- 

 ing as it does a general view of the progress of many public works in 

 this country. In the volume for the present year, we have some very 

 excellent specimens of architecture, w liich clearly show that we mo- 

 derns are not quite so far below the ancients as to be unworthy of 

 notice. Liverpool before many years will have in St. George's Hall 

 and the New Assize Courts, judiciously combined under one roof, and 

 forming a splendid facade of the Corinthian order 420 feet in length, 

 with a portico in the centre of 200 ff>et, one of the most splendid 

 buildings in the country. The name of the talented architect is Mr. 

 W. H. Lonsdale Elmes, the son of Professor Elmes, and it is with 

 pleasure we learn that he is a very young member of the profession, 

 for the design is one of promise. Sincerely do we hope that the 

 Liverpool corporation will not frustrate him in carrying out his views; 

 if allowed to carry out the design to the extent he proposes, Liverpool 

 may then be justly proud of having a noble edifice. 



l>y the same architect there is also another building, and in tlie 

 same town, the Liverpool Collegiate Institution, which shows that Mr. 

 Elmes is equally able in the Gothic as he is in the classic. The wood 

 engraving, which is very badly got up, does not do the architect jus- 

 tice ; we fortunately have seen the drawings and can speak of the 

 building from them, and hope that we shall be able to illustrate our 

 Journal with a view of the building, together with that of St. Georgt's 

 Hali. The other buildings illustrated in the book before us, are 

 Strtatkam Church, arcliitect, Mr. Wild ; St .Mary's Church, Soulhmark, 

 architect, Mr. B. Ferrey, who, as our autlior observes, has shown great 

 discretion in not attempting too much, but endeavouring to produce 

 efFect by form rather than by decoration. Trinity Chapel, Poplar, 

 architect, Mr. Hoskins; he has displayed considerable judgment in the 

 construction of the roof, by which means a clerestory, is very ingeniously 

 obtained, "containing five windows on each side over the galleries, 

 and is formed within the general line of the roof in such a manner that 

 it is not visible externally." — Sarings Bank, Bath, architect, Mr. 

 Alexander. "The structure is entirely faced with freestone, and is a 

 tasteful piece of Italian aslylar composition stamped by certain vigour 

 and breadth. 



We perceive that Oxford is making progress with its various archi- 

 tectural works. 



Bartlett's Index Gcologicus. 



This is a diagram 3 ft. C in. tiy 2 ft. 9 in., containing a coloured section of 

 all the geological strata, with conijilete catalogues of the fossil animal and 

 vegetable remains, and of the series of minerals peculiar to eacli. Anotlier 

 column contains "statistics of tbc soils and indigi-ncms flora," and the locali- 

 ties where the separate strata prevail, not only in Great Britain, but in other 

 parts of the world, are jiarticularly specified. 



As a complete table of convenient reference, embracing in a highly con- 

 densed form and great body of information wiiich bad heretofore to be sought 

 amid heaps of scattered materials throughout the works of many different 

 authors. We strongly recommend the Jndi'r Geotogicus to agriculturists, 

 engineers, students in geology, and all others interested in this most imjiortant 

 branch of natural history. 

 -■/ Description and Historical Account of the Churches in the Dieision of 



Ifolland, in the County if Lincoln, with Illustrations. By Stephen Levvin. 



The fii■^t numl er of this moik contains views of Kirton Church and Algar- 



