May II, 1877] 



NA TURE 



87 



to the air engines which are employed to ventilate the 

 Houses of Parliament. The ease of working and absence 

 of friction and noise is very remarkable. The engines 

 were constructed and the Peaucellier apparatus adapted 

 to them by Mr. Prim, the engineer to the Houses, by 

 whose courtesy I have been enabled to see them, and I 

 can assure you that they well worth a visit. 



Another modification of the cell is shown in Fig. 10. 

 If instead of employing a "kite" and "spear-head" of 



Fig. 10- 



the same dimensions I tike the same " kite " as before but 

 use a "spear head" of half the size of the former one, 

 the angles being, however, kept the same, the product of 

 the heights of the two figures will be half what it was 

 before, but still constant. Now instead of superimposing 

 the links of one figure on the other, it will be seen that in 

 Fig. 10 I fasten the shorter links of each figure together 

 end to end. Then as in the former cases, if I fix the 

 pivot at the point where the links are fixed together, I get 



Fi^. U. 



a cell which may be used by the employment of an extra 

 link, to describe a straight line. A model employing this 

 form of cell is exhibited in the Loan Collection by the 

 Conservatoire des Arts et Ivldtiers of Paris, and is of 

 exquisite workmanship ; the pencil seems to swim along 

 the straight line. 



M. Peaucellier's discovery was introduced into England 

 by Prof. Sylvester in a lecture he delivered at the Royal 

 Institution in January, 1S74, which excited very great in- 



rather quadruple cell, for it may be used in four different 

 ways, shown in Fig. 11. Now Mr. Hart found that if he 

 took an ordinary parallelogram atic linkwork in which the 



adjacent sides are unequal, and crossed the links so as to 

 form what is called a contra-parallelogram. Fig. 12, and 

 then took four points on the four links dividing the dis- 



Ficj.lS 



tcicst aiid was the commencement of the consideration of 

 the subject of linkages in this country. 



In August of the same year Mr. Hart, of Woolwich 

 Academy, read a paper at the British Association meet- 

 ing, in which he showed that M. Peaucellier's cell could 

 be replaced by an apparatus containing only four links 

 instead of six. The new linkage is arrived at thus. 



If to the ordinary Peaucellier cell 1 add two fresh links 

 of the same length as the long ones I get the double, or 



tances between the pivots in the same proportion, those 

 four points had exactly the same properties as the four 

 points of the double cell. That the four points always 

 lie in a straight line is seen thus : considering the triangle 

 aid, since a O : O i : : a P : V 1/ therefore O P 

 is parallel to /' ;/ and the perpendicular distance 

 between the parallels is to the height of the 

 triangle a 6 ti tis O i ii to a i ; the same reason - 

 ing applies to the straight line CO', and since 

 ai: Ob: -.cd-.O'd and the heights of the 

 triangles abd, cbd, are clearly the same, 

 therefore the distances of O P and O' C from 

 bd are the same, and O C P O' lie in the same 

 straight line. 



That the product O C • O P is constant ap- 

 pears at once when it is seen that O i5 C is half 

 a " spear head " and O <r P half a " kite ; " similarly it 

 may be shown that O' P " O' C is constant, as also 

 O C ■ C O' and O P • P O'. Employing then the Hart's 

 cell as we employed Peaucellier's, we get a five-link 

 straight line motion. A model of this is exhibited in the 

 Loan Collection by M. Breguet. 



I now wish to call your attention to an extension of 

 Mr. Hart's apparatus, which was discovered simul- 

 taneously by Prof. Sylvester and myself. In Mr. Hart's 



