184 Transactions. — Miscellaneous, 



that the mere work of shearing the bodies when they come into impact, is 

 such an excessively small fraction of the total energy, in cases of large 

 masses, that it may be absolutely disregarded. As the whole of this 

 reasoning holds good for all cases, of the collision of approximately equal 

 large bodies, it becomes evident therefore that these collisions are partial. 



There is, however, one exception, that where the larger body extends so 

 as to include the smaller body completely in its path. The impact in this 

 case is complete as regards the small body, and tangential on the larger, 

 and although tending to produce rotation possesses none of the definite pro- 

 perties of partial impact. It. is clear that collisions may vary from the 

 mere, graze of the atmosphere of the two bodies, through the stage of cutting 

 off a considerable ratio, up to the extreme case of complete impact, all of 

 which possibilities tend to vary the result. Again, the two bodies may be 

 intensely hot, or one hot and one cold ; either or both may be solid, liquid, 

 or gaseous, or mixtures of these physical conditions. They may have an 

 original rotation of their own, and may have smaller bodies revolving around 

 them. They may have had very different original proper motions, and may 

 be of considerably different mass. Any of these peculiarities tends to alter 

 the result attained at and after impact. Still, on the other hand, there are 

 many broad well-marked generalizations which are sufficiently characteristic 

 to mark out these partial collisions as a clearly defined genus, the phe- 

 nomena resulting from them being easily recognizable to a skilled observer. 



The accompanying diagrams probably represent with some degree of 

 accuracy the stages of a medium case of partial collision. I have attempted 

 to draw these diagrams from independent reasoning on dynamical principles, 

 and have consulted others as to the accuracy of the reasoning. I must 

 acknowledge my indebtedness for several valuable hints from Mr. N. K. 

 Cherrill. The first figure [PI. VI.) shows two bodies coming into impact — it 

 will be seen that the bodies are distorted to an egg shape. The idea of this 

 distortion was first suggested to me by Mr. Beverly, of Dimedin, who has 

 been studying the various mathematical problems of complete cosmical 

 impact for more than a dozen years. It will ultimately be found, when this 

 question is discussed in detail, that this distortion produces some very 

 interesting phenomena. The two following figures show the process of 

 impact, and it is perfectly evident, from the mode of imjpact, the rare out- 

 side of each body meeting with the denser inside of the other, that the two 

 sides of the coalesced mass have a great deal of unbalanced momentum, 

 acting in different dh-ections, and tending to spin the mass on its centre. 

 It is generic of partial impact that it must produce rotation. It wiU also be 

 seen that this same residual motion, and the attraction of the retreating 

 masses, tend to draw the mass into a spindle shape. It is also evident, all 



