16 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL 



[Jan. 



often considerable, and when thick cuts are taken, is usually far larper 

 than the fornier furci". If the beudins were of small exteut, then the 

 force lo be exerted would vary as the square of the tliii kness of the shaving 

 Miuttifjlii"! by some constant, dependent on the nature of the metal operated 

 upon, r.ut the bending very frequently proceeds lo such an extent that 

 the shaving itself is br(.kcn at very short intervals, and some shavings 

 of iron and steel present a continued series of fraitures not quite running 

 through, but yet so i oniplete, that it is impossible even with the most care- 

 ful annealing lo unwind the spiral. This partial severance of the atoms 

 in the shaving itself, will require for its accomplishment a considerable 

 exerlion of force. The law by wliicli this force increases wiib the thickness 

 most probalily embraces higher powers than the first and second, and may 

 be assumed thus 



force =a-\-bt + ct- + di^ + 

 For the present illustration it is unnecessary to consider more terms than 

 those already more particularly explained, namely the constant force, and 

 that which varies as the square of the thickness of the shavmg. If there- 

 fore t be the thickness of the shaving, and A and B two constants, we 

 shall lind amongst the forces required for the separation of the shaving the 

 two lenns 



A + 15i- 



where A, and B, depend upon the nature of the metal acted upon. We 

 may learn from this expression, even williout being acquainted with the 

 values of the constants A and 15, that the force required to remove the 

 same thickness of metal, may vary considerably according to the manner 

 in which it is ell'ected. For example, — if a layer of metal of the thickness 

 of 2/, is to be removed, it may be done at two successive cuts, and the 

 force required will be equal to 



2 A -)- 2 B(2 

 But the same might have been accomplished at one cut, when the force 

 expended would have been 



A + 4 B(V' 



The latter quantity always exceeds the former when t- exceeds — as 



the writer shows algebraically. Consequently, when the square of the 

 thickness exceeds half the ratio of A to B, less force is required to effect 

 the operation by two cuts, than by one. .'Vnd in the same way it may be 

 shown that any number of slices (n) require less force than a single slice 



of »i times the thickness if (- exceed --• 



n B 



" The angle of relief should always be very small, because the point a 

 will in that case have its support nearly in a line directly opposed to that 

 force acting upon it. 



If a tool either for planing or for turning is defectively formed, or if it is 

 presented to its work in such a manner that it has a tendency to dig into 

 it, then a very small angle of relief, in addition to a long back a e, will in 

 some measure counteract the defect. 



The smaller the angle of the tool, the less will be the force necessary for 

 its use. But this advantage of a small angle is counterbalauci d by the 

 weakness which it proiluces in the support of the cutting point. 1 here is 

 also another disadvantage in making the angle of the tool smaller than the 

 escape of the shaving requires ; for the poini of the tool being In immediate 

 connection with a smaller mass of metal, will not so quickly get rid of the 

 heat it acquires from the operation of cutting, as it would if it formed part 

 of a larger mass. 



The angle of escape A a B is of great importance and it varies with the 

 nature of the material to be acted upon. If this angle is very small the 

 action of the tool is that of scraping rather than of cutting, and the matter 

 removed aiiproaclies the form of a powder. If however the material is 

 very llexibic and cohesive, in that case shavings may be removed. The 

 angle 1 have found best for cutting steel is about 27°, but a series of experi- 

 ments upon this subject is much required. 



After the form of the cutting tool is decided upon, the next important 

 point to be considered is ihe manner of its application. The principle 

 which is usually slated for turning toids is, that the point of the tool should 

 be nearly on a level with the axis of the matter to be turned, or rather that 

 it should be very slightly below it. This rule when applied to the greater 

 number of tools and tool-holders is calculated to mislead. Before applying 

 the correct rule it is necessary to consider in each tool or tool-holder, what 

 is the situation of that point aroui.d which the culling point of the tool will 

 turn when any force is put upon the tool. Let this point be called the cen- 

 ter of flexure. Then the correct rule is, that the center of flexure should 

 always be above the line joining the center of the work and the cutting 

 point. 



On looking at Gg. 983, A c is the line joining Ihe cutting point o and the 

 center of the work c. By making the tool weak about U that point be- 

 comes the center on which the point a will bend when any unusual force 

 occurs. On the occurrence of any such unusual force arising from any pin 

 or pointof une(|wal diusity in the matter cut, the point of the tool a, by 

 bending around the center (J will dig deeper into the work and cause some 

 part of the apparatus to give way or break. 



If on the other hand the point P is that around which the point of the 

 tool when resisted tends to turn, It en since this point is above the line Join- 

 ing the cutting poiut and the center of the work, the tendem y of the addi- 



tional strain on the point is to make it sink less deeply into the work, and 

 consequently to relieve itself from the force opposed to it. 



