192 
Proceedings of Royal Society of Edinburgh. [sess. 
. \ since the inclination of the generating line DP to its direction of 
motion PA is equal to that of CP to its direction of motion BP, we 
have CB-PG-AP-DP = DA-PE-PB-CP. 
By applying the properties of generating lines to the products of 
three or more straight lines, as has been done in the last three 
examples, any number of geometrical results may be obtained. 
But for a fuller development of the subject, the writer would refer 
to his work, Parallel Translations of Lines and Surfaces , published 
by A. Brown & Co., Aberdeen, in which the principles are extended 
and applied to other parts of geometry. 
The apparatus for Impact experiments, which was exhibited to 
the Society on 20th February 1888, has been greatly improved by 
the substitution of a very true slab of plate-glass, thinly covered with 
printing-ink, for the sheet of cartridge paper. The record is made 
by a needle-point which projects from the falling body, and which 
is kept in constant contact with the plate by means of a light spring. 
The time of rotation of the plate is given by a tuning-fork, with a 
small bristle attached, which is kept in vibration by a periodic 
current, and records alongside of the other tracings. 
When the paint is dry, the plate is used as a photographic nega- 
tive. To correct for possible shrinkage of the photographic paper, 
circles of known diameter are described on the inked plate at 
various places, and tested when the fixing process is complete. 
The following data give a general idea of the results of a 4 foot 
fall: — the falling body being a block of hard wood, of 5J lbs. mass, 
which impinges on a cylinder of 32 mm. diameter and 32 mm. in 
length, half of which is imbedded in a large mass of lead cemented 
to the asphalt floor. The time is less for more violent impacts. 
Graphic Records of Impact. (Abstract.) 
By Professor Tait. 
(Read July 7, 1890.) 
Material of Cylinder. 
Compression in mm. 
11-5 
2*3 
19*0 
1-9 
Time of Impact. 
0 S '0077 
0 -0014 
0 -0166 
0 -0018 
Vulcanized India-Rubber, 
Vulcanite, 
Cork 
Plane-tree, . 
