Chase. 1 Jg [February. 



The hand, e, has a length of 18", which multiplies, therefore, the 

 movement of the roller, c, and shows it on the arc, I. 



The cord of this arc has a length of 24", and the angle at c, =. 84°, 

 The arc itself has 26.376" in length, which the hand, c, has to 

 pass to make a pressure of 2". 



It is of importance now to give the exact diameter to the roller, 

 c, so that the hand describes exactly the rise of the water of 

 1.7351". The angle at c, being 84°, the roller, c, must have a dia- 

 meter corresponding to 1.7351" for an arc of 84°. 



This diameter is d, = '^'lVj?f^ = 2.3682. 

 ' 84.3.14 



The length of the arc being 26.376", every inch is equivalent to 



a pressure of 2qzi& "^ 0.06578. Fig. 1, of the drawing, represents 



a longitudinal section; Fig. 2, a front view, and Fig. 3, a cross sec- 

 tion. A, is a wooden frame, or rather a box, with a door, B, and a 

 window-glass, C, at its face. D, is the sheet-iron box within ; a, is 

 the swimmer, h, the silk thread, and d, the counter balance; c, is the 

 roller in Fig. 4, in natural size, only designed for a pressure of one 

 inch. The roller, c, is supported by the iron plates, /, fixed by 

 means of small screws to the wooden frame; e, is the hand, and g, 

 denotes the sides of the water-box; h, is a small tube, closed by a 

 cork, m, to regulate the water in the box, and k, another tube, to 

 put the manometer in communication with the blast tube; i, is a 

 glass pipe, to show the level of the water, and to mark any disorder 

 of the instrument. 



Mr. Chase made a communication on the traces of common 

 radicals in the numeration of various languages, and on the 

 original ideas involved in the names of the numbers. 



ON THE RADICAL SIGNIFICANCE OF NUMERALS. 



The facility with which the vowel u and the nasal consonants 

 combine with letters of every contact,* may, perhaps, naturally ac- 

 count for their frequent occurrence in the formation of the substan- 

 tive verb ;f but it is difficult to explain the various derivative ana- 



* See ante, Vol. IX, p. 273. 



f Eg. au, un, to be, ua, one; Cp. un, to he, one; L. sum, unus ; Gr. 

 i'lfAi, ehai; Ger. ein ; Dk. ui), wagka, to be, wai)ca, one; Y. wa, ni, to be; 

 C. we, to be; E. was, were. 