Fortunately the position of this point can always be commanded, for it is 

 always possible, by cutting away matter, to make one particular part 

 Weak. This is indeed a circumstance too frequently neglected in 1i ecoQ- 

 siruction of machinery. Every piece of mechanism exposed to consider- 

 able force is liable to fracture, and it is always desirable to direct it to 

 break at some one particular point if any unexpected strain occurs. In 

 many cases where danger may arise from the interference of the broken 

 part with the rest of the machinery this arrangement is essential. In all 

 cases it is economical, because by making the breaking, if it occur, at a 

 selected spot, provision may he made of duplicate parts and the delay 

 arising from stopping the machine be avoided. 



The results of the preceding inquiry would lead to considerable changes 

 in the forms of tools generally used in cutting metals, and as the time em- 

 ployed in taking a cut is ususally equal whether the shaving be thick or 

 thin, the saving in power by taking thin cuts separately would be accom- 

 panied by a considerable expense of time. This however need not be the 

 case if proper tool holders are employed, in conformity with the followin); 

 several conditions : thus 



The tool-holders should be so contrived as to have several cutters snc- 

 cessively removing equal cuts. — The cutting edges should be easily ad- 

 justed to the work. — The sleel of which the cutters are formed should be 

 of the best kind, and afier it is once hardened should never again be sub- 

 milted lo that process. — The form and position of the cutter should be such 

 that it may, when broken or blunied, be easily ground, having but one or 

 at the utmost but two faces requiring grinding. — It is desirable that wheo 

 being ground it should be fixed into some temporary handle, in order that 

 it may always be ground to the same cutting angles. — The cutters should 

 be very securely, but also very simply tightened in iheir places. — The 

 center of flexure of the cutter should, in turning, be <i6ore the line joining 

 the center of the work and the cutting poiut; — whilst in planing the center 

 of flexure should be in udraiice of a line perpendicular at the cutting point 

 to the surface of the work planed. Examples of some tool-holders of this 

 kind will be given subsequently. 



The elTects of such improved tools would be to diminish greatly the strain 

 put upon lathes and planing machines, and consequently to enable them to 

 turn out better work in the same time and at a less expense of power : 

 whilst tlie machines themselves so used would retain their adjustments 

 much longer without reparation." 



The next paper contains an account of various tool-holders invented by 

 Mr. Babbage. Prof. Willis's papers relate not so much lo the mechanical 

 as to the geometrical Iheoi-y of cutting tools or the relations of their sides 

 and angles, the inclination of the edges required for different metals being 

 assumed to be known. Prof. Willis also describes a new tool-holder in- 

 vented by him, which Mr. Holtzapffel stales to be now generally used in 

 his manufactory. 



Among the papers in this appendix one of the most useful is that on the 

 diversity of gauges of wires and sheet metals, &c. Our author compares 

 the dilleient scales of measurement of rod iron, nail rod, rifle tubes, wire, 

 sheet iron, zinc plates, crown-glass, &c. : he shows that the greatest incon- 

 venience arises from the numerous scales, which are perfectly arbitrary, 

 and vary in different manufactories. He has given a table of the values of 

 several of the principal gauges to three places of decimals of an inch, the 

 measures being ascertained by an exceedingly accurate sliding gauge, con- 

 structed by himself, and indicating by a vernier the thousandths of an inch. 

 In the following extracts the advantage of a general application of decimal 

 uotation to small quantities is admirably illustrated. 



Decimal Gages. 



" The remedy proposed to retnove the arbitrary incongruous system of 

 gages now used, is simply and in every one of the cases above referred to, 

 and also in all other requiring minute measures, to employ the decimal divi- 

 sions uj' ilie inch, and those under their true appellations. 



'I'hus fur most purposes the division of the inch into one hundred parts 

 would be suliiciently minute, and the measures 1. 2. 5. 10. 15 or 100 hun- 

 dredths, would be also sufficiently impressive to the mind ; their quantities 

 might be written down as 1. 2. 5. 10. 15 or 100 hundredths, as the decimal 

 mode of expression might if preferred be safely abandoned, and the method 

 would be abundantly distinct for common use if the word '' Hundredtht" 

 were stamped upon the gage, to show that its numerals denoted hundredths 

 of an inch, quantities which could be easily verified by all. 



In practice no diHicully could be seriously felt even without this pre- 

 caution of marking the gages respectively with the word Hundredths or 

 Thousandths ; as we should not more readily mistake 5 ihousaudths for 5 

 hundredths, than we should 5 tenths or half an inch for 5 whole inches, or 

 5 entire inches for as many feet. 



Neither is illo be admitted that no such gages are attainable as may be 

 read of in hundredths or Ihousandihs. The demand would immediately 

 create the supply, and there could be no more difficulty in constructing the 

 gages of the customary forms, with notches made to sjsteniaiic and definite 

 measures, that may be easily arrived at or tested, than with their present 

 unsystematic and arbitrary measures, ic/iic/i do not admit of verification. 



Besides, for those who desire to possess them, several very correct decl- 



